Deck 11: Additional Topics Using Inference

Question 1

The following table shows the Myers-Briggs personality preferences for a random sample of 401 people in the listed professions. Use the chi-square test to determine if the listed occupations and personality preferences are independent at . What is the level of significance?
$$\begin{array} { l | l | l | l } \text { Occupation } & \text { Extroverted } & \text { Introverted } & \text { Row Total } \\\hline \text { Clergy (all denominations) } & 60 & 48 & 108 \\\hline \text { M.D } & 65 & 94 & 159 \\\hline \text { Lawyer } & 54 & 80 & 134 \\\hline \text { Column Total } & 179 & 222 & 401 \\\hline\end{array}$$ $$\alpha = 0.05$$

A)0.99
B)0.05
C)0.10
D)0.90
E)0.95

Answer 1

0.05

Question 2

A transect is an archaeological study area that is mile wide and 1 mile long. A site in a transect is the location of a significant archaeological find. Let x represent the number of sites per transect. In a section of Chaco Canyon, a large number of transects showed that x has a population variance In a different section of Chaco Canyon, a random sample of 24 transects gave a sample variance for the number of sites per transect. Use an to test the claim that the variance in the new section is greater than 35.2. $\frac { 1 } { 5 }$ $\sigma ^ { 2 } = 35.2$ $s ^ { 2 } = 58.1$ $\alpha = 0.1$ What is the level of significance?

A)95%
B)1%
C)90%
D)99%
E)10%

Answer 2

10%

Question 3

Suppose the age distribution of the Canadian population and the age distribution of a random sample of 531 residents in the Indian community of Red Lake are shown below. $$\begin{array} { l l l } & & \text { Observed Number } \\\text { Age (years) } & \text { Percent of Canadian Population } & \text { in Red Lake Village } \\\hline \text { Under } 5 & 8.9 \% & 49 \\5 \text { to } 14 & 11.9 \% & 41 \\15 \text { to } 64 & 67.8 \% & 389 \\65 \text { and older } & 11.4 \% & 52 \\\hline\end{array}$$ Use to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village. What are the degrees of freedom?
$$\alpha = 0.05$$

A)7
B)3
C)5
D)4
E)6

Answer 3

3

Question 4

Suppose the age distribution of the Canadian population and the age distribution of a random sample of 447 residents in the Indian community of Red Lake are shown below. Use to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village. State the null and alternate hypotheses.
$$\begin{array} { l l l } \hline \text { Age (years) } & \text { Percent of Canadian Population } & \begin{array} { l } \text { Observed Number } \\\text { in Red Lake Village }\end{array} \\\hline \text { Under } 5 & 7.9 \% & 45 \\5 \text { to } 14 & 13.3 \% & 55 \\15 \text { to } 64 & 65.3 \% & 302 \\65 \text { and older } & 13.5 \% & 45 \\\hline\end{array}$$ $\alpha = 0.1$

A)The distributions are equal to zero ; The distributions are not the same. $H _ { 0 } :$ $H _ { 1 } :$
B)The distributions are the same; The distributions are not the same. $H _ { 0 } :$ $H _ { 1 } :$
C)The distributions are equal to zero; The distributions are the same. $H _ { 0 } :$ $H _ { 1 }$
D)The distributions are different; The distributions are equal to zero. $H _ { 0 } :$ $H _ { 1 }$ :
E)The distributions are not equal to zero; The distributions are not the same. $H _ { 0 } :$ $H _ { 1 }$ :

Question 5

The following table shows the Myers-Briggs personality preferences for a random sample of 402 people in the listed professions. $$\begin{array} { l | l | l | l } \text { Occupation } & \text { Extroverted } & \text { Introverted } & \text { Row Total } \\\hline \text { Clergy (all denominations) } & 60 & 46 & 106 \\\hline \text { M.D. } & 70 & 92 & 162 \\\hline \text { Lawyer } & 53 & 81 & 134 \\\hline \text { Column Total } & 183 & 219 & 402 \\\hline\end{array}$$ Use the chi-square test to determine if the listed occupations and personality preferences are independent at . State the null and alternate hypotheses.
$\alpha = 0.01$

A)Myers-Briggs preference and profession are not independent; Myers-Briggs preference is independent whereas profession is not independent $H _ { 0 } :$ $H _ { 1 }$
B)Myers-Briggs preference and profession are independent; Myers-Briggs preference is not independent whereas profession is independent $H _ { 0 } :$ $H _ { 1 }$ :
C)Myers-Briggs preference and profession are not independent; Myers-Briggs preference and profession are independent $H _ { 0 } :$ $H _ { 1 }$ :
D)Myers-Briggs preference is independent whereas profession is not independent; Myers-Briggs preference is not independent whereas profession is independent $H _ { 0 } :$ $H _ { 1 }$ :
E)Myers-Briggs preference and profession are independent; Myers-Briggs preference and profession are not independent $H _ { 0 } :$ $H _ { 1 }$ :

Question 6

The following table shows the Myers-Briggs personality preferences for a random sample of 404 people in the listed professions. $$\begin{array} { l | l | l | l } \text { Occupation } & \text { Extroverted } & \text { Introverted } & \text { Row Total } \\\hline \text { Clergy (all denominations) } & 60 & 45 & 105 \\\hline \text { M.D. } & 65 & 94 & 159 \\\hline \text { Lawyer } & 55 & 85 & 140 \\\hline \text { Column Total } & 180 & 224 & 404 \\\hline\end{array}$$ Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.1 level of significance. Find (or estimate) the P-value of the sample test statistic.

A)0.005 < P-Value < 0.01
B)0.025 < P-Value < 0.05
C)P-Value > 0.5
D)0.01 < P-Value < 0.025
E)0.10 < P-Value < 0.25

Question 7

Suppose the age distribution of the Canadian population and the age distribution of a random sample of 492 residents in the Indian community of Red Lake are shown below. $$\begin{array} { l l l } & & \text { Observed Number } \\\text { Age (years) } & \text { Percent of Canadian Population } & \text { in Red Lake Village } \\\hline \text { Under } 5 & 8.5 \% & 33 \\5 \text { to } 14 & 10.3 \% & 38 \\15 \text { to } 64 & 70.5 \% & 373 \\65 \text { and older } & 10.7 \% & 48 \\\hline\end{array}$$ Use to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village. Given that 0.05 < P-Value < 0.10, will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories?
$$\alpha = 0.01$$

A)Since the P-Value is less than $\alpha$ , we fail to reject the null hypothesis that the variables are independent. At 0.01 level of significance, we conclude that the variables are not independent.
B)Since the P-Value is less than $\alpha$ , we reject the null hypothesis that the variables are independent. At 0.01 level of significance, we conclude that the variables are not independent.
C)Since the P-Value is less than $\alpha$ , we fail to reject the null hypothesis that the variables are not independent. At 0.01 level of significance, we conclude that the variables are independent.
D)Since the P-Value is less than $\alpha$ , we reject the null hypothesis that the variables are not independent. At 0.01 level of significance, we conclude that the variables are independent.
E)Since the P-Value is greater than $\alpha$ , we fail to reject the null hypothesis that the variables are independent. At 0.01 level of significance, we conclude that the variables are not independent.

Question 8

A transect is an archaeological study area that is mile wide and 1 mile long. A site in a transect is the location of a significant archaeological find. Let x represent the number of sites per transect. In a section of Chaco Canyon, a large number of transects showed that x has a population variance In a different section of Chaco Canyon, a random sample of 23 transects gave a sample variance for the number of sites per transect. Use an to test the claim that the variance in the new section is greater than 37.9. $\frac { 1 } { 5 }$ $\sigma ^ { 2 } = 37.9$ $s ^ { 2 } = 61.6$ $\alpha = 0.05$ State the null and alternate hypotheses.

A); $H _ { 0 } :$ $\sigma ^ { 2 } > 37.9$ $H _ { 1 }$ : $\sigma ^ { 2 } < 37.9$
B); $H _ { 0 } :$ $\sigma ^ { 2 } = 37.9$ $H _ { 1 }$ : $\sigma ^ { 2 } \neq 37.9$
C); $H _ { 0 } :$ $\sigma ^ { 2 } \neq 37.9$ $H _ { 1 }$ : $\sigma ^ { 2 } = 37.9$
D); $H _ { 0 } :$ $\sigma ^ { 2 } = 37.9$ $H _ { 1 }$ : $\sigma ^ { 2 } > 37.9$
E); $H _ { 0 } :$ $\sigma ^ { 2 } = 37.9$ $H _ { 1 }$ : $\sigma ^ { 2 } < 37.9$

Question 9

The following table shows the Myers-Briggs personality preferences for a random sample of 399 people in the listed professions. $$\begin{array} { l | l | l | l } \text { Occupation } & \text { Extroverted } & \text { Introverted } & \text { Row Total } \\\hline \text { Clergy (all denominations) } & 64 & 44 & 108 \\\hline \text { M.D. } & 69 & 90 & 159 \\\hline \text { Lawyer } & 52 & 80 & 132 \\\hline \text { Column Total } & 185 & 214 & 399 \\\hline\end{array}$$ Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.01 level of significance. Given P-Value < 0.005, will you reject or fail to reject the null hypothesis of independence?

A)Since the P-value is greater than $\alpha$ , we fail to reject the null hypothesis that the Myers-Briggs personality preference and profession are not independent. At 0.01 level of significance, we conclude that the Myers-Briggs personality preference and profession are independent.
B)Since the P-value is greater than $\alpha$ , we fail to reject the null hypothesis that the Myers-Briggs personality preference and profession are independent. At 0.01 level of significance, we conclude that the Myers-Briggs personality preference and profession are not independent.
C)Since the P-value is less than $\alpha$ , we reject the null hypothesis that the Myers-Briggs personality preference and profession are independent. At 0.01 level of significance, we conclude that the Myers-Briggs personality preference and profession are not independent.
D)Since the P-value is greater than $\alpha$ , we reject the null hypothesis that the Myers-Briggs personality preference and profession are not independent. At 0.01 level of significance, we conclude that the Myers-Briggs personality preference and profession are independent.
E)Since the P-value is less than $\alpha$ , we fail to reject the null hypothesis that the Myers-Briggs personality preference and profession are not independent. At 0.01 level of significance, we conclude that the Myers-Briggs personality preference and profession are independent.

Question 10

A transect is an archaeological study area that is mile wide and 1 mile long. A site in a transect is the location of a significant archaeological find. Let x represent the number of sites per transect. In a section of Chaco Canyon, a large number of transects showed that x has a population variance In a different section of Chaco Canyon, a random sample of 24 transects gave a sample variance for the number of sites per transect. Use an to test the claim that the variance in the new section is greater than 42.1. $$\frac { 1 } { 5 }$$ $\sigma ^ { 2 } = 42.1$ $s ^ { 2 } = 57.7$ $\alpha = 0.1$ What are the degrees of freedom?

A)26
B)23
C)24
D)27
E)25

Question 11

Suppose the age distribution of the Canadian population and the age distribution of a random sample of 454 residents in the Indian community of Red Lake are shown below. $$\begin{array} { l l l } & & \text { Observed Number } \\\text { Age (years) } & \text { Percent of Canadian Population } & \text { in Red Lake Village } \\\hline \text { Under } 5 & 8.9 \% & 34 \\5 \text { to } 14 & 14.1 \% & 58 \\15 \text { to } 64 & 62.4 \% & 302 \\65 \text { and older } & 14.6 \% & 60 \\\hline\end{array}$$ Use to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village. Will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories?
$$\alpha = 0.05$$

A)Since the P-Value is less than $\alpha$ , we reject the null hypothesis that the variables are independent in favor of the alternate hypothesis that the variables are not independent.
B)Since the P-Value is greater than $\alpha$ , we fail to reject the null hypothesis that the variables are not independent in favor of the alternate hypothesis that the variables are independent.
C)Since the P-Value is less than $\alpha$ , we fail to reject the null hypothesis that the variables are independent in favor of the alternate hypothesis that the variables are not independent.
D)Since the P-Value is less than $\alpha$ , we reject the null hypothesis that the variables are not independent in favor of the alternate hypothesis that the variables are independent.
E)Since the P-Value is greater than $\alpha$ , we reject the null hypothesis that the variables are not independent in favor of the alternate hypothesis that the variables are independent.

Question 12

The following table shows the Myers-Briggs personality preferences for a random sample of 400 people in the listed professions. $$\begin{array} { l | l | l | l } \text { Occupation } & \text { Extroverted } & \text { Introverted } & \text { Row Total } \\\hline \text { Clergy (all denominations) } & 63 & 42 & 105 \\\hline \text { M.D. } & 67 & 95 & 162 \\\hline \text { Lawyer } & 52 & 81 & 133 \\\hline \text { Column Total } & 182 & 218 & 400 \\\hline\end{array}$$ Use the chi-square test to determine if the listed occupations and personality preferences are independent at . Find the value of the chi-square statistic for the sample.
$$\alpha = 0.01$$

A)12.22
B)0.01
C)12.01
D)0.22
E)9.20

Question 13

Suppose the age distribution of the Canadian population and the age distribution of a random sample of 406 residents in the Indian community of Red Lake are shown below. Use to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village. Given a value of 10.369 for , find (or estimate) the P-value of the sample test statistic.
$$\begin{array} { l l l } & & \text { Observed Number } \\\text { Age (years) } & \text { Percent of Canadian Population } & \text { in Red Lake Village } \\\hline \text { Under } 5 & 5.9 \% & 13 \\5 \text { to } 14 & 10.6 \% & 31 \\15 \text { to } 64 & 72.4 \% & 318 \\65 \text { and older } & 11.1 \% & 44\\\hline\end{array}$$ $$\alpha = 0.1$$ $$\chi ^ { 2 }$$

A)0.05 < P-Value < 0.10
B)0.10 < P-Value < 0.25
C)0.005 < P-Value < 0.01
D)0.01 < P-Value < 0.025
E)P-Value < 0.005

Question 14

Suppose the age distribution of the Canadian population and the age distribution of a random sample of 452 residents in the Indian community of Red Lake are shown below. Use to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village. Find (or estimate) the P-value of the sample test statistic.
$$\begin{array} { l l l } \hline \text { Age (years) } & \text { Percent of Canadian Population } & \begin{array} { l } \text { Observed Number } \\\text { in Red Lake Village }\end{array} \\\hline \text { Under } 5 & 7.5 \% & 50 \\5 \text { to } 14 & 12.5 \% & 45 \\15 \text { to } 64 & 69.9 \% & 313 \\65 \text { and older } & 10.1 \% & 44 \\\hline\end{array}$$ $$\alpha = 0.05$$

A)P-Value > 0.50
B)0.25 < P-Value < 0.50
C)0.005 < P-Value < 0.01
D)0.025 < P-Value < 0.05
E)0.01 < P-Value < 0.025

Question 15

Suppose the age distribution of the Canadian population and the age distribution of a random sample of 505 residents in the Indian community of Red Lake are shown below. $$\begin{array} { l l l } \hline & & \text { Observed Number } \\\text { Age (years) } & \text { Percent of Canadian Population } & \text { in Red Lake Village } \\\hline \text { Under } 5 & 8.5 \% & 45 \\5 \text { to } 14 & 10.4 \% & 50 \\15 \text { to } 64 & 68.2 \% & 367 \\65 \text { and older } & 12.9 \% & 43 \\\hline\end{array}$$ Use to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village. Find the value of the chi-square statistic for the sample.
$$\alpha = 0.05$$

A)9.231
B)0.274
C)0.124
D)10.945
E)11.136

Question 16

Suppose the age distribution of the Canadian population and the age distribution of a random sample of 470 residents in the Indian community of Red Lake are shown below. $$\begin{array} { l l l } & & \text { Observed Number } \\\text { Age (years) } & \text { Percent of Canadian Population } & \text { in Red Lake Village } \\\hline \text { Under } 5 & 5.9 \% & 44 \\5 \text { to } 14 & 13.7 \% & 58 \\15 \text { to } 64 & 69.9 \% & 324 \\65 \text { and older } & 10.5 \% & 44 \\\hline\end{array}$$ Use to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village. What is the level of significance?
$$\alpha = 0.01$$

A)0.05
B)0.90
C)0.95
D)0.01
E)0.75

Question 17

A transect is an archaeological study area that is mile wide and 1 mile long. A site in a transect is the location of a significant archaeological find. Let x represent the number of sites per transect. In a section of Chaco Canyon, a large number of transects showed that x has a population variance In a different section of Chaco Canyon, a random sample of 24 transects gave a sample variance for the number of sites per transect. Use an to test the claim that the variance in the new section is greater than 36.7. $\frac { 1 } { 5 }$ $\sigma ^ { 2 } = 36.7$ $s ^ { 2 } = 51.7$ $\alpha = 0.05$ Find the value of the chi-square statistic for the sample.

A)35.22
B)47.63
C)49.61
D)33.81
E)45.64

Question 18

The following table shows the Myers-Briggs personality preferences for a random sample of 409 people in the listed professions. $$\begin{array} { l | l | l | l } \text { Occupation } & \text { Extroverted } & \text { Introverted } & \text { Row Total } \\\hline \text { Clergy (all denominations) } & 62 & 44 & 106 \\\hline \text { M.D. } & 70 & 94 & 164 \\\hline \text { Lawyer } & 54 & 85 & 139 \\\hline \text { Column Total } & 186 & 223 & 409 \\\hline\end{array}$$ Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.1 level of significance. What are the degrees of freedom?

A)4
B)3
C)2
D)5
E)6

Question 19

The following table shows the Myers-Briggs personality preferences for a random sample of 406 people in the listed professions. Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.1 level of significance. Depending on the P-value, will you reject or fail to reject the null hypothesis of independence?
$$\begin{array} { l | l | l | l } \text { Occupation } & \text { Extroverted } & \text { Introverted } & \text { Row Total } \\\hline \text { Clergy (all denominations) } & 62 & 44 & 106 \\\hline \text { M.D. } & 66 & 94 & 160 \\\hline \text { Lawyer } & 56 & 84 & 140 \\\hline \text { Column Total } & 184 & 222 & 406 \\\hline\end{array}$$

A)Since the P-value is greater than $\alpha$ , we fail to reject the null hypothesis that the Myers-Briggs personality preference and profession are not independent. At 0.1 level of significance, we conclude that the Myers-Briggs personality preference and profession are independent.
B)Since the P-value is greater than $\alpha$ , we reject the null hypothesis that the Myers-Briggs personality preference and profession are not independent. At 0.1 level of significance, we conclude that the Myers-Briggs personality preference and profession are independent.
C)Since the P-value is less than $\alpha$ , we reject the null hypothesis that the Myers-Briggs personality preference and profession are not independent. At 0.1 level of significance, we conclude that the Myers-Briggs personality preference and profession are independent.
D)Since the P-value is less than $\alpha$ , we reject the null hypothesis that the Myers-Briggs personality preference and profession are independent. At 0.1 level of significance, we conclude that the Myers-Briggs personality preference and profession are not independent.
E)Since the P-value is less than $\alpha$ , we fail to reject the null hypothesis that the Myers-Briggs personality preference and profession are independent. At 0.1 level of significance, we conclude that the Myers-Briggs personality preference and profession are not independent.

Question 20

The following table shows the Myers-Briggs personality preferences for a random sample of 408 people in the listed professions. $$\begin{array} { l | l | l | l } \text { Occupation } & \text { Extroverted } & \text { Introverted } & \text { Row Total } \\\hline \text { Clergy (all denominations) } & 60 & 48 & 108 \\\hline \text { M.D. } & 70 & 91 & 161 \\\hline \text { Lawyer } & 58 & 81 & 139 \\\hline \text { Column Total } & 188 & 220 & 408 \\\hline\end{array}$$ Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.01 level of significance. If and the degrees of freedom are 2, find (or estimate) the P-value of the sample test statistic.
$$\chi ^ { 2 } = 5.402$$

A)0.05 < P-Value < 0.10
B)P-Value > 0.5
C)P-Value < 0.005
D)0.025 < P-Value < 0.05
E)0.25 < P-Value < 0.5

Question 21

A factor in determining the usefulness of an examination as a measure of demonstrated ability is the amount of spread that occurs in the grades. If the spread or variation of examination scores is very small, it usually means that the examination was either too hard or too easy. However, if the variance of scores is moderately large, then there is a definite difference in scores between "better," "average," and "poorer" students. A group of attorneys in a Midwest state has been given the task of making up this year's bar examination for the state. The examination has 400 total possible points, and from the history of past examinations, it is known that a standard deviation of around 56 points is desirable. Of course, too large or too small a standard deviation is not good. The attorneys want to test their examination to see how good it is. A preliminary version of the examination (with slight modification to protect the integrity of the real examination) is given to a random sample of 24 newly graduated law students. Their scores give a sample standard deviation of 77 points. Find a 99% confidence interval for the population variance.

A)3221 to 15,367
B)1704 to 8128
C)3087 to 14,726
D)1775 to 8467
E)1633 to 7789

Question 22

A transect is an archaeological study area that is mile wide and 1 mile long. A site in a transect is the location of a significant archaeological find. Let x represent the number of sites per transect. In a section of Chaco Canyon, a large number of transects showed that x has a population variance In a different section of Chaco Canyon, a random sample of 24 transects gave a sample variance for the number of sites per transect. Use an to test the claim that the variance in the new section is greater than 38.8. $\frac { 1 } { 5 }$ $\sigma ^ { 2 } = 38.8$ $s ^ { 2 } = 64.4$ $\alpha = 0.05$ Given 0.01 < P-Value < 0.05, will you reject or fail to reject the null hypothesis of independence?

A)Since the P-Value is less than the level of significance, we reject the null hypothesis that the variance is equal to 38.8. At 0.05 level of significance, we conclude that the variance is greater than 38.8.
B)Since the P-Value is less than the level of significance, we fail to reject the null hypothesis that the variance is equal to 38.8. At 0.05 level of significance, we conclude that the variance is greater than 38.8.
C)Since the P-Value is greater than the level of significance, we fail to reject the null hypothesis that the variance is greater than 38.8. At 0.05 level of significance, we conclude that the variance is equal to 38.8.
D)Since the P-Value is less than the level of significance, we reject the null hypothesis that the variance is greater than 38.8. At 0.05 level of significance, we conclude that the variance is equal to 38.8.
E)Since the P-Value is greater than the level of significance, we reject the null hypothesis that the variance is equal to 38.8. At 0.05 level of significance, we conclude that the variance is greater than 38.8.

Question 23

A transect is an archaeological study area that is mile wide and 1 mile long. A site in a transect is the location of a significant archaeological find. Let x represent the number of sites per transect. In a section of Chaco Canyon, a large number of transects showed that x has a population variance In a different section of Chaco Canyon, a random sample of 24 transects gave a sample variance for the number of sites per transect. Use an to test the claim that the variance in the new section is greater than 39.1. $\frac { 1 } { 5 }$ $\sigma ^ { 2 } = 39.1$ $s ^ { 2 } = 68.5$ $\alpha = 0.01$ Will you reject or fail to reject the null hypothesis of independence?

A)Since the P-Value is greater than the level of significance, we reject the null hypothesis that the variance is greater than 39.1. At 0.01 level of significance, we conclude that the variance is equal to 39.1.
B)Since the P-Value is less than the level of significance, we reject the null hypothesis that the variance is greater than 39.1. At 0.01 level of significance, we conclude that the variance is equal to 39.1.
C)Since the P-Value is greater than the level of significance, we fail to reject the null hypothesis that the variance is equal to 39.1. At 0.01 level of significance, we conclude that the variance is greater than 39.1.
D)Since the P-Value is greater than the level of significance, we fail to reject the null hypothesis that the variance is greater than 39.1. At 0.01 level of significance, we conclude that the variance is equal to 39.1.
E)Since the P-Value is greater than the level of significance, we reject the null hypothesis that the variance is equal to 39.1. At 0.01 level of significance, we conclude that the variance is greater than 39.1.

Question 24

A transect is an archaeological study area that is mile wide and 1 mile long. A site in a transect is the location of a significant archaeological find. Let x represent the number of sites per transect. In a section of Chaco Canyon, a large number of transects showed that x has a population variance In a different section of Chaco Canyon, a random sample of 24 transects gave a sample variance for the number of sites per transect. Use an to test the claim that the variance in the new section is greater than 43.8. $\frac { 1 } { 5 }$ $\sigma ^ { 2 } = 43.8$ $s ^ { 2 } = 68.9$ $\alpha = 0.05$ Given that the value of is 36.18, find (or estimate) the P-value of the sample test statistic.
$\chi ^ { 2 }$

A)P-Value<0.005
B)0.005 < P-Value < 0.01
C)0.05 < P-Value < 0.1
D)0.01 < P-Value < 0.05
E)0.25 < P-Value < 0.5

Question 25

A transect is an archaeological study area that is mile wide and 1 mile long. A site in a transect is the location of a significant archaeological find. Let x represent the number of sites per transect. In a section of Chaco Canyon, a large number of transects showed that x has a population variance In a different section of Chaco Canyon, a random sample of 24 transects gave a sample variance for the number of sites per transect. Use an to test the claim that the variance in the new section is greater than 40.7. $\frac { 1 } { 5 }$ $\sigma ^ { 2 } = 40.7$ $s ^ { 2 } = 56.3$ $\alpha = 0.01$ Find (or estimate) the P-value of the sample test statistic.

A)0.01 < P-Value < 0.05
B)0.25 < P-Value < 0.5
C)0.05 < P-Value < 0.1
D)0.005 < P-Value < 0.01
E)0.1 < P-Value < 0.25