Question 1

The critical value of χ2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the
χ2 statistic in Problem 8 had been 4.216, state your conclusion about the relationship between
gender and colorblindness.

Accepted Answer

The answer of The critical value of χ2 for a...

Question 2

The margin of error in estimating the population mean of a normal population is E = 6.3 when the sample standard deviation is 8.2. If the sample standard deviation were increased to 9.1 and the sample size stayed the same, would the margin of error be larger or smaller than 6.3? Explain your answer.

Accepted Answer

The answer of The margin of error in estimating the...

Question 3

The following data were analyzed using one-way analysis of variance. $$\begin{array} { c c c } 
\text { A } & \text { B } & \text { C } \
\hline 34 & 27 & 19 \
26 & 23 & 21 \
31 & 29 & 22 \
28 & 21 & 12
\end{array}$$ ` Which one of the following statements is correct?

Accepted Answer

The purpose of one-way analysis of variance is to test the hypothesis that the population means of the three groups are equal.

Question 4

-Resulted in a sample mean of 184.2 yards and a sample standard deviation of 5.8 yards. Assuming normality, carry out a hypothesis test at the 0.05 significance

Accepted Answer

The answer of 
-Resulted in a sample mean of 184.2...

Question 5

A simple random sample from a normal distribution is taken in order to obtain a 95% confidence interval for the population mean. If the sample size is 12, the sample mean x
is 22, and the sample standard deviation s is 5.5, what is the margin of error? Show your answer to 2 decimal places.

Accepted Answer

The answer of A simple random sample from a normal...

Question 6

The following data were analyzed using one-way analysis of variance. $$\begin{array} { c c c } 
\text { A } & \text { B } & \text { C } \
\hline 29 & 27 & 19 \
26 & 23 & 21 \
25 & 29 & 25 \
28 & 21 & 17
\end{array}$$ ` Which one of the following statements is correct?

Accepted Answer

The purpose of one-way analysis of variance is to test the hypothesis that the population means of the three groups are equal.

Question 7

A 95% confidence interval for the mean of a normal population is found to be 15.6 < µ < 24.8. What is the margin of error?

Accepted Answer

The answer of A 95% confidence interval for the mean...

Question 8

The analysis of the data in Problem 9 resulted in the following output from Excel.

Anova: Single Factor

$\text { SUMMARY }$
$\begin{array}{lrrrr}
\hline\text { Groups }&\text { Count } &{\text { Sum }} & {\text { Average }} &{\text { Variance }} \
\hline A&4 & 108 &27 & 3.333333 \
B&4 & 100 & 25 & 13.33333 \
C&4 &82 & 20.5 & 11.66667 \
\hline
\end{array}$

$\begin{array}{lrrrrrr}
\text { ANOVA }\
\hline \text { Source of Variation } & \text { SS } & d f & M S & F & \text { P-value } & \text { F crit } \
\hline\text { Between Groups } & 88.66667& 2 & 44.33333&4.694118 &0.040148 & 4.256492\
\text { Within Groups } & 85& 9 & 9.444444 & & &\
\
\text { Total}& 173.6667&11\
\hline
\end{array}$

If the significance level for the test is 0.05, which conclusion below is correct?

Accepted Answer

The answer of The analysis of the data in Problem...

Question 9

A 95% confidence interval for the mean of a normal population is found to be 17.6 < µ < 23.6.
What is the margin of error?

Accepted Answer

The answer of A 95% confidence interval for the mean...

Question 10

A simple random sample from a normal distribution is taken in order to obtain a 95% confidence
interval for the population mean. If the sample size is 12, the sample mean x
is 32, and the
sample standard deviation s is 7.5, what is the margin of error? Show your answer to 2 decimal
places.

Accepted Answer

The answer of A simple random sample from a normal...

Question 11

State the null and alternative hypothesis for the test associated with the data in Problem 7.

Accepted Answer

The answer of State the null and alternative hypothesis for...

Question 12

$\begin{array}{|l|c|c|c|} \hline & \text { Colorblind } & \text { Not Colorblind } & \text { Total } \ \hline \text { Male } & 8 & 52 & 60 \ \hline \text { Female } & 2 & 38 & 40 \ \hline \text { Total } & 10 & 90 & 100 \ \hline \end{array}$ -The critical value of ?²for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the ?²statistic is 4.613, state your conclusion about the relationship between gender and colorblindness.

Accepted Answer

The answer of \(\begin{array}{|l|c|c|c|}
\hline & \text { Colorblind } &...

Question 13

$\begin{array}{|l|c|c|c|}
\hline & \text { Colorblind } & \text { Not Colorblind } & \text { Total } \
\hline \text { Male } & 8 & 52 & 60 \
\hline \text { Female } & 2 & 38 & 40 \
\hline \text { Total } & 10 & 90 & 100 \
\hline
\end{array}$
-State the null and alternative hypothesis for the test associated with the data.

Accepted Answer

The answer of \(\begin{array}{|l|c|c|c|}
\hline & \text { Colorblind } &...

Question 14

One hundred people are selected at random and tested for colorblindness to determine whether
gender and colorblindness are independent. The following counts were observed.
Colorblind Not Colorblind Total $\begin{array}{|l|c|c|c|}
\hline & \text { Colorblind } & \text { Not Colorblind } & \text { Total } \
\hline \text { Male } & 8 & 52 & 60 \
\hline \text { Female } & 2 & 38 & 40 \
\hline \text { Total } & 10 & 90 & 100 \
\hline
\end{array}$

If gender and colorblindness are independent, find the expected values corresponding to the four combinations of gender and colorblindness, and enter them in the following table along with row

$\begin{array}{|l|l|l|l|}
\hline & \text { Colorblind } & \text { Not Colorblind } & \text { Total } \
\hline \text { Male } & & & \
\hline \text { Female } & & & \
\hline \text { Total } & & & \
\hline
\end{array}$

Accepted Answer

The answer of One hundred people are selected at random...

Question 15

The t distribution can be used when finding a confidence interval for the population mean
with a small sample whenever the sample comes from a symmetric population.

Accepted Answer

The answer of The t distribution can be used when...

Question 16

level and determine whether the ball meets the golfer's requirements. Use the partial t-table
above.
-One hundred people are selected at random and tested for colorblindness to determine whether
gender and colorblindness are independent. The following counts were observed. $\begin{array}{|l|c|c|c|}
\hline & \text { Colorblind } & \text { Not Colorblind } & \text { Total } \
\hline \text { Male } & 4 & 36 & 40\
\hline \text { Female } &  2 & 58 & 60 \
\hline \text { Total } & 6 & 94 & 100 \
\hline
\end{array}$

If gender and colorblindness are independent, find the expected values corresponding to the four combinations of gender and colorblindness, and enter them in the table below along with row and

$\begin{array}{|l|l|l|l|}
\hline & \text { Colorblind } & \text { Not Colorblind } & \text { Total } \
\hline \text { Male } & & & \
\hline \text { Female } & & & \
\hline \text { Total } & & & \
\hline
\end{array}$

Accepted Answer

The answer of level and determine whether the ball meets...

Question 17

Find the value of the χ2 statistic for the data in Problem 7.
131

Accepted Answer

The answer of Find the value of the χ2 statistic...

Question 18

-The t distribution can be used when finding a confidence interval for the population mean with a small sample anytime the population standard deviation is unknown.

Accepted Answer

The answer of 
-The t distribution can be used when...

Question 19

A golfer wished to find a ball that would travel more than 180 yards when hit with his 5-iron witha club speed of 90 miles per hour. He had a golf equipment lab test a low compression ball by having a robot swing his club 7 times at the required speed. State the null and alternative hypotheses for this test.

Accepted Answer

The answer of A golfer wished to find a ball...

Question 20

The analysis of the data in Problem 9 resulted in the following output from Excel.

Anova: Single Factor

$\text { SUMMARY }$
$\begin{array}{lrrrr}
\hline\text { Groups }&\text { Count } &{\text { Sum }} & {\text { Average }} &{\text { Variance }} \
\hline A&4 & 109 &27.25 & 8.916667 \
B&4 & 100 & 25 & 13.33333 \
C&4 & 94 & 23.5 & 27 \
\hline
\end{array}$

$\begin{array}{lrrrrrr}
\text { ANOVA }\
\hline \text { Source of Variation } & \text { SS } & d f & M S & F & \text { P-value } & \text { F crit } \
\hline\text { Between Groups } & 28.5 & 2 & 14.25 &0.86802 &0.452161 & 4.256492 \
\text { Within Groups } & 147.75 & 9 & 16.41667 & & &\
\
\text { Total}& 176.25&11\
\hline
\end{array}$

If the significance level for the test is 0.05, which conclusion below is correct?

Accepted Answer

The p-value (0.452161) is greater than the significance level (0.05), so we fail to reject the null hypothesis. This means that the data do not provide sufficient evidence to conclude that the population means of groups A, B, and C are different.

Quiz 10: T Tests, Two-Way Tables, and Anova

The critical value of χ2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the χ2 statistic in Problem 8 had been 4.216, state your conclusion about the relationship between gender and colorblindness.

The margin of error in estimating the population mean of a normal population is E = 6.3 when the sample standard deviation is 8.2. If the sample standard deviation were increased to 9.1 and the sample size stayed the same, would the margin of error be larger or smaller than 6.3? Explain your answer.

The following data were analyzed using one-way analysis of variance. $\begin{array} { c c c } \text { A } & \text { B } & \text { C } \\\hline 34 & 27 & 19 \\26 & 23 & 21 \\31 & 29 & 22 \\28 & 21 & 12\end{array}$ ` Which one of the following statements is correct?

-Resulted in a sample mean of 184.2 yards and a sample standard deviation of 5.8 yards. Assuming normality, carry out a hypothesis test at the 0.05 significance

A simple random sample from a normal distribution is taken in order to obtain a 95% confidence interval for the population mean. If the sample size is 12, the sample mean x is 22, and the sample standard deviation s is 5.5, what is the margin of error? Show your answer to 2 decimal places.

The following data were analyzed using one-way analysis of variance. $\begin{array} { c c c } \text { A } & \text { B } & \text { C } \\\hline 29 & 27 & 19 \\26 & 23 & 21 \\25 & 29 & 25 \\28 & 21 & 17\end{array}$ ` Which one of the following statements is correct?

A 95% confidence interval for the mean of a normal population is found to be 15.6 < µ < 24.8. What is the margin of error?

A 95% confidence interval for the mean of a normal population is found to be 17.6 < µ < 23.6. What is the margin of error?

A simple random sample from a normal distribution is taken in order to obtain a 95% confidence interval for the population mean. If the sample size is 12, the sample mean x is 32, and the sample standard deviation s is 7.5, what is the margin of error? Show your answer to 2 decimal places.

State the null and alternative hypothesis for the test associated with the data in Problem 7.

The t distribution can be used when finding a confidence interval for the population mean with a small sample whenever the sample comes from a symmetric population.

Find the value of the χ2 statistic for the data in Problem 7. 131

-The t distribution can be used when finding a confidence interval for the population mean with a small sample anytime the population standard deviation is unknown.