Question 1

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 11, the sample mean x is 32, and the sample standard deviation s is 12.6, what is the margin of error? Show your answer to 2 decimal places.

Accepted Answer

$$\mathrm { df } = 8 ; E = 2.228 \frac { 12.6 } { \sqrt { 11 } } = 8.46$$

Question 2

-The t distribution can be used when finding a confidence interval for the population mean whenever the sample size is small.

Accepted Answer

False

Question 3

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 8, the sample mean x is 22, and the sample standard deviation s is 6.3, what is the margin of error? Show your answer to 2 decimal places.

Accepted Answer

$$\mathrm { df } = 7 ; E = 2.365 \frac { 6.3 } { \sqrt { 8 } } = 5.869$$

Question 4

The partial t-table below can be used where necessary.

-The t distribution can be used when finding a confidence interval for the mean with a small sample whenever the data comprise a simple random sample.

Accepted Answer

The answer of The partial t-table below can be used...

Question 5

-Data from the test in Problem 5 resulted in a sample mean of 163.2 yards with a sample standard deviation of 5.8 yards. Assuming normality, carry out a hypothesis test at the 0.05

Accepted Answer

The answer of 
-Data from the test in Problem 5...

Question 6

$\begin{array}{|l|c|c|c|}
\hline & \text { Colorblind } & \text { Not Colorblind } & \text { Total } \
\hline \text { Male } & 8 & 52 & 60 \
\hline \text { Female } & 2 & 38 & 40 \
\hline \text { Total } & 10 & 90 & 100 \
\hline
\end{array}$
-Find the value of the ?2 statistic for the data .

Accepted Answer

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

Question 7

One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.
 
$\begin{array}{|l|c|c|c|}
\hline & \text { Colorblind } & \text { Not Colorblind } & \text { Total } \
\hline \text { Male } & 8 & 52 & 60 \
\hline \text { Female } & 2 & 38 & 40 \
\hline \text { Total } & 10 & 90 & 100 \
\hline
\end{array}$
If gender and colorblindness are independent, find the expected values corresponding to the four combinations of gender and colorblindness, and enter them in the table below along with row and column totals.

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

Accepted Answer

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

Question 8

$\begin{array}{|l|c|c|c|}
\hline & \text { Colorblind } & \text { Not Colorblind } & \text { Total } \
\hline \text { Male } & 8 & 52 & 60 \
\hline \text { Female } & 2 & 38 & 40 \
\hline \text { Total } & 10 & 90 & 100 \
\hline
\end{array}$
-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 9

A 95% confidence interval for the mean of a normal population is found to be 15.6 < µ < 25.2. What is the margin of error?

Accepted Answer

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

Question 10

$\begin{array}{|l|c|c|c|} \hline & \text { Colorblind } & \text { Not Colorblind } & \text { Total } \ \hline \text { Male } & 8 & 52 & 60 \ \hline \text { Female } & 2 & 38 & 40 \ \hline \text { Total } & 10 & 90 & 100 \ \hline \end{array}$ -The critical value of ?² for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the ?² statistic iS 3.427, 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 11

A 95% confidence interval for the mean of a normal population is found to be 13.2 < µ < 22.4. What is the margin of error?

Accepted Answer

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

Question 12

The analysis of the data in Problem 9 resulted in the following output from Excel.
 Anova: Single Factor

$\text { SUMMARY }$
$\begin{array}{lrrrr}
\hline\text { Groups }&\text { Count } &{\text { Sum }} & {\text { Average }} &{\text { Variance }} \
\hline A&4 & 119 & 29.75 & 12.25 \
B&4 & 100 & 25 & 13.33333 \
C&4 & 94 & 23.5 & 27 \
\hline
\end{array}$

$\begin{array}{lrrrrrr}
\text { ANOVA }\
\hline \text { Source of Variation } & \text { SS } & d f & M S & F & \text { P-value } & \text { F crit } \
\hline\text { Between Groups } & 85.16667 & 2 & 42.58333 & 2.429477 & 0.143319 & 4.256492 \
\text { Within Groups } & 157.75 & 9 & 17.52778 & & &\
\
\text { Total}& 242.9167&11\
\end{array}$

If the significance level for the test is 0.05, which conclusion below is correct?
A) The data do not provide sufficient evidence to conclude that the groups A, B, and C are somehow related.
B) The data do not provide sufficient evidence to conclude that the population means of groups A, B, and C are different.
C) The data do not provide sufficient evidence to conclude that the population variances of groups A, B, and C are different.
D) The data do provide sufficient evidence to conclude that the population means of groups A, B, and C are different.
E) None of the above.

Accepted Answer

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

Question 13

$$\begin{array} { | l | c | c | c | } 
\hline & \text { Colorblind } & \text { Not Colorblind } & \text { Total } \
\hline \text { Male } & 7 & 53 & 60 \
\hline \text { Female } & 1 & 39 & 40 \
\hline \text { Total } & 8 & 92 & 100 \
\hline
\end{array}$$ 
-Find the value of the ?2 statistic for the data

Accepted Answer

The answer of \[\begin{array} { | l | c |...

Question 14

The following data were analyzed using one-way analysis of variance.
 $$\begin{array} { c c c } 
\mathrm { A } & \mathrm { B } & \mathrm { C } \
\hline 34 & 27 & 19 \
26 & 23 & 31 \
31 & 29 & 22 \
28 & 21 & 22
\end{array}$$ ` Which one of the following statements is correct?
A) The purpose of the analysis is to determine whether the groups A, B, and C are independent.
B) The purpose of the analysis is to test the hypothesis that the population means of the three groups are equal.
C) The purpose of the analysis is to test the hypothesis that the population variances of the three groups are equal.
D) The purpose of the analysis is to test the hypothesis that the sample means of the three groups are equal.

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 15

A golfer wished to find a ball that would travel more than 160 yards when hit with his 7-iron with a 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 8 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 16

One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.
 $$\begin{array} { | l | c | c | c | } 
\hline & \text { Colorblind } & \text { Not Colorblind } & \text { Total } \
\hline \text { Male } & 7 & 53 & 60 \
\hline \text { Female } & 1 & 39 & 40 \
\hline \text { Total } & 8 & 92 & 100 \
\hline
\end{array}$$ 
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 column totals. 
$$\begin{array} { | l | l | l | l | } 
\hline & \text { Colorblind } & \text { Not Colorblind } & \text { Total } \
\hline \text { Male } & & & \
\hline \text { Female } & & & \
\hline \text { Total } & & & \
\hline
\end{array}$$

Accepted Answer

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

Question 17

-Resulted in a sample mean of 171.6 yards with a sample standard deviation of 2.4 yards. Assuming normality, carry out a hypothesis test at the 0.05 significance

Accepted Answer

The answer of 
-Resulted in a sample mean of 171.6...

Question 18

The following data were analyzed using one-way analysis of variance. $$\begin{array} { c c c } 
\text { A } & \text { B } & \text { C } \
\hline 24 & 27 & 19 \
26 & 23 & 31 \
31 & 29 & 22 \
28 & 21 & 22
\end{array}$$ ` Which one of the following statements is correct?
A) The purpose of the analysis is to determine whether the groups A, B, and C are independent.
B) The purpose of the analysis is to test the hypothesis that the population means of the three groups are equal.
C) The purpose of the analysis is to test the hypothesis that the population variances of the three groups are equal.
D) The purpose of the analysis is to test the hypothesis that the sample means of the three groups are equal.

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 19

A golfer wished to find a ball that would travel more than 170 yards when hit with his 6-iron with a club head speed of 90 miles per hour. He had a golf equipment lab test a low compression ball by having a robot swing his club 12 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

$$\begin{array} { | l | c | c | c | } \hline & \text { Colorblind } & \text { Not Colorblind } & \text { Total } \ \hline \text { Male } & 7 & 53 & 60 \ \hline \text { Female } & 1 & 39 & 40 \ \hline \text { Total } & 8 & 92 & 100 \ \hline \end{array}$$ -The critical value of ?² for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the ?² statistic is 3.179, state your conclusion about the relationship between gender and colorblindness.

Accepted Answer

The answer of \[\begin{array} { | l | c |...

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

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 11, the sample mean x is 32, and the sample standard deviation s is 12.6, what is the margin of error? Show your answer to 2 decimal places.

-The t distribution can be used when finding a confidence interval for the population mean whenever the sample size is small.

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 8, the sample mean x is 22, and the sample standard deviation s is 6.3, what is the margin of error? Show your answer to 2 decimal places.

The partial t-table below can be used where necessary. -The t distribution can be used when finding a confidence interval for the mean with a small sample whenever the data comprise a simple random sample.

-Data from the test in Problem 5 resulted in a sample mean of 163.2 yards with a sample standard deviation of 5.8 yards. Assuming normality, carry out a hypothesis test at the 0.05

$\begin{array}{|l|c|c|c|}\hline & \text { Colorblind } & \text { Not Colorblind } & \text { Total } \\\hline \text { Male } & 8 & 52 & 60 \\\hline \text { Female } & 2 & 38 & 40 \\\hline \text { Total } & 10 & 90 & 100 \\\hline\end{array}$ -Find the value of the ?2 statistic for the data .

A 95% confidence interval for the mean of a normal population is found to be 15.6 < µ < 25.2. What is the margin of error?

A 95% confidence interval for the mean of a normal population is found to be 13.2 < µ < 22.4. What is the margin of error?

$\begin{array} { | l | c | c | c | } \hline & \text { Colorblind } & \text { Not Colorblind } & \text { Total } \\\hline \text { Male } & 7 & 53 & 60 \\\hline \text { Female } & 1 & 39 & 40 \\\hline \text { Total } & 8 & 92 & 100 \\\hline\end{array}$ -Find the value of the ?2 statistic for the data

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

-Resulted in a sample mean of 171.6 yards with a sample standard deviation of 2.4 yards. Assuming normality, carry out a hypothesis test at the 0.05 significance

The following data were analyzed using one-way analysis of variance. $\begin{array} { c c c } \text { A } & \text { B } & \text { C } \\\hline 24 & 27 & 19 \\26 & 23 & 31 \\31 & 29 & 22 \\28 & 21 & 22\end{array}$ ` Which one of the following statements is correct?