Question 1

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

Accepted Answer

H0: Colorblindness and gender are independent characteristics.
Ha: Colorblindness and gender are related in some way.

Question 2

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

Accepted Answer

χ2 = 2.02/6.0 + 2.02/54.0 + 2.02/4.0 + 2.02/36.0 = 1.852

Question 3

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

$$\begin{array} { | l | c | c | c | } 
\hline & \text { Colorblind } & \text { Not Colorblind } & \text { Total } \
\hline \text { Male } & 6.0 & 54.0 & 60 \
\hline \text { Female } & 4.0 & 36.0 & 40 \
\hline \text { Total } & 10.0 & 90.0 & 100 \
\hline
\end{array}$$

Question 4

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 5

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 6

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

Accepted Answer

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

Question 7

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?

Accepted Answer

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.

Question 8

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

A) True 
 B)False

Question 9

$$\begin{array} { | l | c | c | c | } \hline & \text { Colorblind } & \text { Not Colorblind } & \text { Total } \ \hline \text { Male } & 7 & 53 & 60 \ \hline \text { Female } & 1 & 39 & 40 \ \hline \text { Total } & 8 & 92 & 100 \ \hline \end{array}$$ -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 |...

Question 10

$\begin{array}{|l|c|c|c|}
\hline & \text { Colorblind } & \text { Not Colorblind } & \text { Total } \
\hline \text { Male } & 8 & 52 & 60 \
\hline \text { Female } & 2 & 38 & 40 \
\hline \text { Total } & 10 & 90 & 100 \
\hline
\end{array}$
-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 11

$\begin{array}{|l|c|c|c|}
\hline & \text { Colorblind } & \text { Not Colorblind } & \text { Total } \
\hline \text { Male } & 8 & 52 & 60 \
\hline \text { Female } & 2 & 38 & 40 \
\hline \text { Total } & 10 & 90 & 100 \
\hline
\end{array}$
-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 12

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 13

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 14

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

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.

Question 15

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 16

-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 17

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 18

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

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.

Question 19

-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

A) True 
 B)False

Question 20

-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...

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

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

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.

$\begin{array} { | l | c | c | c | } \hline & \text { Colorblind } & \text { Not Colorblind } & \text { Total } \\\hline \text { Male } & 7 & 53 & 60 \\\hline \text { Female } & 1 & 39 & 40 \\\hline \text { Total } & 8 & 92 & 100 \\\hline\end{array}$ -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?

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.

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

A 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.

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?

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.

-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

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?

-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.

-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