Question 1

A company has claimed that the standard deviation of the monthly incomes of its employees is less than or equal to $120. To test its claim, a random sample of 15 employees of the company was taken, and it was determined that the standard deviation of their incomes was $135. At a 5% level of significance, test the company's claim.

Accepted Answer

The answer of A company has claimed that the standard...

Question 2

A lumber company has claimed that the standard deviation for the lengths of its six-foot boards is 0.5 inch or less. To test its claim, a random sample of 17 six-foot boards is selected, and it is determined that the standard deviation of the sample is .43. Do the results of the sample support the company's claim? Use α = .1.

Accepted Answer

The answer of A lumber company has claimed that the...

Question 3

A sample of 30 items provided a sample mean of 28 and a sample standard deviation of 6. Test the following hypotheses using α = .05. What is your conclusion? H₀: σ² ≤ 25 H_a: σ² > 25

Accepted Answer

The answer of A sample of 30 items provided a...

Question 4

There is a .90 probability of obtaining a ?² value such that _____.

Accepted Answer

The probability of obtaining a $\chi^2$ value between $\chi^2_{0.05}$ and $\chi^2_{0.95}$ is 0.90.

Question 5

A coach is deciding on whether to buy stopwatches from company A or company B. A test was set up to see how many seconds each stopwatch was off in a precise 10-minute test period. For samples of watches from companies A and B, the following information on stopwatch errors was found. $\begin{array}{lcc} 
& \text { Company A } & \text { Company B } \
\text { Sample size } & 5 & 8 \
\text { Sample mean (seconds) } & .18 & .15 \
\text { Sample variance } & .3 & 1.1
\end{array}$ Test the hypothesis of equal variances using a .05 level of significance. Be sure to state the null and alternative hypotheses being tested and the final conclusions of the test.

Accepted Answer

The answer of A coach is deciding on whether to...

Question 6

In practice, the most frequently encountered hypothesis test about a population variance is a _____.

Accepted Answer

In practice, tests about population variance often involve checking if the variance is greater than a specified value, leading to a one-tailed test with the rejection region in the upper tail.

Question 7

A sample of 61 items provided a sample mean of 932, a sample mode of 900, and a sample standard deviation of 11. Test the following hypotheses using α = .05. What is your conclusion? H₀: α² ≤ 80 H_a: α² > 80

Accepted Answer

The answer of A sample of 61 items provided a...

Question 8

The average grade of a sample of 25 students on their second statistics examination was 85 with a standard deviation of 9. Is the variance of the population significantly more than 80? Use a .05 level of significance.

Accepted Answer

The answer of The average grade of a sample of...

Question 9

At α = .1, test to see if the population variances from which the following samples were drawn are equal. Group $1 \quad$ Group 2
$\begin{array} { l l } 
n _ { 1 } = 21 & n _ { 2 } = 19 \
s _ { 1 } = 18 & s _ { 2 } = 16
\end{array}$ ​

Accepted Answer

The answer of At α = .1, test to see...

Question 10

Do the following data indicate that the variance of the population from which this sample has been drawn is 17? Use α = .05. $$\begin{array} { l l l l l } 
12 & 5 & 9 & 14 & 10
\end{array}$$

Accepted Answer

The answer of Do the following data indicate that the...

Question 11

Which of the following rejection rules is proper?

Accepted Answer

The proper rejection rule is to reject the null hypothesis H₀ if the p-value is less than or equal to the significance level $\alpha$.

Question 12

Two classes in business statistics showed the following results on a recent test. $\begin{array}{lll}
&\text { Class } 1 & \text { Class 2 }\
\text { Sample size } & 25 & 21 \
\text { Sample mean } & 82 & 84 \
\text { Sample standard deviation } & 6.2 & 7.6
\end{array}$ Carry out a test to determine whether the difference in the variance of the scores on this test is due to chance variation or is statistically significant with a .02 level of significance.

Accepted Answer

The answer of Two classes in business statistics showed the...

Question 13

We are interested in determining whether or not the variances of the sales at two small grocery stores are equal. A sample of 16 days of sales at each store indicated the following: $\begin{array} { l l } 
\text { Store A } & \text { Store B } \
n _ { 1 } = 16 & n _ { 2 } = 16 \
s _ { 1 } = \$ 125 & s _ { 2 } = \$ 105
\end{array}$ Are the variances of the populations (from which these samples came) equal?
Use α = .05.

Accepted Answer

The answer of We are interested in determining whether or...

Question 14

A sample of 16 students showed that the variance in the number of hours they spend studying is 25. At a 5% level of significance, test to see if the variance of the population is significantly different from 30.

Accepted Answer

The answer of A sample of 16 students showed that...

Question 15

The standard deviation of the ages of a sample of 16 executives from the northern states was 8.2 years, while the standard deviation of the ages of a sample of 25 executives from the southern states was 12.8 years. At α = .1, test to see if there is any difference in the standard deviations of the ages of all the northern and southern executives.

Accepted Answer

The answer of The standard deviation of the ages of...

Question 16

We are interested in determining whether or not the variances of the starting salaries of accounting majors are significantly different from the starting salaries of management majors. The following information was gathered from two samples: $$\begin{array} { l c c } 
& \text { Accounting } & \text { Management } \
\text { Sample size } & 16 & 16 \
\text { Average monthly income } & \$ 2,400 & \$ 2,500 \
\text { Standard deviation } & \$ 105 & \$ 125
\end{array}$$ At a 5% level of significance, test to determine whether or not the variances are equal.
​

Accepted Answer

The answer of We are interested in determining whether or...

Question 17

The standard deviation of the daily temperatures in Honolulu last year was 3.2 degrees Fahrenheit. A random sample of 19 days resulted in a standard deviation of 4 degrees Fahrenheit. Has there been a significant change in the variance of the temperatures? Use α = .02.

Accepted Answer

The answer of The standard deviation of the daily temperatures...

Question 18

An egg-packing company has stated that the standard deviation of the weights of its grade A large eggs is 0.07 ounce or less. The sample variance for 51 eggs was 0.0065 ounce. Can this sample result confirm the company's claim? Use α = .1.

Accepted Answer

The answer of An egg-packing company has stated that the...

Question 19

Student advisors are interested in determining if the variances of the grades of day students and night students are the same. The following samples are drawn: $$\begin{array} { l l } 
\text { Day } & \text { Night } \
n _ { 1 } = 25 & n _ { 2 } = 31 \
s _ { 1 } = 9.8 & s _ { 2 } = 14.7
\end{array}$$ Test the equality of the variances of the populations at 95% confidence.

Accepted Answer

The answer of Student advisors are interested in determining if...

Question 20

Test scores of two independent samples of students from UA and UB on a national examination are given below. At a .05 level of significance, test to determine if there is a significant difference between the variances of the two populations. $$\begin{array} { l l } 
\text { UA } & \text { UB } \
82 & 70 \
90 & 80 \
65 & 60 \
83 & 90 \
80 & 75
\end{array}$$

Accepted Answer

The answer of Test scores of two independent samples of...

Quiz 11: Inferences About Population Variances

A sample of 30 items provided a sample mean of 28 and a sample standard deviation of 6. Test the following hypotheses using α = .05. What is your conclusion? H₀: σ² ≤ 25 H_a: σ² > 25

There is a .90 probability of obtaining a ?² value such that _____.

In practice, the most frequently encountered hypothesis test about a population variance is a _____.

A sample of 61 items provided a sample mean of 932, a sample mode of 900, and a sample standard deviation of 11. Test the following hypotheses using α = .05. What is your conclusion? H₀: α² ≤ 80 H_a: α² > 80

The average grade of a sample of 25 students on their second statistics examination was 85 with a standard deviation of 9. Is the variance of the population significantly more than 80? Use a .05 level of significance.

At α = .1, test to see if the population variances from which the following samples were drawn are equal. Group $1 \quad$ Group 2 $\begin{array} { l l } n _ { 1 } = 21 & n _ { 2 } = 19 \\s _ { 1 } = 18 & s _ { 2 } = 16\end{array}$

Do the following data indicate that the variance of the population from which this sample has been drawn is 17? Use α = .05. $\begin{array} { l l l l l } 12 & 5 & 9 & 14 & 10\end{array}$

Which of the following rejection rules is proper?

A sample of 16 students showed that the variance in the number of hours they spend studying is 25. At a 5% level of significance, test to see if the variance of the population is significantly different from 30.

The standard deviation of the daily temperatures in Honolulu last year was 3.2 degrees Fahrenheit. A random sample of 19 days resulted in a standard deviation of 4 degrees Fahrenheit. Has there been a significant change in the variance of the temperatures? Use α = .02.

An egg-packing company has stated that the standard deviation of the weights of its grade A large eggs is 0.07 ounce or less. The sample variance for 51 eggs was 0.0065 ounce. Can this sample result confirm the company's claim? Use α = .1.

Quiz 11: Inferences About Population Variances

A sample of 30 items provided a sample mean of 28 and a sample standard deviation of 6. Test the following hypotheses using α = .05. What is your conclusion? ​ H0: σ2 ≤ 25 Ha: σ2 > 25

There is a .90 probability of obtaining a ?2 value such that _____.

In practice, the most frequently encountered hypothesis test about a population variance is a _____.

A sample of 61 items provided a sample mean of 932, a sample mode of 900, and a sample standard deviation of 11. Test the following hypotheses using α = .05. What is your conclusion? ​ H0: α2 ≤ 80 Ha: α2 > 80

The average grade of a sample of 25 students on their second statistics examination was 85 with a standard deviation of 9. Is the variance of the population significantly more than 80? Use a .05 level of significance.

At α = .1, test to see if the population variances from which the following samples were drawn are equal. Group 11 \quad1 Group 2 n1=21n2=19s1=18s2=16\begin{array} { l l } n _ { 1 } = 21 & n _ { 2 } = 19 \\s _ { 1 } = 18 & s _ { 2 } = 16\end{array}n1​=21s1​=18​n2​=19s2​=16​ ​

Do the following data indicate that the variance of the population from which this sample has been drawn is 17? Use α = .05. 12591410\begin{array} { l l l l l } 12 & 5 & 9 & 14 & 10\end{array}12​5​9​14​10​

Which of the following rejection rules is proper?

A sample of 16 students showed that the variance in the number of hours they spend studying is 25. At a 5% level of significance, test to see if the variance of the population is significantly different from 30.

The standard deviation of the daily temperatures in Honolulu last year was 3.2 degrees Fahrenheit. A random sample of 19 days resulted in a standard deviation of 4 degrees Fahrenheit. Has there been a significant change in the variance of the temperatures? Use α = .02.

An egg-packing company has stated that the standard deviation of the weights of its grade A large eggs is 0.07 ounce or less. The sample variance for 51 eggs was 0.0065 ounce. Can this sample result confirm the company's claim? Use α = .1.

A sample of 30 items provided a sample mean of 28 and a sample standard deviation of 6. Test the following hypotheses using α = .05. What is your conclusion? H₀: σ² ≤ 25 H_a: σ² > 25

There is a .90 probability of obtaining a ?² value such that _____.

A sample of 61 items provided a sample mean of 932, a sample mode of 900, and a sample standard deviation of 11. Test the following hypotheses using α = .05. What is your conclusion? H₀: α² ≤ 80 H_a: α² > 80

At α = .1, test to see if the population variances from which the following samples were drawn are equal. Group $1 \quad$ Group 2 $\begin{array} { l l } n _ { 1 } = 21 & n _ { 2 } = 19 \\s _ { 1 } = 18 & s _ { 2 } = 16\end{array}$

Do the following data indicate that the variance of the population from which this sample has been drawn is 17? Use α = .05. $\begin{array} { l l l l l } 12 & 5 & 9 & 14 & 10\end{array}$