Question 1

An egg packing company has stated that the standard deviation of the weights of their grade A large eggs is .07 ounces or less.The sample variance for 51 eggs was .0065 ounces.Can this sample result confirm the company's claim? Use α = .1.

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Question 2

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

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Question 3

Do the following sample data indicate that the variance of the population from which it has been drawn is significantly more than 17? Use α = .05.
X
12
5
9
14
10

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Question 4

A random sample of 20 observations showed a standard deviation of 8.At a .05 level of significance, test to see if the variance of the population is significantly less than 65.Use the critical value approach.

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Question 5

At α = .1, test to see if the population variances from which the following samples were drawn are equal. Sample 1 Sample 2 n₁ = 21 n₂ = 19 s₁ = 18 s₂ = 16

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Question 6

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 between the variances of the ages of all the northern and all the southern executives.

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Question 7

The average score of a sample of 30 students on their second statistics examination was 85 with a standard deviation of 11.Is the variance of the population significantly more than 80? Use a .05 level of significance.

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Question 8

A company claims that the standard deviation in their delivery times is less than 5 days.A sample of 27 past customers was taken.The average delivery time in the sample was 14 days with a standard deviation of 4.5 days.At the 5% level of significance, test the company's claim.Use the critical value approach.

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Question 9

A lumber company has claimed that the standard deviation for the lengths of their six-foot boards is .4 inches or less.To test their claim, a random sample of 16 six-foot boards is selected; and it is determined that the variance of the sample is .3.Do the results of the sample support the company's claim? Use α = .1.

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Question 10

A random sample of 22 employees of a local utility firm showed that their monthly incomes had a sample standard deviation of $110.Provide a 90% confidence interval estimate for the standard deviation of the incomes of all employees of the firm.

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Question 11

We are interested in determining whether or not the variances of the starting salaries of accounting majors is significantly different from management majors.The following information was gathered from two samples.
Accounting
Management
Sample Size
21
18
Average Monthly Income
$3600
$3500
Variance
$900
$400
​
At the .1 level of significance, test to determine whether or not the variances are equal.

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Question 12

A random sample of 41 scores of students taking the ACT test showed a standard deviation of 8 points.Provide a 98% confidence interval estimate for the standard deviation of all the ACT test scores.

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Question 13

Student advisors are interested in determining if the variances of the scores of day students and night students are the same.The following samples are drawn: Day Night n₁ = 25 n₂ = 31 s₁ = 9.8 s₂ = 14.7 Test the equality of the variances of the populations.Let α = .05.

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Question 14

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

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Question 15

A sample of 22 bottles of soft drink showed a variance of .64 in their contents.At the 5% level, determine whether or not the standard deviation of the population is significantly different from .7 ounces.Use the critical value approach.

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Question 16

A large company has claimed that the standard deviation of the monthly incomes of their employees is less than or equal to $120.To test their claim, a random sample of 76 employees of the company was taken; and it was determined that the standard deviation of their incomes was $135.Using α = .10, test the company's claim.

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Question 17

We are interested in determining whether or not the variances of the sales are equal for two small grocery stores.A sample of 16 days of sales at each store indicated the following. Store A Store B n₁ = 16 n₂ = 16 s₁ = $130 s₂ = $100 Are the variances of the populations (from which these samples came) equal? Use α = .05.

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Question 18

A random sample of 21 checking accounts at a bank showed an average daily balance of $430 with a standard deviation of $50.
a.
Provide a 95% confidence interval estimate for the variance of the population of the checking accounts.
b.
Provide a 95% confidence interval estimate for the standard deviation of the population of the checking accounts.

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Question 19

The standard deviation of the daily temperatures in Honolulu last year was 4 degrees Fahrenheit.A random sample of 25 days resulted in a standard deviation of 5.8 degrees Fahrenheit.Has there been a significant increase in the variance of the temperatures? Use α = .05.

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Question 20

A sample of 14 items provides a sample mean of 20 and a sample variance of 18.Compute a 95% confidence interval estimate for the standard deviation of the population.

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Quiz 11: Inferences About Population Variances