# Hypothesis Tests for Population Variances

## Question

Assignment 5 - Chi-square and F Tests for Variances

Hypothesis tests for population variances

Data Set:
4.2    -1.3    -3.4    1.5    2.8    -3    2.9    -3.1    0    0.6    -3.1    0.6

1.    Business Statistics in Practice by Bruce L. Bowerman, Richard T. O’Connell and Emily S. Murphree, based on Sections 11.1 and 11.2 of the 7th edition of our text on page 413 (Sections 9.6 and 9.7 of the 6th edition of our text on page 384). Airlines face the challenging task of keeping their planes on schedule. One key measure is the number of minutes a plane deviates from the targeted arrival time, negative values indicate the plane arrived prior to the targeted arrival time and positive values indicate the plane arrived after the targeted arrival time. Ideally, the measure for each arrival will be zero minutes, indicating that the plane arrived at the targeted time. Suppose Major Airways has set a company goal that requires the planes to arrive an average of zero minutes late with a standard deviation not to exceed 2 minutes. To determine whether these goals are being met, the airline selects a random sample of 12 arrivals and compares the electronically recorded arrival time to the targeted arrival time to determine the number of minutes early or late each flight is. For last month’s sample, the times, rounded to the nearest one-tenth minute, are:
a.            State the appropriate null and alternative hypotheses to be used to determine if the standard deviation goal is being met.
b.            Report the critical value(s) for this test using a significance level of 5%.
c.             Report the test statistic.
d.            Draw a conclusion and in one sentence interpret your results.

2.   Based on Section 10.3 of the text (7th ed) on page 398 or Section 10.5 of the text (6th ed) on page 425. Phone Solutions provides assistance to users of a personal finance software package. Users of the software call with their questions and trained consultants provide answers and information. Phone Solutions seeks to reduce the average variability in the time each consultant spends with each caller. A study of this issue is currently underway at the company’s three call centers. Each call center manager has randomly sampled 50 days of calls and the times collected, in minutes, are in the file Phone Solutions.

Can the manager conclude there is greater variability in the length of phone calls for Call Center 3 than for Call Center 2? State the null and alternative hypotheses, report the critical value(s) at the 10% significance level, report the value of the test statistic, and draw your conclusion.

See Question.xlsx

## Solution Preview

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1. a. Null Hypothesis (Ho): Population standard deviation is equal to or greater 2 minutes. (σ ≥ 2)
Alternative Hypothesis (Ho): Population standard deviation is less than 2 minutes. (σ < 2)
b. Lower critical value at 5% level of significance with 11 degree of freedom is 4.3087...

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