Fundamentals of Statistics (5th Edition)
5th Edition
ISBN: 9780134508306
Author: Michael Sullivan III
Publisher: PEARSON
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Chapter B.3, Problem 2AYU
- (a) Determine the critical value for a right-tailed test of a population standard deviation with 16 degrees of freedom at the α = 0.01 level of significance.
- (b) Determine the critical value for a left-tailed test of a population standard deviation for a
sample of size n = 14 at the α = 0.01 level of significance. - (c) Determine the critical values for a two-tailed test of a population standard deviation for a sample of size n = 61 at the α = 0.05 level of significance.
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A random sample of 32 items from the first population showed a mean of 112 and a standard deviation of 19. A sample of 28 items for the second population showed a mean of 106 and a standard deviation of 8. Test the assumption that the population variances are equal with 0.10 significance level. Then, using a 0.05 significance level, test the hypothesis that the population means are equal. 
Determine the critical values for these tests of a population standard deviation.
(a) A right-tailed test with 16 degrees of freedom at the α=0.1 level of significance
(b) A left-tailed test for a sample of size n=28 at the α=0.05 level of significance
(c) A two-tailed test for a sample of size n=29 at the α=0.05 level of significance
Round to three decimal places.
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Chapter B.3 Solutions
Fundamentals of Statistics (5th Edition)
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- A newspaper article reports that the mean cost for preventative dental care per year is $175 with a standard deviation of $35 (assume that this is the population standard deviation). You want to test whether the mean cost for preventative dental care in your company is different from what was reported in the article. You take a random sample of 250 employees and find the mean cost is $171. Does this significantly differ from what was reported in the article? Run the appropriate test at α=0.05.1) the appropriate null and alternative hypotheses; 2) the appropriate test; 3) the decision rule; 4) the calculation of the test statistic; and 5) your conclusion including a comparison to alpha or the critical value.arrow_forwardAmerican Theatre owners knew that a certain hit movie ran an average of 84 days or more in each city, and the corresponding deviation is 10 days. The manager of the south-eastern district is interested in comparing the movies popularity in his region with that in all of American’s other theatres. He randomly chose 25 theatres in his region and found that they ran the movie on an average of 81.5 days. Test this claim at α = 0.05 level of significance. Population mean μ = 84 days Sample mean x̅ = 81.5 days Population standard deviation σ = 10 days Sample size n = 75 1. State the null and alternative hypothesis. Ho: = 84 Ha: ≠ 84 2. At 95% confidence level, what is the level of significance? 3. Determine what type of test to use and determine the critical value. 4. Calculate the test statistic using the appropriate formula. 5 .Compare the calculated test statistics with that of the critical value. 6. Make a decision. 7. Interpret the result.arrow_forwardA random sample of 81 eighth grade students' scores on a national mathematics assessment test has a mean score of 274. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 270. Assume that the population standard deviation is 35. At α=0.02, is there enough evidence to support the administrator's claim.arrow_forward
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