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# Testing of Hypothesis

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1. A machine produces 5-inch nails. A sample of 12 nails was selected and their lengths determined. The results are as follows:
4.96 4.97 4.87 4.81 4.84 4.89 4.96 4.84 4.86 4.83 4.83 4.91
Assuming that = 0.01, test the hypothesis that the population mean is equal to 5.
?&#61472;State the null and alternate hypotheses
?&#61472;Calculate the mean and standard deviation
?&#61472;Determine which test statistic applies, and calculate it
?&#61472;Determine the critical value(s).
?&#61472;State your decision: Should the null hypothesis be rejected?

2. A sample of size n = 20 is selected from a normal population to construct a 95% confidence interval estimate for a population mean. The interval was computed to be (4.30 to 5.20). Determine the sample standard deviation.

3. A random sample of 51 observations was selected from a normally distributed population. The sample mean was = 6, and the sample variance was s2 = 30.0. Does the sample show sufficient reason to conclude that the population standard deviation is not equal to 7 at the 0.05 level of significance? Use the p-value method.
?&#61472;State the null and alternate hypotheses
?&#61472;Determine which test statistic applies, and calculate it
?&#61472;Determine the corresponding probability, and compare to
?&#61472;State your decision: Should the null hypothesis be rejected?

4. An insurance company states that 85% of its claims are settled within 5 weeks. A consumer group selected a random sample of 50 of the company's claims and found 37 of the claims were settled within 5 weeks. Is there enough evidence to support the consumer group's claim that fewer than 85% of the claims were settled within 5 weeks? Test using the traditional approach with &#945; = 0.02.
?&#61472;State the null and alternate hypotheses
?&#61472;Calculate the sample proportion
?&#61472;Determine which test statistic applies, and calculate it
?&#61472;Determine the critical value(s).
?&#61472;State your decision: Should the null hypothesis be rejected?

5. A teacher wishes to compare two different groups of students with respect to their mean time to complete a standardized test. The time required is determined for each group. The data summary is given below. Test the claim at = 0.10, that there is no difference in variance. Give the critical region, test statistic value, and conclusion for the F test.
n1 = 120 s1 = 42
n2 = 120 s2 = 48
= 0.10
?&#61472;State the null and alternate hypotheses
?&#61472;Determine which test statistic applies, and calculate it
?&#61472;Determine the critical region
?&#61472;State your decision: Should the null hypothesis be rejected?

6. A machine produces 9 inch latex gloves. A sample of 85 gloves is selected, and it is found that 36 are shorter than they should be. Find the 98% confidence interval on the proportion of all such gloves that are shorter than 9 inches.

7. The pulse rates below were recorded over a 30-second time period, both before and after a physical fitness regimen. The data is shown below for 8 randomly selected participants. Is there sufficient evidence to conclude that a significant amount of improvement took place? Assume pulse rates are normally distributed. Test using = 0.05.
?&#61472;State the null and alternate hypotheses
?&#61472;Calculate the mean and standard deviation
?&#61472;Determine which test statistic applies, and calculate it
?&#61472;Determine the critical value(s).
?&#61472;State your decision: Should the null hypothesis be rejected?
Before 51 31 33 44 39 48 40 54
After 46 35 48 50 32 52 59 48

8. You are given the following data. Test the claim that there is a difference in the means of the two groups. Use = 0.05.
Group A Group B
= 7 = 1
= 0.1 = 0.4
= 48 = 39
?&#61472;State the null and alternate hypotheses
?&#61472;Determine which test statistic applies, and calculate it
?&#61472;Determine the critical value(s).
?&#61472;State your decision: Should the null hypothesis be rejected?