# Statistics Practice Problems

1) The health of employees is monitored by periodically weighing them in. A sample of 54 employees has a mean weight of 183.9 lb. Assuming that σ is known to be 121.2 lb, use a 0.10 significance level to test the claim that the population mean of all such employees weights is less than 200 lb. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim.

2) A researcher wants to check the claim that convicted burglars spend an average of 18.7 months in jail. She takes a random sample of 11 such cases from court files and finds that the sample mean = 20.5 months and s = 7.9 months. Test the null hypothesis that μ = 18.7 at the 0.05 significance level. Test the given claim using the traditional method of hypothesis testing. Assume that the sample has been randomly selected from a population with a normal distribution. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim.

3) A researcher wishes to determine whether people with high blood pressure can reduce their blood pressure by following a particular diet. Use the sample data below to test the claim that the treatment population's mean μ1 is smaller than the control population's mean μ2. Test the claim using a significance level of 0.01. Test the indicated claim about the means of two populations. Assume that the two samples are independent and that they have been randomly selected. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim.

(see attached file for data)

4) Use the sample data above to construct a 99% confidence interval for u1 - u2 where u1 and u2 represent the mean for the treatment group and the control group respectively. Interpret the confidence interval in the context of the study described in problem 3 above.

5) Five students took a math test before and after tutoring. Their scores were as follows.

Using a 0.01 level of significance, test the claim that the tutoring improves the math scores. Use the traditional method of hypothesis testing to test the given claim about the means of two populations. Assume that two dependent samples have been randomly selected from normally distributed populations. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim.

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#### Solution Summary

This solution is comprised of a detailed explanation on appropriate statistic method used for the objectives defined in the problem. Full description is given for the method along with the null and alternative hypotheses is provided in the solution.