# Sample size, Significance level, Hypothesis, Mean, P-Value

1. Assume that you plan to use a significance level of ? = .05 to test the claim that p1 =p2. Use the given sample sizes and numbers of successes to find the pooled estimate p. Round to the nearest thousandth

n1 = 34 n2 = 414

x1 = 15 x2 =105

2. Assume that you plan to use a significance level of ? = .05 to test the claim that p1 =p2. Use the given sample sizes and numbers of successes to find the z test statistic for the hypothesis test.

3. In a vote on the Clean Water bill, 44% of the 205 Democrats voted for the bill while 46% of the 230 Republicans voted for it. Use the traditional method to test the given hypothesis. Assume that the samples are independent and that they have been randomly selected

4. In a random sample of 500 people aged 20-24 22% were smokers. In a random sample of 450 people aged 25-29, 14% were smokers. Test the claim that the proportion of smokers in the two age group is the same. Use a significance level of .01

5. Test the indicated claim about the means of two populations. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Use the traditional method or P â?"value method as indicated.

A researcher was interested in comparing the response times of two different cab companies. Companies A and B were each called 50 randomly selected times. The calls to company A were made independently of the calls to company B. The response time for each call was recorded. The summary statistics were as follows:

Company A Company B

Mean response time

7.6 6.9

Standard deviation

1.4 1.7

Use a .02 significance level to test the claim that the mean response time for the company A is the same as the mean response time for company B. Use the P-value method of hypothesis testing

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#### Solution Summary

Complete, Neat and Step-by-step Solutions are provided in the attached Excel file.

Test and analyze US family size, victims of burglary, hours of TV watching per week

1. The average U.S. family includes 3.13 persons. To determine whether families in her city tend to be smaller in size compared to those across the United States, a city council member selects a simple random sample of 25 families. She finds the average number of persons in a family to be 2.78, with a standard deviation of 0.89.

a) What is the appropriate null and alternate hypothesis to determine if families in the city council member's city tend to be smaller in size compared to those across the United States?

b) What is the p-value for the hypothesis test?

c) Using ± = 0.01, draw a conclusion for the hypothesis test.

d) Using ± = 0.05, draw a conclusion for the hypothesis test.

2. Each year 3.0% of all U.S. households are victims of burglary. A random sample of 300 households in one particular city shows that 18 were burglarized.

a) What is the appropriate null and alternate hypothesis if this cities burglary rate

exceeds the national average?

b) What is the p-value for the hypothesis test?

c) Using ± = 0.01, draw a conclusion for the hypothesis test.

d) Using ± = 0.05, draw a conclusion for the hypothesis test.

3. A researcher is comparing the number of hours of television viewed per week for high school seniors versus sophomores. The researcher collects data on 32 seniors and finds an average of 3.9 hours and a standard deviation of 1.2 hours. The researcher collects data on 30 sophomores and finds an average of 3.5 hours and a standard deviation of 1.4 hours.

a) What are the null and alternative hypotheses to test if seniors and sophomores watch a different amount of television.

b) Using ± = 0.05, what is the critical value for the hypothesis test?

c) What is the test statistic for the hypothesis test?

d) Draw a conclusion for the hypothesis test.

e) What is the p-value for the hypothesis test?