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# Hypothesis Testing of Mean & Proportion: P-value Method

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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?