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Statistics - Null and Alternative Hypotheses

1. The National Safety Council reported that 52% of American turnpike drivers are men. A sample of 300 cars traveling southbound on the New Jersey Turnpike yesterday revealed that 170 were driven by men. With an α = 0.01 can it be concluded that a larger proportion of men were driving on the New Jersey Turnpike than the national statistics indicate?

a. State the Null and Alternative Hypotheses.
b. Determine the test statistic.
c. Determine and interpret the p-value
d. State your decision and interpret the results

2. A national TV News program reported that the mean price nationwide was $2.10 per gallon for self-serve regular unleaded gasoline. A random sample of 35 stations in the Milwaukee, Wisconsin, area revealed that the mean price was $2.12 per gallon and that the sample standard deviation was $0.05 per gallon. At the 0.05 significance level, can we conclude that the price of gasoline is significantly different in the Milwaukee area? Use the p-value method.

a. State the null and alternative hypotheses:
b. Compute the test-statistic.
c. Determine the p-value.
d. State your decision and interpret the results

3. Typically during any year, the mean amount of acid rain being deposited on New York city when measured by an electronic device is computed to be 0.75 parts per million (ppm) with a standard deviation of 0.01 ppm. Some critics believe that there has been a change in acid rain. Test this claim using the 0.05 level of significance, when a recent sample of 100 acid rain readings had a sample mean of 0.7522 ppm.

a. State the null and alternative hypotheses:
b. What is the critical value?
c. Compute the test-statistic.
d. State your decision and interpret the results
e. Determine and interpret the p-value

4. A researcher wishes to be 95% confident that her estimate of the true proportion of individuals who travel overseas is within 0.04 of the true proportion. Find the sample size necessary. In a prior study, a sample of 200 people showed that 80 traveled overseas last year.

5. A washing machine manufacturer reported that an American family of 4 washes an average of one ton (2000 pounds) of clothes each year. If the standard deviation is known to be 187.5 pounds, find the probability that the mean of a randomly selected sample of 50 families of four will be between 1980 and 1990 pounds.

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