Given the following sets of null and alternative hypotheses, determine the location of the critical region, that is, is the test left-tailed, right-tailed, or two-tailed? [Caution: Look before you leap.]
For each of the following sets of circumstances, state the null and alternative hypotheses; and state what it would mean to commit a Type I Error (respectively, a Type II Error).
a. In 2005, about 15% of all registered voters were of Hispanic origin. A sociologist believes that this percentage has increased since then. What would it mean if the null hypothesis were rejected?
b. Last year, the mean contribution to the United Way charities in a certain city was $200. A reporter for Philanthropy Today magazine feels that it has changed since then. What does it mean if the null hypothesis is not rejected?
c. According to the Department of Transportation, last year the mean price of a gallon of regular gasoline was $2.50. Because of increased demand, the department feels that the mean price has increased since then. What does it mean if the null hypothesis is not rejected?
d. Last year, reading comprehension scores in Mr. Smith's fourth grade class averaged 85 points. Due to lack of reading practice, video games, TV, and so on, Mr. Smith feels that this year's scores might have decreased a bit. What does it mean if the null hypothesis is rejected?
e. According ...