Hypothesis Testing.

For each problems, perform each of the following steps.

1. Determine the null hypothesis 0 and alternative hypothesis

2. Identify the statistical test to be used, the value of , and the critical value of the test statistic.

3. Computation

4. Decision (reject or not to reject 0)

5. Conclusion (in non-technical terms)

1.A researcher claims that the yearly consumption of soft drinks per person is 52 gallons. In a sample of 50 randomly selected people, the mean of the yearly consumption was 56.3 gallons. The standard deviation of the population is 3.5 gallons. Is researcher's claim correct? Set = 0.05.

2.A store manager hypothesizes that the average number of pages a person copies on the store's copy machine is less than 40. A sample of 50 customers' orders is selected. At = 0.05, is there enough evidence to support the claim?

3.The U.S. average for state and local taxes for a family of four is $4172. A random sample of 20 families in a northeastern state indicates that they paid an annual amount of $4560 with a standard deviation of $1590. At = 0.05, is there sufficient evidence to conclude that they pay more than the national average of $4172?

4.A survey of 15 large U.S. cities finds that the average commute time one way is 25.4 minutes. A chamber of commerce executive feels that the commute in his city is less and wants to publicize this. He randomly selects 25 commuters and finds the average is 22.1 minutes with a standard deviation of 5.3 minutes. At = 0.10, is he correct?

5.The Old Farmer's Almanac stated that the average consumption of water per person per day was 123 gallons. To test the hypothesis that this figure may no longer be true, a researcher randomly selected 16 people and found that they used on average 119 gallons per day and = 5.3. At = 0.05, is there enough evidence to say that the Old Farmer's Almanac figure might no longer be correct?

6.A large university reports that the mean salary of parents of an entering class is $91,600. To see how this compares to his university, a president surveys 28 randomly selected families and finds that their average income is $88,500. If the standard deviation is $10,000, can the president conclude that there is a difference? At = 0.10, is he correct?

7. The average 1-ounce chocolate chip cookie contains 110 calories. A random sample of 15 different brands of 1-ounce chocolate chip cookies resulted in the following calorie amounts. At the = 0.01 level, is there sufficient evidence that the average calorie content is greater than 110 calories.

100 160 155 100 135 125 185 145 150 120 150 125 160 140 110