# Statistical Hypothesis Testing

1. State the null and alternative hypothesis for the following situations.

a) A federal auditor believes that a health care company has overcharged its patients.

b) The editor of a magazine believes that the mean income of subscribers to its magazine is $75,000.

c) An operations manager must maintain machines that produce 50 pound bags of fertilizer.

d) A manufacturer believes that the average life of its competitor's battery is less than 10 hours.

2. A crime reporter was told that, on the average, 3,000 burglaries per month occurred in his city. The reporter examined past data, which were used to compute a 95% confidence interval for the number of burglaries per month. The confidence interval was from 2,176 to 2,784. At a 5% level of significance, do these data tend to support the alternative hypothesis, Ha: μ ≠3,000?

3. A movie theater complex will raise its ticket price if the average ticket price of theaters in southern California exceeds $7.50. A random sample of 36 theaters resulted in a mean of $7.80. The population standard deviation is $1.00. What conclusion can be made at the 10% significance level? How about at the 5% significance level?

4. The producer of Take-a-Bite, a snack food, claims that each package weighs 175 grams. A representative of a consumer advocate group selected a random sample of 70 packages. From this sample, the mean is 172 grams. The population standard deviation is known to be 8 grams. Find and interpret the p-value for testing that the mean weight of Take-a-Bite is less than 175grams.

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#### Solution Preview

1. State the null and alternative hypothesis for the following situations.

a) A federal auditor believes that a health care company has overcharged its patients.

Null hypothesis: a health care company has not overcharged its patients;

Alternative hypothesis: a health care company has overcharged its patients.

b) The editor of a magazine believes that the mean income of subscribers to its magazine is $75,000.

Null hypothesis: the mean income of subscribers to its magazine is $75,000;

Alternative hypothesis: the mean income of subscribers to its magazine is not equal to $75,000.

c) An operations manager must maintain machines that produce 50 pound bags of fertilizer.

Null hypothesis: the mean production number of fertilizer bags is equal to ...

#### Solution Summary

The solution states statistical hypothesis testing. Why an operations manager must maintain machines that produce 50 pound bags of fertilizers is determined.