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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.

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.

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