1. Ginger root is used by many as a dietary supplement. A manufacturer of supplements produces capsules that are advertised to contain at least 500 mg. of ground ginger root. A consumer advocacy group doubts this claim and tests the hypotheses

H0:α = 500 Ha:α < 500

based on measuring the amount of ginger root in a SRS of 100 capsules. Suppose the results of the test fail to reject H0 when, in fact, the alternative hypothesis is true. In this case the consumer advocacy group will have

A. committed a Type I error.
B. committed a Type II error.
C. no power to detect a mean of 500.

2. Suppose that in the population of adult males, weights are normally distributed with standard deviation=24 pounds. A doctor records the weight of four adult male patients who come to his office one day and finds their mean weight to be 192.1 pounds. He computes a 90% confidence interval for the mean weight of all adult males based on his sample, and finds that it is 192.1 19.7 pounds. We may correctly conclude that

A. he has made an error. The correct value is 192.1 23.5 pounds.
B. if he continues to weigh groups of four of his male patients and compute a 90% confidence interval for each group, approximately 90% of these intervals will contain the true mean weight for the population of all adults males.
C. Neither choice is correct.

3. The diameter of a spindle in a small motor is supposed to be 5 mm. If the spindle is either too small or too large, the motor will not perform properly. Assume the population of spindles produced by a manufacturer is normally distributed with unknown mean m and standard deviation = 0.02 mm. The manufacturer measures a SRS of 16 spindles produced by his company and finds their mean diameter to be = 5.01 mm. The P-value of a test of the hypotheses

A. 0.0228.
B. 0.0456.
C. less than 0.0005.