1. I use computer software to do the following. I generate ten random numbers from a N(500, 100) distribution. From these ten numbers I compute a 95% confidence interval for the mean using the formula

where x' is the mean of the ten random numbers. I then repeat this process (generating a new set of 10 random numbers from a N(500, 100) distribution each time) until I have produced 1000 such intervals. Which of the following will be true?
A. Approximately 95% of the intervals will contain the value 500.
B. Approximately 95% of the intervals will contain the value 100.
C. Approximately 97.5% of the intervals will contain the true mean because the probability that a standard Normal random variable is less than 1.96 is 0.975. I have incorrectly used the formula for a 97.5% confidence interval.

2. 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 μ: = 500 H_a: μ < 500

They take a random sample of 100 ginger root capsules produced by the manufacturer and compute the test statistic

where x' is the mean amount of ginger root in the 100 capsules sampled. Based on other information, the advocacy group knows the value of . If the test statistic z has value 2.39, we may conclude that
A. we reject H0 at level α = 0.05 but not at level = 0.01.
B. we reject H0 at level α = 0.01.
C. we do not reject H₀ at level = 0.05.