It is believed that the lower than normal level of human calcitonin (HCT) in men with rheumatoid arthritis is a risk factor in developing osteoporosis. In 64 men with rheumatoid arthritis, the observed HCT mean was 32.5pg/mL with a standard deviation of 23.6. In normal healthy men, the mean was 47.9pg/mL. From the sample information, can we conclude that the HCT mean in men with rheumatoid arthritis is less than that in normal men? Assume a significance level of 0.05.

A sample of 36 observations is selected from a normal population. The sample mean is 12, and the population standard deviation is 3. Conduct the following test of hypothesis using the 0.01 significance level: H0: μ ≤ 10 H1: μ > 10

a. Is this a one- or two-tailed test?

b. What is the decision rule, Reject H0 when Z > 2.33 or when Z <= 2.33 ?

c. What is the value of the test statistic? (Round the final answer to 1 decimal place.)

d. What is your decision regarding H0? (Reject or Accept) ?

e. What is the p-value, one, zero, or close to zero ? 

A random sample of size 25 is taken from a normal population having a mean of 80 and a standard deviation of 5. A second random sample of size 36 is taken from a different normal population having a mean of 75 and a standard deviation of 3. Find the probability that the sample mean computed from the 25 measurements will exceed the sample mean computed from the 36 measurements by at least 3.4 but less than 5.9. Assume the difference of the means to be measured to the nearest tenth.