Find a 95% confidence interval estimate for the mean head circumference of all two-month old babies. What aspect of this problem is not realistic?

In order to identify baby growth patterns that are unusual, we need to construct a confidence interval estimate of the mean head circumference of all babies that are 2 months old. A random sample of 100 babies is obtained and the mean head circumference is found to 40.6cm. Assuming that the population standard deviation is known to be 1.6 cm., Find a 95% confidence interval estimate for the mean head circumference of all two-month old babies. What aspect of this problem is not realistic?

A study was conducted to estimate hospital costs for accident victims who wore seat belts. Twenty randomly selected cases have a distribution which appears to be symmetric and bell-shaped with a mean of \$9004 and a standard deviation of \$5629. based on data from the U. S. Department of Transportation. Construct a 99% confidence interval for the mean of all such costs.
N= 20, mean= 9004, std. deviation= 5629
99% CI, DF= 19, T=2.861
99% CI= 9004 +/- (2.861*5629/v20)
9004 +/- (364.01)
= (9368.01, 8639.99)

For the following problems:
1. State the Null Hypothesis and the Alternative Hypothesis
2. Determine the test statistic.
3. Determine the P-value
4. Make a decision regarding the hypotheses based on the P-value and the Level of
Significance.

In a recent year, some professional baseball players complained that umpires were calling more strikes than the average rate of 61% called the previous year. At one point in the season, umpire Dan Morrison called strikes in 2231 of 3581 pitches (based on data from USA Today). Use a 0.05 significance level to test the claim that his strike rate is greater than 61%.

The health of the bear population in Yellowstone National Park is monitored by periodic measurements taken from anesthetized bears. A sample of 54 bears has a mean weight of 182.9lbs. Assuming that the population standard deviation is known to be 121.8lbs, use a 0.05 level of significance to test the claim the population mean of all such bear weights is less than 200lbs.
N= 54, Std. Dev.= 121.8, DF= 54-1= 53, T= .05
H0: µ= 182.9 , HA: µ not= 182.9
182.9 +/- .05*121.8
182.9 +/- 6.09
St. Error (188.99-176.81)/ .05
St. Error= 243.6

The birth weights (in kilograms) are recorded for a sample of male babies born to mothers taking a special vitamin supplement (based on data from the New York Department of Health). When testing the claim that the mean birth weight for all male babies of mothers given vitamins is equal to 3.39kg, which is the mean weight of the population of all male babies, a sample of 16 babies had a mean of 3.675kg and a standard deviation of 0.657. Based on these results, does the vitamin supplement appear to have any effect on the mean birth weight? Use the 0.01 level of significance.

Patients with Chronic Fatigue Syndrome were tested, and then retested after being
treated with fludrocortisone. The changes in fatigue after treatment were measured
(based on data from “The Relationship between Neurally Mediated Hypotension and
the Chronic Fatigue Syndrome” by Bou-Holaigah, Rowe, Kan, and Calkins, Journal
of the American Medical Association, Vol.274, No. 12). A standard scale from -7 to
+7 was used with positive values representing improvements. The sample of 21
patients had a mean score of 4 on the scale with a sample standard deviation, s = 2.17
Use a 1% level of significance level to test the hypothesis that the mean change is
positive(i.e. there is improvement.). Does the treatment appear to be effective?