Does Vitamin Supplement Impact Birth Weight?

[ghost305]

10. 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.
Null Hypothesis: H0: µ = 3.39kg
Alternate Hypothesis: HA µ ≠ 3.39 kg
Two sided test: 99% C.I
Z = 3.675± 2.575 * 0.657
Z (1.983, 5.366)
Since M0 falls inside this confidence interval, we cannot reject the Null Hypothesis. at 1% level of significance we can reject Ha.Did i get it right?

 

[statdad]

Some comments

1) You shouldn't write "Z = " and then give a confidence interval; the appropriate test statistic should be calculated

2) For a sample of $$n = 16$$ observations, and with only the sample standard deviation given ("a sample of ... a standard deviation of 0.657") you should use the 1-sample t rather than the 1-sample Z. the test statistic is

$$t = \frac{\bar X - \mu_0}{\dfrac s {\sqrt n}}$$

3) Since the question is "does the vitamin supplement have any effect ...", the appropriate
hypothesis is indeed two-sided, and you have it correct. Many people would
automatically use ">"