For a randomly selected sample of 20 new mothers in the year 2000, the mean age was 24.6 years. For a randomly selected sample of 10 new mothers in 1970, the mean age was 21.4 years. The difference between the mean ages is 3.2 years, and the standard error of the difference is 1.366 . Assume that the ages of new mothers are normally distributed, do not assume the population variances are equal, and use the conservative by hand estimate for the degrees of freedom. Calculate a 99 confidence interval for the difference in population mean ages of new mothers in the two years (year 2000 year 1970).
a. (1.24, 7.64)
b. (1.13, 7.53)
c. (0.47, 5.93)
d. None of the above
Question 2
Which one of the following statements is false?
a. A sampling distribution is the probability distribution of a sample statistic. It describes how values of a sample statistic vary across all possible random samples of a specific size that can be taken from a population.
b. For all five scenarios considered, the sampling distribution is approximately normal as long as the sample size(s) are large enough.
c. The mean value of a sampling distribution is the mean value of a sample statistic over all possible random samples. For the five scenarios, this mean equals the value of the statistic.
d. The standard deviation of a sampling distribution measures the variation between all possible values of the sample statistic and their mean over all possible random samples. For the five scenarios, this mean equals the value of the parameter.
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