Twenty-two women between the ages of 70 and 80 were randomly selected from the general population of women in this age group to take part in a special program to decrease reaction time (speed). After the course, the women had an average reaction time of 2.0 seconds. Assume that the mean reaction time for the general population of women in this age group is 2.1, with a standard deviation of 0.4 seconds. (Assume that the population is approximately normal).

a.) Carry out a Z test using the five steps of hypothesis testing (use the 0.01 level). Choose a research hypothesis and a null hypothesis.

O A. The research hypothesis is the mean of the sample population is less than the mean of the general population. The null hypothesis is the mean of the sample population is greater than or equal to the mean of the general population. O B. The research hypothesis is the mean of the populations are the same. The null hypothesis is the mean of the populations are not the same. O C. The research hypothesis is the mean of the populations are not the same. The null hypothesis is the mean of the populations are the same. O D. The research hypothesis is the mean of the sample population is greater than or equal to the mean of the general population. The null hypothesis is the mean of the sample population is less than or equal to the mean of the general population.Assume that the distribution of means is approximately normal. What is/are the cutoff sample score(s) on the comparison distribution at which the null hypothesis should be rejected? (Use a comma to separate answers as needed. Type an integer or decimal rounded to two decimal places as needed.)O A. O B. O C. O D. X X X X(c) Explain your answer to someone who is familiar with the general logic of hypothesis testing. the normal curve, 2 scores. and probability, but not with the idea of a distribution of means. The distribution of means uses many samples of 1" with each sample randomly taken from the population of individuals. Since the sample score could occur by chance E the resultsl: the hypothesis that the women who take part in the program have lower reaction times. (d) Figure the 99% condence interval. Explain your answer to someone who is familiar with the general logic of hypothesis testing, the normal curve, Z scores, probability, and the idea of a distribution of means, but has not heard of confidence intervals. A 99% confidence interval is the range of values that one can be confident contains the population mean. The lower limit and upper limit of this interval are the respectively, which have a chance of claiming that the sample value is that value for the distribution of means