Problem 1 (2 Point):

If a sample Mean = 22, and SD = 2.3, a) find the 95% Confidence Interval, b) find the 99% Confidence Interval

Problem 2 (2 Point):

If a sample Mean = 4.5, and SD = 1.09, a) find the 95% Confidence Interval, b) find the 99% Confidence Interval

Problem 3 (4 Points):

One hundred individuals in a sample were given a new medication for treatment of depression. Following the treatment all the individuals in the sample were given a test of depression. The sample mean on the test was 82.The general population mean for the test of depression is 81, and standard deviation is 8, and follows a normal distribution (bell shaped curve). You want to find out if the mean score of your sample is different from the general population. Answer the following:

a) is this a one-tailed test, or a two-tailed test? Why? b) carry out a Z test at the 0.05 significance level (show your work), c) state if the difference between the sample mean and the population mean is significant or not, and explain why?; d) If the result is significant, find the effect size; e) is the effect size small, medium, or large? Why?

Problem 4 (4 Points):

A completely different sample of ten individuals were given the same medication as stated in Problem 3. Following the treatment, all ten individuals in the sample were given the same test of depression. The sample mean on the test was 84.You also want to find out if the mean score of this sample is different from the general population. Answer the following:

a) is this a one-tailed test, or a two-tailed test? Why? b) carry out a Z test at the 0.05 significance level (show your work), c) state if the difference between the sample mean and the population mean is significant or not, and explain why?; d) If the result is significant, find the effect size; e) is the effect size small, medium, or large? Why?

Problem 5 (4 Points)

Please refer to Slide 13 of Chapter 10 Slide and Notes in the module. Read the stated problem:

a) is this a one-tailed test, or a two-tailed test? Why? b) carry out a Z test at the 0.05 significance level (show your work), c) state if the difference between the sample mean and the population mean is significant or not, and explain why?; d) If the result is significant, find the effect size; e) is the effect size small, medium, or large? Why?

For problem 6, please state the null and alternate hypothesis in words, and not just symbols

Problem 6 (4 Points)

A researcher hypothesizes that people who have experienced trauma result in an increase in the number of dreams they can recall per month. The researcher knows that the population mean for the number of dreams that people are able to recall per month is 5, with a standard deviation of 4. The researcher randomly selects 36 individuals who have recently experienced a traumatic event, and record the number of dreams they can recall. The mean number of dreams recalled by the sample is 8.

a) state the null hypothesis; b) stated the alternate hypothesis; c) carry out a Z test at the 0.01 significance level (show your work), d) state if the difference between the sample mean and the population mean is significant or not, and explain why?; e) If the result is significant, find the effect size; f) is the effect size small, medium, or large? Why?