1. Construct the specified confidence interval. (6 points each)
(a) A 90% confidence interval for the difference in the proportion of blue candies and
the proportion of red candies used in all bags of peanut M & M’s if in two
independent samples each of size 600 we find 123 blue candies and 99 red
candies respectively
(b) A 95% confidence interval for the difference in the mean score for all male high
school students and the mean score for all female high school students on the
ACT exam if in a random sample of 12 male students the mean score was 28.2
with a standard deviation of 3.45 and in a random sample of 15 female students
the mean score was 25.3 with a standard deviation of 2.89 (Assume the scores on
the ACT exam for male and female students are normally distributed.)
2. The following table gives the cholesterol levels for six adults before and then after
they completed a study with a new experimental cholesterol drug.
BEFORE
147
159
122
98
101
145
AFTER
132
142
102
88
94
127
(a) Determine the line of best fit (regression line) for these data points using
BEFORE as the x variable. (5 points)
(b) Use the equation in part (a) to predict a person’s cholesterol level after taking the
drug if their level BEFORE is 130. (5 points)
(c) What is value of the correlation coefficient? (3 points)
(d) Does Table A-6 indicate that there is significant linear correlation between the
BEFORE and AFTER data? Explain how you determined your answer. (5 pts)
(e) On your calculator draw the scatterplot of this data together with the graph of the
line of best fit. Show me these graphs in an appropriate calculator window. (5 pts)
3. Use the data in problem 2 to set up and conduct a hypothesis test at 5% level of
significance to determine if the manufacturer of this new drug can claim that its use will
lower a person’s cholesterol on average by more than 10 points. Assume all necessary
conditions are satisfied in order to be able to conduct this test. (15 points)
4. (a) For the test conducted in problem 3, what is the probability that a Type I error will
occur? (3 points)
(b) Is the p-value (observed level of significance) for the test conducted in problem 3
more or less than 5%? (3 points)
5. The standard deviation in the weight of all widgets is 1.35 ounces. A random sample
of 60 widgets found a mean weight of 14.25 ounces with a standard deviation of 1.54
ounces. Set up and conduct a hypothesis test at a 5% level of significance to
determine if the mean weight of all widgets is different from 14 ounces. (15 points)
6. Determine the p-value (observed level of significance) for the test conducted in
problem 5. (5 points)
7. For which of the following values of  would we fail to reject the null hypothesis in
problem 5. Circle all that apply. (6 points)
  0.20
  0.16
  0.12
  0.08
  0.04
  0.01