Overview
For this HW, all calculations are to be done by hand unless otherwise specified.
Use software to generate plots if needed.
Include software outputs/plots in your submission
Question 1
Consider the computer output shown below:
a) Fill in the missing values in the output. Can the null hypothesis be rejected at the 0.05 level?
Why?
b) Is this a one-sided or a two-sided test?
c) If the hypotheses had been H0: µ=90 vs H1: µ¹90 would you reject the null hypothesis at
0.05 level?
d) Use the output in the table to find a 99%two-sided confidence interval on the mean.
e) Find a range for the p-value if the alternative hypothesis is H1: µ>90 (to find p-value, we find
the alpha on Z tables or T tables that corresponds the test statistic we calculated. Usually we
cannot find the exact p-value by looking at the tables, we find the closest two values (range),
or we interpolate.)
Question 2
The breaking strength of a fiber is required to be at least 150 psi. Past experience has indicated that
the standard deviation of breaking strength is σ _= 3 psi. A random sample of four specimens is tested.
The results are y1=145, y2=153, y3=150 and y4=147.
a) State the hypotheses that you think should be tested in this experiment.
b) First, calculate sample mean. Then test the hypothesis you set up in part a using α _= 0.05.
What are your conclusions?
c) Find the P-value for the test in part (b). What would be your conclusion if you used p-value
approach in testing the hypothesis?
d) Construct a 95 percent confidence interval on the mean breaking strength. What would be
your conclusion if you used Confidence interval approach in testing the hypothesis?
Question 3)
Suppose that we are testing H0
: μ1 = μ2 versus H1
: μ1 > μ2 with a sample size of n1 = n2 = 10. Both sample
variances are unknown but assumed equal. Find bounds on the P-value for the following observed
values of the test statistic:
a) t0 =2.31
b) t0=3.6
c) t0=1.95
d) t0=2.19
Question 4
Front housings for cell phones are manufactured in an injection molding process. The time the part is
allowed to cool in the mold before removal is thought to influence the occurrence of a particularly
troublesome cosmetic defect, flow lines, in the finished housing. After manufacturing, the housings
are inspected visually and assigned a score between 1 and 10 based on their appearance, with 10
corresponding to a perfect part and 1 corresponding to a completely defective part. An experiment
was conducted using two cool-down times, 10 seconds and 20 seconds, and 20 housings were evaluated at
each level of cool-down time. All 40 observations in this experiment were run in random order. The data
are shown below. (Assume equal variance)
) Is there evidence to support the claim that the longer cool-down time results in fewer
appearance defects? Use α _= 0.05. (Use Minitab to perform this analysis.)
b) Find a 95% confidence interval on the difference in means. Provide a practical interpretation
of this interval.
Question 5
An investigator is interested to measure the intelligence score of 10 set of identical twins. The data
are obtained as follows:
a) What kind of test would you choose to test whether there is a difference in intelligence of the
twins?
b) Is there any evidence that the mean score depends on the birth order? Test appropriate
hypotheses indicating that the mean score does not depend on birth order.