Stat 145 Worksheet Ch 13B Name _____________________________
Some “informal” hypothesis testing
You read that the average weight (X) of Airedales is 90 lbs, with a standard deviation of 8. That is
X ~N(90,8). From an SRS of 16 Airedales in Albuquerque, you calculate x =85.
1a) What is: P( x 85) ?
1b). From the above answer, do you consider it unusual to get an x =85?
1c) Do you think Albuquerque Airedales are representative of Airedales in general? Yes/No, explain.
2. You assume the heights of females at UNM is approximately normal, and H~N(65, 2.7) You take an
SRS of 9. Your sample average is, h 66 .
2a)What is: P( h 66) ?
2b). From the above answer, (n=9), do you consider a sample average of 66(or larger) “unusual”.
MORE “FORMAL” HYPOTHESIS TESTING:
An SRS of twenty-five seniors from a large metropolitan area school district had a mean Math SAT score
of x = 450. (Note: previous years’ averages were always at 490) Suppose we know that Math SAT
scores for seniors in the district is approximately Normally, with a standard deviation of 100. The local
newspaper’s headline is: Local SAT Scores DROP
Perform all 4 steps for a test of significance of the above.
3a. The hypotheses of interest are H 0 : =
Ha : <
3b. The z test statistic is:
3c. Therefore the pvalue, the probability that P( x 450) under the null hypothesis, is:
3d. Your conclusion is:
4. The amount of time customers at a “Quick-Change” motor oil store spend waiting for their cars to be
serviced has a Normal distribution with mean and standard deviation = 4 minutes. It is company
policy that the customer wait time should be 20 minutes (or less). The manager of a particular store
selects a random sample of 50 customer wait times and observes a mean wait time of 21 minutes. Is there
evidenced that the average wait time has increased??? Perform the appropriate test of significance.
4a. The hypotheses of interest are: H0 : =
4b. The sample z test statistic is:
4c. The pvalue, the probability that P( x 21) under the null hypothesis is:
4d. Your conclusion is:
5. A snack food producer produces bags of peanuts labeled as containing 3 ounces. The actual weight of
peanuts packaged in individual bags is Normally distributed with mean and standard deviation = 0.2
ounces. As part of quality control, n bags are selected randomly and their contents are weighed.
The inspector believes the machines are “out of calibration”, he samples 20 bags and calculates a the
sample mean weight, x = 2.9 ounces
5a. The hypotheses of interest are H 0 : =
5b. He calculates that the sample z test statistic, to be:
5c. The pvalue, the probability that the sample average would take a value as extreme or more extreme (in
either direction) under null hypothesis is:
5d. His conclusion is :