QUIZ
Hypothesis Tests for a Population Mean, (, (( unknown)
If a SRS is drawn from a normally distributed population, the test statistic for a significance test about (, (H0: ( = (0) is:
[pic], and df = n – 1.
Note that in the rare situations where the population standard deviation, (, is known, s can be replaced with ( and then z, standard normal, is used instead of the Student’s t.
I. An auto maker claims that the new high efficiency passenger car they make gets, on the average, at least 40 mpg. A consumer group doubts this claim and tests a sample of 9 of these cars. Driving the cars under varying driving conditions they obtain a sample mean of 37.5 mpg with a standard deviation of 4.5 mpg. Complete the following hypothesis test to answer the question: Do the data provide statistically significant evidence that the manufacturer’s claim is false?
1. State the assumptions.
2. State appropriate null and alternative hypotheses. (Be careful, we are trying to show that the manufacturer’s claim is false.)
H0: ___________________ HA: ___________________
3. Compute the value of the appropriate test statistic. (t in this case). (Do it by hand and verify with your calculator’s T-Test command.)
4. Give the P-value __________
5. What conclusion would you draw?
REPEAT steps 3 – 5 for n = 16.
3. Compute the value of the appropriate test statistic. (t in this case). (Do it by hand and verify with your calculator’s T-Test command [STAT/TESTS/2:T-Test].)
4. Give the P-value __________
5. What conclusion would you draw?
II. Boxes of oranges are labeled “net wt. 44 lbs.” The quality control department at the packing plant occasionally takes a random sample of ten boxes to try to determine if the mean weight is actually 44 lbs. For one lot a sample yielded the following weights :
44.8, 45.3, 43.6, 44.9, 45.7, 43.5, 46.1, 45.7, 44. 2 43.9.
Enter the data into your calculator and complete the significance test (2:T-Test) to determine if the mean weight for all boxes that lot is different than 44 lbs.
1. State the assumptions.
2. State appropriate null and alternative hypotheses.
H0: ___________________ HA: ___________________
3. Enter the data and compute the value of the appropriate test statistic with your calculator’s T-Test command.)
4. Give the P-value __________
5. What conclusion would you draw?
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