certain viral infection for 80% of all patients. Suppose the drug is given to 20 randomly selected patients.
If the company’s claim is true, what is the probability that drug will relieve the symptoms of at least 14 of
5. A pizza store wants to estimate its average delivery time (time between receiving the order and
delivering it). They recorded the delivery time for a random sample of 40 orders. The sample had a mean
of 34.5 minutes, and a standard deviation of 4.6 minutes. Calculate a 95% confidence interval for the true
mean. Do you think that the store can claim that their average delivery time is less than 30 minutes?
6. Is it possible that a statistical test would reject a null hypothesis when in fact it is true? Justify your
7. An industrial engineer inspected two types of steel wires to test “H
: the mean strengths of the two
types of steel wires are the same,” against “H
: the mean strengths are different.” It is revealed
subsequently that in coming to his decision, the engineer had committed a Type II error. What was his
decision, and what was the actual state of affairs?
8. Suppose the 65th percentile of a normal distribution is 32, and the 85th percentile of the distribution is
46. Find the mean and the standard deviation of the distribution.
9. Suppose while analyzing a data set you used a particular statistical test (that you have learned in this
course) to test a specific null hypothesis against a specific alternative hypothesis. Suppose your test did
not reject the null hypothesis at 5% level of significance. Could your test have rejected the null hypothesis
at 3% level of significance? Explain your answer.