Fowle Marketing Research, Inc., bases charges to a client on the assumption that telephone surveys can be completed in a mean t

Fowle Marketing Research, Inc., bases charges to a client on the assumption that telephone surveys can be completed in a mean time of 15 minutes or less. If a longer mean survey time is necessary, a premium rate is charged. Suppose a sample of 35 surveys produces the data in the Microsoft Excel Online file below. Use a known σ = 3.6 minutes. Is the premium rate justified?

Open spreadsheet

1. Formulate the null and alternative hypotheses for this application.
   H0: μ
   greater than or equal to 15greater than 15less than or equal to 15less than 15equal to 15not equal to 15
   Ha: μ
   greater than or equal to 15greater than 15less than or equal to 15less than 15equal to 15not equal to 15
2. Compute the value of the test statistic (to 2 decimals).
   fill in the blank 4
3. What is the p-value (to 4 decimals)?
   fill in the blank 5
4. Using ???? = .01, is a premium rate justified for this client?

   YesNo

One of the reasons health care costs have been rising rapidly in recent years is the increasing cost of malpractice insurance for physicians. Also, fear of being sued causes doctors to run more precautionary tests (possibly unnecessary) just to make sure they are not guilty of missing something. These precautionary tests also add to health care costs. Data in the Excel Online file provided below are consistent with findings in the Reader's Digest article and can be used to estimate the proportion of physicians over the age of 55 who have been sued at least once. Construct a spreadsheet to answer the following questions.

Open spreadsheet

a. Formulate hypotheses that can be used to see if these data can support a finding that more than half of physicians over the age of 55 have been sued at least once.

 <>≤≥=≠ 0.50 <>≤≥=≠ 0.50

b. Use the Excel Online file provided above to compute the sample proportion of physicians over the age of 55 who have been sued at least once (to 2 decimals).

Calculate the value of the test statistic (to 2 decimals).

What is the -value (to 4 decimal places)? Do not round intermediate calculations.

c. At , what is your conclusion?

Since -value 

≤>  , we rejectfail to reject . We conclude that we have sufficientinsufficient evidence to suggest that the proportion of physicians over the age of 55 who have been sued at least once is greater than .50.