Chapter 6

 

1.       The report of a sample survey of 1500 adults says, “With 95% confidence, between 27% and 33% of all American adults believe that drugs are the most serious problem facing our nation’s public schools.” Explain to someone who knows no statistics what the phrase “95% confidence” means in this report.

 

2.       When an instrument in a chemistry laboratory makes repeated measurements on the same specimen, the readings are known to vary normally with standard deviation 0.03. It is customary to make 3 readings and use the sample mean as the final result. For a particular specimen, the readings are

53.12   53.08   53.17

       Give a 95% confidence interval for the mean of the distribution of readings for this specimen.

 

3.       How many readings made with the instrument in problem #2 must be averaged to obtain a margin of error of  0.01 in a 95% confidence interval for the true value?

 

4.       The salaries (in thousands of dollars) of a random sample of 10 of the 380 full professors at a large university are 73, 62, 68, 112, 54, 59, 93, 84, 43, 76. The z or similar procedure should not be used to give a confidence interval for the mean salary of a full professor at this university. Why not?

 

5.       Give a brief answer to each of the following questions.

a.       What is the number such that exactly 1% of the probability in a standard normal distribution falls above it?

b.       A chemical production process has had mean output  = 1100 pounds of product per shift. New pollution controls have been added to the process. Management wants to know if there is evidence that the new controls have reduced production. What are  and ?

c.       The potency of a pharmaceutical product is supposed to be 78. Three potency measurements are taken from each batch produced to check whether the potency has deviated from the desired level. What are  and  for this test?

d.       If a statistical test is significant at the 1% level, is the same test using the same data always significant at the 5% level?

 

6.       You read an article that describes a study of the voting patterns of various groups in society based on a large sample survey. The article says, “Persons who identified themselves as evangelicals were significantly (P < .01) more likely to favor Republican presidential candidates than were other white Protestants.” Explain to someone who knows no statistics what “significantly (P<.01)” means.

 

7.       The diastolic blood pressure for American women aged 18 to 44 has the normal distribution with

        mean 75 milliliters of mercury (mm Hg) and standard deviation 10 mm Hg. We suspect that regular

        exercise will lower the blood pressure. A sample of 25 women who jog at least 5 miles a week

        gives sample mean blood pressure  = 71 mm Hg. Is this good evidence that the mean blood

        diastolic blood pressure for the population of regular exercisers is lower than 75 mm Hg?

a.       State  and .

b.       Carry out the test, assuming that standard deviation 10 is true. Use Table A to give the P-value.

c.       Is the result of your test significant at the 5% level? Is it significant at the 1% level?

 

8.       A milling machine produces rods that are supposed to be 5 centimeters (cm) in diameter. When the machine is in control, the rod diameters vary normally with a mean of 5 cm and standard deviation

       0.002 cm. The standard deviation measures the precision of the milling machine. A sample of 5 rods

       is measured each hour for process control purposes. This hour’s sample gives

5.9    5.0007   5.0010   5.0009   5.0010

       Is there evidence that the process mean has moved away from the target value? Answer this question

       by stating hypotheses and carrying out a significance test. Give the P-value and state your conclusion.