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Chapter 9: Q.15 (page 547)
When asked to explain the meaning of the P-value in Exercise 13, a student
says, 鈥淭his means there is only probability 0.01 that the null hypothesis is true.鈥� Explain clearly why the student鈥檚 explanation is wrong.
The student鈥檚 explanation is wrong.
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Pressing pills A drug manufacturer forms tablets by compressing a granular material that contains the active ingredient and various fillers. The hardness of a sample from each batch of tablets produced is measured to control the compression process. The target value for the hardness is . The hardness data for a random sample of tablets are
Is there significant evidence at the level that the mean hardness of the tablets differs from the target value? Carry out an appropriate support your answer.
Losing weight A Gallup Poll found that 59% of the people in its sample said 鈥淵es鈥� when asked, 鈥淲ould you like to lose weight?鈥� Gallup announced: 鈥淔or
results based on the total sample of national adults, one can say with 95% confidence that the margin of (sampling) error is 魛伅3 percentage points.鈥�16 Can we use this interval to conclude that the actual proportion of U.S. adults who would say they want to lose weight differs from 0.55? Justify your answer.
A change is made that should improve student satisfaction with the parking situation at your school. Right now, 37% of students approve of the parking that鈥檚 provided. The null hypothesis is tested against the alternative.
The recommended daily allowance (RDA) of calcium for women between the ages of 18 and 24 years is 1200 milligrams (mg). Researchers who were involved in a large-scale study of women鈥檚 bone health suspected that
their participants had significantly lower calcium intakes than the RDA. To test this suspicion, the researchers measured the daily calcium intake of a random sample of 36 women from the study who fell in the desired age range. The Minitab output below displays descriptive statistics for these data, along with the results of a significance test.
(a) Determine whether there are any outliers. Show your work.
(b) Interpret the P-value in context.
(c) Do these data give convincing evidence to support the researchers鈥� suspicion? Carry out a test to help your answer
Your company markets a computerized device for detecting high blood pressure. The device measures an individual鈥檚 blood pressure once per hour at a randomly selected time throughout a 12-hour period. Then it calculates the mean systolic (top number) pressure for the sample of measurements. Based on the sample results, the device determines whether there is significant evidence that the individual鈥檚 actual mean systolic pressure is greater than 130. If so, it recommends that the person seek medical attention.
(a) State appropriate null and alternative hypotheses in this setting. Be sure to define your parameter.
(b) Describe a Type I and a Type II error, and explain the consequences of each.
(c) The blood pressure device can be adjusted to decrease one error probability at the cost of an increase in the other error probability. Which error probability would you choose to make smaller, and why?
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