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Chapter 9: Q.18 (page 547)
Write a few sentences comparing what the P-values in Exercises 13 and 14 tell you about statistical significance in each of the two studies.
For P-value in exercisethe convincing evidence is stronger
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Sweetening colas Cola makers test new recipes for loss of sweetness during storage. Trained tasters rate the sweetness before and after storage. From experience, the population distribution of sweetness losses will be close to Normal. Here are the sweetness losses (sweetness before storage minus sweetness after storage) found by tasters from a random sample of batches of a new cola recipe:
Are these data good evidence that the cola lost sweetness? Carry out a test to help you answer this question.
Slow response times by paramedics, firefighters, and policemen can have serious consequences for accident victims. In the case of life-threatening injuries, victims generally need medical attention within 8 minutes of the accident. Several cities have begun to monitor emergency response times. In one such city, the mean response time to all accidents involving life-threatening injuries last year was M 6.7 minutes. Emergency personnel arrived within 8 minutes after 78% of all calls involving life-threatening injuries last year. The city manager shares this information and encourages these first responders to “do better.” At the end of the year, the city manager selects an SRS of 400 calls involving life-threatening injuries and examines the response times.
(a) State hypotheses for a significance test to determine whether the average response time has decreased. Be sure to define the parameter of interest.
(b) Describe a Type I error and a Type II error in this setting, and explain the consequences of each.
(c) Which is more serious in this setting: a Type I error or a Type II error? Justify your answer.
Filling cola bottles Bottles of a popular cola are supposed to contain milliliters (ml) of cola. There is some variation from bottle to bottle because the filling machinery is not perfectly precise. From experience, the distribution of the contents is approximately Normal. An inspector measures the contents of six randomly selected bottles from a single day’s production. The results are
Study more! The significance test in Exercise yields a P-value of .
(a) Describe a Type I and a Type II error in this setting. Which type of error could you have made in Exercise ? Why?
(b) Which of the following changes would give the test a higher power to detect minutes: using or ? Explain.
Significance and sample size A study with subjects reported a result that was statistically significant at the level. Explain why this result might not be particularly large or important.
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