A medical device company has developed a new needle that they claim reduces the incidence of injection-site reactions for a particular medication. An experiment is to be conducted to determine if there is sufficient evidence to make that claim. Which of the following is a correct description and consequence of a Type I error?

A baseball pitcher, concerned about losing speed from his fastball, undertook a new training regimen during the offseason. His team's pitching coach measured the speed of 20 random fastballs (in miles per hour) thrown by the pitcher during spring training, and compared it with a sample of 20 random fastballs thrown during the pitcher's last five starts in the previous season. The results are shown in the following table. Assume that the pitcher's fastball speeds had a standard deviation of 2.9 miles per hour both before and after the training regimen and that the speeds for both time periods are normally distributed. Let the pitcher's fastball speeds in the previous season be the first sample, and let the pitcher's fastball speeds in spring training be the second sample. At the 0.05 level of significance, is there evidence that the pitcher is throwing fastballs at higher speeds? Find the test statistic, rounded to two decimal places, and the p-value, rounded to three decimal places.…

The authors of a paper compared two different instruments for measuring a person's capacity for breathing out air. (This measurement is helpful in diagnosing various lung disorders.) The two instruments considered were a Wright peak flow meter and a mini-Wright peak flow meter. Seventeen people participated in the study, and for each person air flow was measured once using the Wright meter and once using the mini-Wright meter. The Wright meter is thought to provide a better measure of air flow, but the mini-Wright meter is easier to transport and to use. Use of the mini-Wright meter could be recommended as long as there is not convincing evidence that the mean reading for the mini-Wright meter is different from the mean reading for Wright meter. For purposes of this exercise, you can assume that it is reasonable to consider the 17 people who participated in this study as representative of the population of interest. Data values from this paper are given in the accompanying table.…

Welsh, Davis, Burke, and Williams (2002) conducted a study to evaluate the effectiveness of a carbohydrate-electrolyte drink on sports performance and endurance. Experienced athletes were given either a carbohydrate-electrolyte drink or a placebo while they were tested on a series of high-intensity exercises. One measure was how much time it took for the athletes to run to fatigue. Data similar to the results obtained in the study are shown in the following table. Time to Run to Fatigue (in minutes)                                                         Mean                               SE Placebo                                          21.7                                  2.2 Carbohydrate- electrolyte          28.6                                  2.7   a) Construct a bar graph that incorporates all of the information in the table. b) Looking at your graph, do you think that the carbohydrate-electrolyte drink helps performance?