Manufacturers are testing a die to make sure that it is fair (has a uniform distribution). They roll the die 100 times and record the outcomes. They conduct a chi-square Goodness-of-Fit hypothesis test at the 1% significance level. The null and alternative hypotheses are: H0: The die has the uniform distribution. Ha: The die does not have the uniform distribution. The test statistic for the data is χ20=28.165. The critical value is χ20.01=15.086. What conclusions can be made? Select all that apply. Select all that apply: We should reject H0. We should not reject H0. At the 1% significance level, there is sufficient evidence to conclude that the die is not fair. At the 1% significance level, there is not enough evidence to conclude that the die is not fair.

An annual marathon covers a route that has a distance of approximately 26 miles. winning times for this marathon are all over 2 hours. the following data are the minutes over 2 hours for the winning male runners over two periods of 20 years each. earlier period 14 12 15 22 13 10 19 13 9 14 20 18 16 20 23 12 18 17 6 13 recent period 7 11 7 14 8 9 11 14 8 7 9 8 7 9 9 9 9 8 10 8 (a) make a stem-and-leaf display for the minutes over 2 hours of the winning times for the earlier period. use two lines per stem. (use the tens digit as the stem and the ones digit as the leaf. enter none in any unused answer blanks. for more details, view how to split a stem.) minutes beyond 2 hours earlier period 0 1 2 (b) make a stem-and-leaf display for the minutes over 2 hours of the winning times for the recent period. use two lines per stem. (use the tens digit as the stem and the ones digit as the leaf. enter none in any unused answer blanks.) minutes beyond 2 hours recent period (c) compare the two distributions. how many times under 15 minutes are in each distribution