A controversial issue in the sport of professional soccer is the use of instant replay for making difficult goal line decisions. Each person in a representative sample of 102 players, fans, coaches, and officials was asked his or her opinion about the use of instant replay for goal-line decisions. The data are summarized in the two-way frequency table below.OpinionCategory Favor Use Oppose Use Players 222 Fans 186 Coaches 1526 Officials 310 In testing to see whether opinion with respect to the use of instant replay is independent of the category of the person interviewed, a chi-square test statistic of 27.99 and a p-value less than 0.001 were calculated. Which of the following statements is correct?a. The number of degrees of freedom for the test is 8 - 1 = 7.b. The chi-square test should not have been used because two of the counts in the table are less than 5.c. The null hypothesis states that there is an association between category and opinion about the use of instant replay, and the small p-value suggests that the null hypothesis should be rejected.d. The small p-value suggests that there is evidence of an association between category and opinion about the use of instant replay.e. The chi-square test shows that fans favor the use of instant replay.

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A controversial issue in the sport of professional soccer is the use of instant replay for making difficult goal line decisions. Each person in a representative sample of 102 players, fans, coaches, and officials was asked his or her opinion about the use of instant replay for goal-line decisions. The data are summarized in the two-way frequency table below.OpinionCategory Favor Use  Oppose Use  Players 222 Fans 186 Coaches 1526 Officials 310 In testing to see whether opinion with respect to the use of instant replay is independent of the category of the person interviewed, a chi-square test statistic of 27.99 and a p-value less than 0.001 were calculated. Which of the following statements is correct?a. The number of degrees of freedom for the test is 8 - 1 = 7.b. The chi-square test should not have been used because two of the counts in the table are less than 5.c. The null hypothesis states that there is an association between category and opinion about the use of instant replay, and the small p-value suggests that the null hypothesis should be rejected.d. The small p-value suggests that there is evidence of an association between category and opinion about the use of instant replay.e. The chi-square test shows that fans favor the use of instant replay.

toeneepnla · Accepted Answer

Given information:The two-way frequency table is provided as:OpinionCategory Favor Use  Oppose Use  Players 222 Fans 186 Coaches 1526 Officials 310 The chi-square test statistic is obtained as /χ2=27.99 with a p-value of less than 0.001.It is required to choose the correct one out of the provided statements regarding this problem.The correct statement is D; that is, the small p-value suggests that there is evidence of an association between category and opinion about the use of instant replay.Reason:The null and the alternative hypothesis for this problem are:H0: There is no relation between category and opinion about the use of instant replay.Ha: There is an association between category and opinion about the use of instant replay.Since the p-value is less than 0.001, a very small p-value, also less than any level of significance (0.10, 0.05, or 0.01); therefore, the null hypothesis gets rejected. Hence, it indicates that the small p-value suggests that there is evidence of an association between category and opinion about the use of instant replay.

Warenberg56i · Accepted Answer

Reasons for the wrong options:a. The number of degrees of freedom for the test is obtained as:df=(number of rows−1)×(number of columns−1)=(4−1)×(2−1)=3Hence, statement a is wrong.b. The chi-square test should not have been used because two of the counts in the table are less than 5.This statement is also wrong since the assumption of the Chi-square test is for the expected counts of each cell to be greater than 5, not for the observed counts of each cell.c. The null hypothesis states that there is an association between category and opinion about the use of instant replay, and the small p-value suggests that the null hypothesis should be rejected.This statement is also wrong because of the framing of the wrong null hypothesis. The correct null hypothesis states that there is no association between category and opinion about the use of instant replay.e. The chi-square test shows that fans favor the use of instant replay.This statement is also wrong since the chi-square test for this problem will only indicate whether there is an association between category and opinion about the use of instant replay or not. It will not provide any result regarding the statement: fans favor the use of instant replay.

A controversial issue in the sport of professional soccer is the use of instant replay for making di

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