Question

In Class Group Work 1) In a nationwide study of the weights of adults with gym memberships, researchers obtain a random sample of gym members and group them into three age categories. They conduct an ANOVA test and provide the StatCrunch outputs shown here. Weight 100 Analysis of Variance results: Responses: Weight (kg) Factors: Bin(Age) 80 Response statistics by factor Bin(Age) n Mean Std. Dev. Std. Error 60 O to 25 180 66.060556 12.163718 0.90663 25 to 50 304 70.750329 13.880549 0.79610408 40 50 to 75 23 72.121739 10.78846 2.2495494 O to 25 25 to 50 50 to 75 Bin(Age) ANOVA table Source DF SS MS F-Stat P-value Bin(Age) 2 2699.7154 1349.8577 7.7819725 0.0005 Error 504 87423.629 173.45958 Total 506 90123.344 Which conclusions are appropriate at the 5% level of significance? Check all that apply. We cannot draw a conclusion because conditions for the ANOVA F-test are not met. The differences observed in sample mean weights do not provide strong evidence of a difference in population mean weights for the adult gym members in these three age groups. There are statistically significant differences in sample mean weights for the three age groups. This study provides strong evidence that the mean weights differ for the three populations of gym members defined by these age groups. This study provides strong evidence that the mean weight of all gym members who are under 25 is less than the mean weight for all members who are in the 50-75 age group. This study suggests that the mean weights are the same for the three populations of gym members defined by these three age categories.

Answer 1

In Class Group Work 1) In a nationwide study of the weights of adults with gym memberships, researchers obtain a random sample of gym members and group them into three age categories. They conduct an ANOVA test and provide the StatCrunch outputs shown here. Weight 100 Analysis of Variance results: Responses: Weight (kg) Factors: Bin(Age) 80 Response statistics by factor Bin(Age) n Mean Std. Dev. Std. Error 60 O to 25 180 66.060556 12.163718 0.90663 25 to 50 304 70.750329 13.880549 0.79610408 40 50 to 75 23 72.121739 10.78846 2.2495494 O to 25 25 to 50 50 to 75 Bin(Age) ANOVA table Source DF SS MS F-Stat P-value Bin(Age) 2 2699.7154 1349.8577 7.7819725 0.0005 Error 504 87423.629 173.45958 Total 506 90123.344 Which conclusions are appropriate at the 5% level of significance? Check all that apply. We cannot draw a conclusion because conditions for the ANOVA F-test are not met. The differences observed in sample mean weights do not provide strong evidence of a difference in population mean weights for the adult gym members in these three age groups. There are statistically significant differences in sample mean weights for the three age groups. This study provides strong evidence that the mean weights differ for the three populations of gym members defined by these age groups. This study provides strong evidence that the mean weight of all gym members who are under 25 is less than the mean weight for all members who are in the 50-75 age group. This study suggests that the mean weights are the same for the three populations of gym members defined by these three age categories.