A large gym wants to promote an exercise routine they developed. They split the classes they teach into one of two groups: one group that works out with the exercise routine currently implemented (this is group 1) and one group that works out with the new exercise routine (this is group 2). They then randomly select samples of size 35 and 27 from each group and measure the weight loss from one week and find the mean and standard deviation for each exercise routine. Weight loss is approximately normally distributed.

Are the conditions for a confidence interval for the difference between two means satisfied?

Are the data from the two samples random?

no
yes

Correct

Are the observations independent? In other words, is n1≤0.05N1 and n2≤0.05N2?

Yes, because in a large gym there is likely more than 700 individuals who did classes with the current routine and more than 540 individuals who did the class with the new routine.
No, because the gym is a small gym and so it is not likely that more than 700 individuals who did classes with the current routine and that more than 540 individuals did the class with the new routine.

Correct

Are the two samples large enough?

Yes, because the population is approximately normal and n1≥30

and n2≥30 . No, because although the population is approximately normal either n1<30 or n2<30 , or both are less than 30. No, because the population is not approximately normal and either n1<30 or n2<30 , or both are less than 30. It is impossible to know given the information. Yes, because although either n1<30 or n2<30

, or both are less than 30, the population is approximately normal.

Correct

Are the samples independent?

No, because individuals who are in group 1 are matched with individuals in group 2.
Yes, because individuals who are in group 1 are not matched with individuals in group 2.

Correct

Part 2 of 2

Give a 99% confidence interval, for μ1−μ2

given the following information.

¯x1=2.94 , s1=0.59, n1=35 ¯x2=3.41, s2=0.42, n2=27

± Correct Rounded to 2 decimal places.