Question

Which hypothesis test is appropriate? Match. THESE are all connected. AN)VA, chi square, f test for two variances, one sample left tailed t, one sampled right tailed t

1.Research shows that there is one critical dimension on yo-yos. If the dimension falls within a certain range of values, it drastically improves yo-yo performance. You have some ideas for manufacturing processes which will keep the mean value of that dimension the same, while potentially reducing the standard deviation. You want to compare these processes to the current process.

2.Research shows that there is one critical dimension on yo-yos. If the dimension falls within a certain range of values, it drastically improves yo-yo performance. You have some ideas for manufacturing processes which will keep the mean value of that dimension the same, while potentially reducing the standard deviation. You want to compare these processes to the current process.

3. You poll people across the USA (across 5 regions), asking their favorite brand of soda (coca-cola, diet-coke, pepsi, diet-pepsi etc.). You want to understand if soda preference is independent of region.

4.You want to understand if the mean weight of 10-year-old boys in your town is greater than the national average.

5.You own a major corporation with franchise locations. There are five franchise owners, which each own more than 100 stores. You want to understand if there is a statistically significant difference in mean profit across these stores by franchise owners.

Answer 1

Solution:

1) For the given scenario the F test for two variances is appropriate. It is given that there are some processes which will keep the mean value of that dimension same while reducing the standard deviation. We want to compare these processes with current process which will be done by comparing the variance of both the processes. We use F test for comparing the two population variances. Hence, F test for population variance is appropriate.

2) First question and second question both are same. So here also the F Test is appropriate.

3) For the given scenario chi square test is appropriate. Here, we have to check whether two attributes are independent or not. In our question we have two attributes one is regions of people and the other is soda preference. We want to check whether soda preference is independent of region or not. Chi square test is used to test the independence of attributes. Hence, Chi square test for independence of attributes is appropriate here.

4) For the given scenario one sample right tailed t-test is appropriate. Here we want to test that whether mean weight of 10 year old boys is greater than the national average weight or not, means we want to test that population mean is equal to the some specified value. The t-test is used to test that population mean is equal to specified value. Also according to the given scenario alternative should be in form of greater than national average weight. Therefore, here one sample right tailed t-test is appropriate.

5) For the given scenario Anova is appropriate. There are 5 owners and each of them have more than 100 stores. We want to test if there is significant difference between the mean profit across the stores by owners. The scenario tells that we have 5 samples and we want to test the equality of their mean. We use Anova to do the same. Hence Anova is appropriate here.