Question

For the following below you should decide

a) What test would you use?

b) Why would you use this test?

1. You want to test and see if there is a relationship between favorite type of dog and political affiliation. You ask 25 conservative, 25 liberal, 25 reform and 25 NDP supporters if they have a large medium or small dog.

2. The average number of books owned by a professor is 543 with a st dev of 124. The professors in your department own an average of 576 books each with a st dev of 112. Do they own significantly more books than average?

3. You wish to determine if there is a difference in the efficiency of three types of furnaces. You select 5 from manufacturer A, 5 from manufacturer B, and 5 from manufacturer C. You ask your assistant to measure how efficient each furnace was but he did not understand your directions and only reported the data to you in terms of most efficient to least efficient across all groups.

4. You want to know if there is a difference in the grade given out by faculty based on whether or not they have tenure. You obtain the records of 7 professors from the years prior to and the year after they receive tenure. While entering the data into your computer you notice that the marks follow a very typical pattern for university grades (lots of relatively high marks with a small minority of very low grades).

Answer 1

1. We will use a Chi square test of Independence here. We will use this test since we want to check if there's a dependence between the variables Favourite type of dog and political affiliation. We have also collected data accordingly which can be presented in observed 3*3 table counts.

2. We will use a z test for the comparison of the means here. We want to test if the means of the books owned by the professor's in our department >543 (the population average). We also know tha population SD ie 124 so we can use z test here.

3. We will use a one way ANOVA test here. We want to test if the there's a difference in the efficiency of the three types of furnaces and this can be done by the comparison of the means of the three groups through the ANOVA.

4. We will use a dependent samples t test here. Since we are interested in testing if there's a difference in the grades given out by the faculty based on whether or not they have tenure, and we use the same 7 people's grades given before and after they have tenure, it's a matched pairs design.