Question

It’s time to play America’s favorite game show: NAME THAT STATISTICAL TEST. For each of the scenarios described below, please state which of the tests or measurements discussed in class would be most appropriate to use in testing the claim at hand. Do not carry out any actual computations.

a) You have random samples of athletes from four men’s college sports: 12 baseball players, 8 wrestlers, 7 tennis players, and 10 golfers. You wish to determine whether athletes’ heights are the same across all four sports. Unfortunately, a couple of the samples contain noticeable outliers.

b) 200 adults are sampled. For each adult in the sample, administrators recorded whether the subject had more than one active credit card, and whether the subject carries an unpaid balance on at least one card. The researchers would like to determine whether there is a relationship between carrying more than one credit card and carrying an unpaid balance on at least one card.

c) You would like to determine the strength and direction of the relationship between the volume (in decibels) that background music is played in a store and the length of time that customers stay in the store. A residual analysis showed the bivariate data were binormal and homoscedastic.

d) You wish to compare the mean annual salaries of male and female lawyers, based on random samples of 45 men and 40 women. Salary data tend to be skewed right. Population standard deviations are not known.

e) A sample of 14 high school athletes participate in a conditioning study. VO2 max levels (a measure of oxygen consumption) for each athlete were taken before participating in the conditioning program, and again after one month of conditioning. No outliers were observed in the measurements. You wish to determine whether VO2 max levels improved after one month of conditioning.

Answer 1

a) To test if the population mean heigths of the athletes among the four groups are the same, we can use a One Way ANOVA test. (It compares population means for more than 2 groups under the assumption that the sample comes from a Normally distributed population)

b) To test if there's a relationship between carrying more than one card and whether not it has an unpaid balance we can conduct a chi square test of Independence. Here total expected frequency would be 200.

c) To test if there's a relationship between the volume that the background music is played and the length of time the customer stays in the store, we can use a correlations test.

d) We can use independent samples t test here to compare the population means (since population SD is unknown for the two groups, we will use t test)

e) We will use a dependent samples t test for the population mean here. Since the 14 people are tested before and after this is a dependent samples test.