Question

1. What type of statistical test should I use for the following? Where relevant, please indicate if I should use a one or a two sided test. Please don’t do the tests themselves! (2 points each)

   1. A researcher has collected head width and body weight for 45 ants. She wants to know whether the two variables have a linear relationship.

2. You want to know whether Biology majors or P.E. Majors run faster. You get a group of 20 Biology and 20 P.E. Majors together and have them run from A&S to the Apollo Fountain and back. Unfortunately your stopwatch broke, so you only know who beat whom.

3. Dr. Mobility is looking at crowd behavior in the public transport system. He counts the number of people on a subway platform waiting for a subway to arrive. Then he notes how many get into each into each of the 8 different subway cars. He wants to know if more people get into some carriages than others

4. Dr. Mobility believes that he should be able to predict how many people choose to enter different subway cars based on their distance from the entrance. He measures the distance from the entrance to the approximate stopping point of each car and the number of people entering each car.

5. Dr. Mobility now wants to look at how public transportation is used at night. He has picked 20 bus stops and measures how many people use each bus stop during the night, for one week. Then a bright light and emergency phone is installed at each of the 20 bus stops. He then measures how many people use each bus stop at night for another week, after the changes have been made to the stops.

6. Ten stone crabs were selected from each of four areas. The researcher wanted to compare the weight of the crabs in different areas.

7. To determine whether or not there really are a thousand chips in every bag of Chip’s Ahoy cookies you randomly select ten bags of these cookies and count the chips.

Answer 1

A researcher has collected head width and body weight for 45 ants. She wants to know whether the two variables have a linear relationship.
Statistical Test: Correlational analysis (two-tailed test) because we want to know the linear relationship between the variables.

You want to know whether Biology majors or P.E. Majors run faster. You get a group of 20 Biology and 20 P.E. Majors together and have them run from A&S to the Apollo Fountain and back. Unfortunately, your stopwatch broke, so you only know who beat whom.
Statistical Test: Two-sample proportion Z test (two-tailed test). It can be done by obtaining the number of winners for both the majors.

Dr. Mobility is looking at crowd behaviour in the public transport system. He counts the number of people on a subway platform waiting for a subway to arrive. Then he notes how many get into each of the 8 different subway cars. He wants to know if more people get into some carriages than others
Statistical Test: Chi-square goodness of fit which tells whether the proportion of people entering the carriage is more for some than others.

Dr. Mobility believes that he should be able to predict how many people choose to enter different subway cars based on their distance from the entrance. He measures the distance from the entrance to the approximate stopping point of each car and the number of people entering each car.
Statistical Test: Regression analysis using which a model can be determined in order to predict the number of people entering different subways based on their distance.

Dr. Mobility now wants to look at how public transportation is used at night. He has picked 20 bus stops and measures how many people use each bus stop during the night, for one week. Then a bright light and emergency phone is installed at each of the 20 bus stops. He then measures how many people use each bus stop at night for another week, after the changes have been made to the stops.
Statistical Test: Paired t-test (two-tailed test) as the data is collected before the installation of bright light (that is the treatment) and after the treatment.

Ten stone crabs were selected from each of four areas. The researcher wanted to compare the weight of the crabs in different areas.
Statistical Test: One-Way ANOVA because there are 4 different groups to compare.

To determine whether or not there really are a thousand chips in every bag of Chips Ahoy cookies you randomly select ten bags of these cookies and count the chips.

Statistical Test: Chi-square goodness of fit because it is required to check whether the proportion of chips in each bag is same or not.