Question

Choose the proper statistical technique to use for each scenario from the list below.

A. One sample test for a mean

B. One sample test for a proportion

C. Two sample test for means- independent

D. Two sample test for means – paired

E. Two sample test for proportions

F. Chi square test of independence

G. Chi square test for homogeneity of proportions

H. One Way Analysis of Variance

I. Correlation

J. Simple regression

K. Multiple regression

L. Time series forecasting.

1. What is the statistical technique if you want to predict stock ownership (number of shares) based upon annual income?

2. A study has been carried out to determine if there is a difference in the average dollar contributions made by clerical workers at three different firms.

3. AAA wants to determine EPA mileage ratings of new cars based upon their weight and whether they are standard or automatic transmission.

4. According to the ICR Research Group, 63% of Americans in the 18-34 age group say they are comfortable filing income tax returns electronically, compared to just 49% of those 55-64. They sampled 200 people from each age group to determine if the younger set were more comfortable with electronic filing than those in the older group.

5. It has been reported that the average visitor from Japan spent $1953 during a trip to the United States, while the average for a visitor from the United Kingdom was $1738. Does the visitor from the United Kingdom spend significantly higher than a visitor from Japan?

6. One of the measures of the effectiveness of a stimulus is how much the viewers pulse rate increases on exposure to it. In testing a lively music theme for its television commercials, an advertising agency shows ads with the new music to 25 viewers and their mean pulse rate is 20.5 beats per minute while the mean pulse rate per minute for another sample of 25 viewers seeing the same ads with the old music was 16.9 beats per minute. Is the new music theme better?

7. A trucking firm is considering the installation of a new, low restriction engine air filter for its long-haul trucks, but doesn’t want to make the switch unless the new filter can be shown to improve the fuel economy (miles per gallon) of these vehicles. A test is set up so that each of 10 trucks makes the same run twice- once with the old filtration system and once with the new version.

8. A movie complex has a sellout for three movies rated G, PG, and R that they show simultaneously on a Friday evening. A sample of patrons from each movie is observed to determine if they purchase snacks or do not. Could the percentage buying snacks be the same for each movie?

Answer 1

1.

Simple regression

(since there is one independent variable: annual income and one dependent variable: number of shares).

2.

One Way Analysis of Variance

(since means are being compared at more than 2 different firms).

3.

Multiple regression

(since there are two independent variables: weight and standard/automatic transmission and one dependent variable: EPA mileage ratings).

4.

Two sample test for proportions

(since two proportions are being compared).

5.

Two sample test for means- independent

(since two means from independent groups are being compared).

6.

Two sample test for means- independent

(since two means from independent groups are being compared. They are independent samples because the subjects/participants are not same in both the samples).

7.

Two sample test for means – paired

(since two means from the paired samples/groups are being compared. They are paired samples because the subjects/trucks are same in both the samples).

8.

Chi square test for homogeneity of proportions

(More than two proportions of the same categorical variable, purchasing snacks are being compared to determine if the frequency counts are distributed identically across different populations).