Question

1. Congratulations! After passing your course in Business Statistics, you received a job as a statistical analyst at a major business corporation. Your first task is to decide which statistical test would be the most appropriate to use to analyze the following   problems.    Luckily, you remember learning about the following statistical tests in your favorite (and only) business statistics course.

A.   z-test for one sample mean                                           H.    t- test for paired data

B. z -test for one sample proportion                                   I.    F-test for the equality of variances

C.   t-test for one sample mean                                            J.    Single factor ANOVA

D.   t-test for two independent sample means                     K.    Chi square test for independence

E.   Chi-square test for a difference in two proportions        L.    Chi-square goodness of fit test.

F. Simple Regression Analysis                                                   

G.   Multiple Regression                      

                                                                                           

a.   Gas Buddy reported that the mean gas price nationwide is $1.24 per liter for unleaded gas. The nationwide standard deviation is $0.19 per liter. A random sample of the price per liter for unleaded gas is taken at 35 gas stations in Vancouver. Which statistical test should be used to determine whether the average price of gas in Vancouver is significantly higher than the nationwide average?

Test: ____________ (from the above list, choose the letter that corresponds to the most appropriate test to analyze the data)

b A study of the effect of television commercials on 9 year old children measured attention span time (in seconds). There were three different commercial groups based on Food, Movies, or Games. A sample of 36 children were randomly assigned to one of the three commercial groups. Which statistical test should be used to determine whether there is a significant difference in the mean attention span time among the children in the three different commercial groups?

Test: ___________ (from the above list, choose the letter that corresponds to the most appropriate test to analyze the data)

c.   YVR has been redesigned with the goal of reducing flight delays. The delays (in minutes) for a random sample of flights before and after the upgrade are recorded. Which statistical test should YVR use to analyze the data in order to determine if the upgrades significantly reduced the average flight delay times?

Test: ___________ (from the above list, choose the letter that corresponds to the most appropriate test to analyze the data)

  d. A retirement center previously reported that residents spend an average of 4 hours per week using the computer. The retirement director thinks that time has increased. He asks a sample of 40 residents about their computer usage last week. Which statistical test should the director use to determine if the average computer usage time has significantly increased?

Test: ____________ (from the above list, choose the letter that corresponds to the most appropriate test to analyze the data)

Answer 1

Answer a.

A - z-test for one sample mean

Explanation:

We want to test Ho: The average price per litre of gas in Vancouver is 1.24 versus Ha: The average price per litre of gas in Vancouver is significantly higher than the nationwide average (1.24).

Since the population standard deviation is known , we will use Z- Test i.e. Normal Distribution

Answer b.

J - Single Factor ANOVA

Explanation:

We want to test Ho: There is no significant difference in the mean attention span time among the children in the three different commercial groups versus Ha: There is a significant difference in the mean attention span time among the children in the three different commercial groups.

Now when we want to compare the means of more than one group, t-test or Z-test are not as powerful as ANOVA so we use One Factor ANOVA in this case .

Answer c.

H - t-test for paired samples

Explanation:

Here we are measuring the average delay times of flights before and after the upgrade using the sample sample of flights i.e. there is one to one correspondence in before and after timings. This means that the delay time for one flight befor upgrade is compared to the time of the same flight after the upgrade and cannot be compared to any other flight.

So we use t-test for dependent or paired samples.

Answer d.

C - t-test for one sample mean

Explanation:

Here we are trying to test whether the average time spent on computer has increased or not. SInce, no information about population standard deviation is given so we will use t-test for one sample.