Discuss the below:
Q1. During recent seasons, Major League Baseball has been criticized for the length of the games. A report indicated that the average game lasts 3 hours and 30 minutes. A sample of 17 games revealed the following times to completion. (Note that the minutes have\ been changed to fractions of hours, so that a game that lasted 2 hours and 24 minutes is reported at 2.40 hours.
Can we conclude that the mean time for a game is less than 3.50 hours? Use the .05 significance level.
| 2.98 |
2.4 |
2.7 |
2.25 |
3.23 |
3.17 |
2.93 |
3.18 |
| 2.38 |
3.75 |
3.2 |
3.27 |
2.52 |
2.58 |
4.45 |
2.45 |
|
|
|
|
|
|
|
|
Q2. Banner Mattress and Furniture Company wishes to study the number of credit applications received per day for the last 300 days. The information is reported on the next page. To interpret, there were 50 days on which no credit applications were received, 77 days on which only one application was received, and so on. Would it be reasonable to conclude that the population distribution is Poisson with a mean of 2.0? Use the .05 significance level.
Hint: To find the expected frequencies use the Poisson distribution with a mean of 2.0. Find the probability of exactly one success given a Poisson distribution with a mean of 2.0. Multiply this probability by 300 to find the expected frequency for the number of days in which there was exactly one application. Determine the expected frequency for the other days in a similar manner.
Q3. Martin Motors has in stock three cars of the same make and model. The president would like to compare the gas consumption of the three cars (labeled car A, car B, and car C) using four different types of gasoline. For each trial, a gallon of gasoline was added to an empty tank, and the car was driven until it ran out of gas. The following table shows the number of miles driven in each trial. Using the .05 level of significance:
a. Is there a difference among types of gasoline?
b. Is there a difference in the cars?