STAT 3300 Homework #1 Due Friday, 05/15/2020

Note: Answer these questions on a separate piece of paper. In the top right corner, include your name, SMU ID, and course number. Please include a title for the assignment so that it is clear to the graders. If you miss class the day the assignment is turned in, submit this before class in order to receive credit.

Question 1 (20 points total, 5 for each part) In each of the following situations, identify what is wrong and then either explain why it is wrong or change the wording of the statement to make it true.

a) As the degrees of freedom k decrease, the t distribution density curve gets closer to the N (0, 1) curve.

b) The standard error of the sample mean is s 2

n .

c) A researcher wants to test Ho : x? = 30 versus the one-sided alternative Ha : x? < 30. d) The 95% margin of error for the mean µ of a Normal population with unknown ? is the same for all SRS of size n. Question 2 (20 points total, 5 each) The one-sample t statistic for testing Ho : µ = 8 Ha : µ > 8

from a sample of n = 22 observations has the value t = 2.24.

a) What are the degrees of freedom for this statistic?

b) Give the two critical values t? from Table D that bracket t.

c) Between what two values does the p-value of the test fall?

d) Is the value t = 2.24 significant at the 5% level? Is it significant at the 1% level?

Question 3 (20 points total) Although the Environmental Protection Agency (EPA) establishes the tests to determine the fuel economy of new cars, it often does not perform them. Instead, the test protocols are given to the car companies, and the companies perform the tests themselves. To keep the industry honest, the EPA runs some spot checks each year. Recently, the EPA announced that Hyundai and Kia must lower their fuel economy estimates for many of their models. Below is a sample of 16 city miles per gallon (mpg) values for one of the models the EPA investigated:

## [1] 28.0 25.7 25.8 28.0 28.5 29.8 30.2 30.4 26.9 28.3 29.8 27.2 26.7 27.7 29.5 ## [16] 28.0

GIve a 95% confidence interval for µ, the mean city mpg for this model.

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Question 4 (20 points total) Refer to the data from the previous exercise. The vehicle sticker information for this model stated a city average of 30 mpg. Does the sample give us evidence to conclude the mean MPG differs from 30? Perform a significance test using the 0.05 significance level. Be sure to specify the hypotheses, the test statistic, the p-value, and your conclusion.

Question 5 (20 points total) Insurance adjustors are concerned that Dave’s Auto Repair is charging higher-than-necessary prices to their clients. To see if the estimates are unreasonably high, a sample of 10 damaged cars was taken to Dave’s and another repair shop and the estimates (in dollars) were recorded. Here are the results:

Car 1 2 3 4 5 6 7 8 9 10 Dave’s 1410 1550 1250 1300 900 1520 1750 3600 2250 2840 Other 1250 1300 1250 1200 950 1575 1600 3380 2125 2600

a) (4 points) For each car, subtract the estimate of the other garage from Dave’s estimate. Find the mean and standard deviation for the differences. You do not need to find the mean or sd by hand – use a calculator, Excel, or R.

b) (8 points) Test whether the mean difference is positive (which would be consistent with Dave’s charging more for the same car, on average). Show all the steps as demonstrated in class.

c) (8 points) Construct a 95% confidence interval for the difference in estimates.

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Question 1 (20 points total, 5 for each part)
Question 2 (20 points total, 5 each)
Question 3 (20 points total)
Question 4 (20 points total)
Question 5 (20 points total)