1. Suppose you are the manager of Speedy Oil Change which claims that it will change the oil in customers' cars in less than 30 minutes on average. Further suppose that several complaints have been filed from customers stating that their oil change took longer than 30 minutes. Upper-level management at Speedy Oil Change headquarters has requested that you investigate the complaints. To begin your investigation, you randomly audit 36 oil changes performed by Speedy Oil Change and record the time each customer waited for the oil change. The number of minutes to complete each of the 36 oil changes is reported below.
|
42
|
29
|
19
|
11
|
10
|
27
|
|
41
|
27
|
22
|
26
|
28
|
32
|
|
17
|
15
|
25
|
35
|
32
|
22
|
|
13
|
31
|
17
|
30
|
33
|
25
|
|
18
|
24
|
28
|
21
|
40
|
19
|
|
34
|
30
|
14
|
23
|
22
|
10
|
(Data similar to https://org.elon.edu/econ/sac/Descriptive.htm)
In the questions below, you will test if the mean is significantly less than 30minutes at a significance level of 0.01. Show all five steps as we did in class, include
1. List the requirements that should be met for this hypothesis test.
2. Write the null and alternative hypothesis.
3. Calculate the test statistic and the P-value. Label each accordingly.
4. Would you reject the null hypothesis? Justify your answer using a complete sentence and proper grammar.
5. Is the company fulfilling its promise to "change the oil in customers' cars in less than 30 minutes on average?"
2. Researchers wondered whether the size of a person's brain was related to the individual's mental capacity. They selected a sample of right-handed introductory psychology students who had SAT scores higher than 1350. The subjects took the Wechsler Adult Intelligence Scale-Revised to obtain their IQ scores. MRI scans were performed at the same facility for the subjects. The scans consisted of 18 horizontal MR images. The computer counted all pixels with a nonzero gray scale in each of the 18 images, and the total count served as an index for brain size.
| MRI Count |
IQ |
| 816,932 |
133 |
| 951,545 |
137 |
| 991,305 |
138 |
| 833,868 |
132 |
| 856,472 |
140 |
| 852,244 |
132 |
| 790,619 |
135 |
| 866,662 |
130 |
| 857,782 |
133 |
| 948,066 |
133 |
a) On the axes above, draw a scatter diagram treating MRI count as the explanatory variable and IQ as the response variable. Label the graph!
b) Test whether there is a linear relationship between MRI count and IQ.
c) Predict the IQ score for a subject who has an MRI count of 850,000.
3. One of the biggest factors in determining the value of a home is the square footage. The following data represent the square footage and asking price (in thousands of dollars) for a random sample of homes for sale in Naples, Florida, in December 2010.
| Square Footage |
Asking Price ($) |
| 1148 |
154,000 |
| 1096 |
159,900 |
| 1142 |
169,000 |
| 1288 |
169,900 |
| 1322 |
170,000 |
| 1466 |
179,900 |
| 1344 |
180,000 |
| 1544 |
189,000 |
a) On the axes above, draw a scatter diagram treating the square footage as the explanatory variable and asking price as the response variable. Label the graph!
There is a linear relationship between the square footage and asking price. For each of the following, use the proper format for the monetary values.
b) State the linear correlation coefficient
c) Find the least-squares regression line.
d) Predict the asking price if the square footage is 1500.
e) Would a prediction for the asking price of a home that is 3350 square feet be reasonable? Why or Why not? Use a complete sentence and proper grammar.
f) Interpret the slope. Use a complete sentence and proper grammar.
g) Is it reasonable to interpret the y-intercept? Why or why not?