1. If you pay more in tuition to go to a top business school, will it necessarily result in a higher probability of a job offer at graduation? Let y = percentage of graduates with job offers and x= tuition cost; then fit the simple linear model, E(y) = β0 + β1X, to the data below. Is there sufficient evidence (at α = 0.05) of a positive linear relationship between y and x?
|
School
|
Annual tuition ($)
|
% with Job Offer
|
|
1
|
39,647
|
94
|
|
2
|
39,279
|
92
|
|
3
|
39,069
|
85
|
|
4
|
38,736
|
98
|
|
5
|
38,353
|
98
|
|
6
|
37,782
|
87
|
|
7
|
37,261
|
85
|
|
8
|
37,138
|
83
|
|
9
|
37,129
|
82
|
|
10
|
36,932
|
95
|
Give the null and alternative hypotheses for testing whether there exists a positive linear relationship between y and x?
A. H0: β0 = 0 B. H0: β1 = 0
Ha: β0 > 0 Ha: β1 < 0
C. H0: β0 = 0 D. H0: β1 = 0
Ha: β0 < 0 Ha: β1 ≠ 0
E. H0: β0 = 0 F. H0: β1 = 0
Ha: β0 ≠ 0 Ha: β1 > 0
Find the test statistic.
Find the p-value.
2. Suppose the mean GPA of all students graduating from a particular university in 1975 was 2.60. The registrar plans to look at records of students graduating last year to see if the mean GPA has decreased. Define notation and state the null and alternative hypotheses for this investigation.
Choose the correct null and alternative hypotheses.
A. H0: μ = 2.60 B. H0: μ = 2.60 C. H0: μ = 2.60
Ha: μ > 2.60 Ha: μ < 2.60 H0: μ ≠ 2.60
D. H0: μ < 2.60 E. H0: μ > 2.60 F. H0: μ ≠ 2.60
Ha: μ = 2.60 Ha: μ = 2.60 H0: μ = 2.60
3. What is the difference between what σx and σ-x measure?
A. σx is the standard deviation of the population and is a measure of the average deviation of the individual values in the population from the mean μx; σ-x; is the standard error of the mean (the standard deviation of a sample) and measures the deviation of a sample from the sample mean
B. σx is the standard deviation of the population and is a measure of the average deviation of the individual values in the population from the mean μx; σ-x; is the standard error of the mean (the standard deviation of the sampling distribution of the sample mean) and measures the deviation of the sample means from sample to sample
C. σx is the standard error of the mean (the standard deviation of the sampling distribution of the sample mean) and measures the deviation of the sample means from sample to sample; σ-x;a; is the standard deviation of the population and is a measure of the average deviation of the individual values in the population of x from the mean μx.
D. σx is the standard error of the mean (the standard deviation of the sampling distribution of the sample mean) and measures the deviation of the sample means from sample to sample; σ-x; is the standard deviation of the population and is a measure of the average deviation of the individual values in a sample from the mean μx.
4. Confidence interval estimation
A. is reliable since X- will will always equal μ.
B. will always result in an interval estimate that includes the true location of the unknown population parameter.
C. is unnecessary if proper sampling techniques are used because the sample mean will always equal the population mean if random sampling is used.
D. is preferred to relying on a point estimate because the confidence interval estimator includes information about the amount of sampling error that might have occurred.