Question

A researcher with the Department of Education followed a cohort of students who graduated from high school in a certain​ year, monitoring the progress the students made toward completing a​ bachelor's degree. One aspect of his research was to determine whether students who first attended community college took longer to attain a​ bachelor's degree than those who immediately attended and remained at a​ 4-year institution. The data in the table attached below summarize the results of his study. Complete parts​ a) through​ e) below.

	Community College Transfer	No Transfer
n	263263	11811181
Sample mean time to​ graduate, in years	5.315.31	4.414.41
Sample standard deviation time to​ graduate, in years	1.153	1.004

a) What is the response variable in this​ study? What is the explanatory​ variable?

A. The response variable is the number of students. The explanatory variable is the time to graduate.

B. The response variable is the use of community college or not. The explanatory variable is the time to graduate.

C. The response variable is the time to graduate. The explanatory variable is the use of community college or not.

D. The response variable is the time to graduate. The explanatory variable is the number of students.

b) Explain why this study can be analyzed using inference of two sample means. Determine what qualifications are met to perform the hypothesis test about the difference between two means. Select all that apply.

A. The samples can be reasonably assumed to be random.

B. The sample sizes are not more than​ 5% of the population.

C. The samples are independent.

D. The sample sizes are large​ (both greater than or equal to​ 30).

E. The population is given to be normally distributed.

c) Does the evidence suggest that community college transfer students take longer to attain a​ bachelor's degree?

Use an α=0.01 level of significance. Perform a hypothesis test. Determine the null and alternative hypotheses.

A. Upper H 0H0​: mu Subscript community college Baseline equals mu Subscript no transferμcommunity college=μno transfer​,

Upper H 1H1​: mu Subscript community college Baseline greater than mu Subscript no transferμcommunity college>μno transfer

B. Upper H 0H0​: mu Subscript community college Baseline greater than mu Subscript no transferμcommunity college>μno transfer​,

Upper H 1H1​: mu Subscript community college Baseline less than mu Subscript no transferμcommunity college<μno transfer

C.Upper H 0H0​: mu Subscript community college Baseline less than mu Subscript no transferμcommunity college<μno transfer​,

   Upper H 1H1​: mu Subscript community college Baseline greater than mu Subscript no transferμcommunity college>μno transfer

D.Upper H 0H0​: mu Subscript community college Baseline equals mu Subscript no transferμcommunity college=μno transfer​,

   Upper H 1H1​: mu Subscript community college Baseline less than mu Subscript no transferμcommunity college<μno transfer

Determine the test statistic.

t=_______ ​(Round to two decimal places as​ needed.)

Determine the​ P-value.

​P-value=_______ ​(Round to three decimal places as​ needed.)

Should the hypothesis be​ rejected?

▼(Do not reject, Reject) the null hypothesis. The evidence ▼(does, does not) suggest that community college transfer students take longer to attain a​ bachelor's degree at the

α=0.01 level of significance.

d) Construct a 99​% confidence interval for mu Subscript community college Baseline minus mu Subscript no transferμcommunity college−μno transfer

to approximate the mean additional time it takes to complete a​ bachelor's degree if you begin in community college.

The confidence interval is the range from _______ to ________.​(Round to three decimal places as​ needed.)

e) Do the results of parts​ c) and​ d) imply that community college causes you to take extra time to earn a​ bachelor's degree?

No

Yes

Answer 1