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:

n:268

Sample mean time to​ graduate, in years 5.49

Sample standard deviation time to​ graduate, in years 1.144

No Transfer

n 1175

Sample mean time to​ graduate, in years 4.51

Sample standard deviation time to​ graduate, in years 1.013

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

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

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

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

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

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

B.The population is given to be normally distributed.

C. The samples are independent.

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

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

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

alpha equals 0.01α=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 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

D. 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

Answer 1

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

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

​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.

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

The population is given to be normally distributed.(B)

The samples are independent.(C)

c).Determine the null and alternative hypotheses.

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

Upper H1​:mu Subscript community college Baseline greater than mu Subscript no transferμcommunity college>μno transfer (A)

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