Question

# The college board claims that 32% of community college students take five semesters to complete a...

The college board claims that 32% of community college students take five semesters to complete a two-year program. In a survey of 1400 randomly selected community college students enrolled in a two-year program, 401 of them took five semesters to complete their two-year program. Test the college board's claim at a level of significance of 0.01.

Calculate the test statistics associated with this hypothesis.

(Round your answer to 2 decimal places)

Calculate the P-Value associated with the test statistics that you have found in part 3.

(Round your answer to 4 decimal places)

Based on your finding in part 4, please choose the appropriate decision.

 Reject the Null Hypothesis Fail to Reject the Null Hypothesis Accept the Alternative Hypothesis Accept the Null Hypothesis

Based on your finding from part 5,

a) What type of error could have occurred potentially?

b.) Explain the reasoning of the type of error of your choice.

Based on your results from parts 1-5, which one of the statements below would be the correct interpretation of this hypothesis testing?

 At a level of significance of 0.01, the College Board claim is correct. At a level of significance of 0.01, the College Board claim is not correct. At a level of significance of 0.01, there is enough evidence to support the claim. At a level of significance of 0.01, there is not enough evidence to support the claim.

The statistical software output for this problem is:

From above output:

Test statistic = -2.69

P - value = 0.0071

Reject the Null Hypothesis

Based on your finding from part 5,

What type of Error: Type I error

Explain the reasoning: Since we are rejecting the null hypothesis, the associated error could be Type I error.

Conclusion: At a level of significance of 0.01, the College Board claim is not correct.