Question

9A A personnel researcher has designed a questionnaire and she would like to estimate the average time to complete the questionnaire. Suppose she samples 100 employees and finds that the mean time to take the test is 27 minutes with a standard deviation of 4 minutes. Construct a 90% confidence interval for the mean time to complete the questionnaire. Also, write a short explanation about the findings to the human resources director of your company summarizing the results. – Use Excel for this analysis.

9B. For the problem in part A, the human resources director wants to know whether these is sufficient sample evidence to conclude that the average time to complete the questionnaire is not 27 minutes. Set up the hypotheses (in statistical terms) and, based only on the confidence interval you have constructed in part A, what would you conclude regarding the hypotheses?

H0 :

H1 :

Answer 1

Solution:

A)Given:

Sample size = n = 100

Sample mean = x̄ = 27 minutes

Sample standard deviation =s =4 minutes

We have to find 90% confidence interval.

Given confidence level = 0.90

Therefore, α = level of significance= 1-0.90=0.10

To find 90% confidence interval, formula to be used is,

Lower bound = x̄ - E

Upper bound = x̄ + E

Where E is margin of error and can be found using excel formula:

=CONFIDENCE(0.10,4,100)

Hence, E = 0.658

Therefore, 90% confidence interval is,

Lower bound = 27-0.658 = 26.342

Upper bound = 27+0.658 =27.658

Hence, average time to complete the questionnaire is between interval (26.342,27.658)

B)

Now we have to test, null and alternative hypothesis,

H₀:μ = 27

H_a:μ ≠ 27

90% confidence interval for mean is (26.342,27.658)

27 contained in the above interval. Hence null hypothesis is not rejected.

Therefore, there is insufficient sample evidence to conclude that the average time to complete the questionnaire is not 27 minutes.

Done