Question

5 multiple choice 1.43 points a professor at cypress college wanted to determine the average commute time for students attending cypress college. the professor randomly selects students across campus and asks them to disclose how long it takes them to get to campus (in minutes). the data is given below. construct and interpret a 90% confidence interval for the mean commute time for a cypress college student. (make sure to verify the requirements before constructing the confidence interval.) 12 13 16 22 35 42 5 16 25 19 37 60 we are 90% confident that the mean commute time for a cypress college student will lie between 19.2 and 30.8 minutes. we are 90% confident that the mean commute time for a cypress college student will lie between 18.5 and 31.5 minutes. we are 90% confident that the mean commute time for a cypress college student will lie between 17.1 and 33.3 minutes. we are 90% confident that the mean commute time for a cypress college student will lie between 16.8 and 33.2 minutes.

Explanation:

Step1: Calculate sample mean

Data: 5,12,13,16,16,19,22,25,35,37,42,60. Sum = 302. Mean $\bar{x}=\frac{302}{12}\approx25.17$.

Step2: Calculate sample standard deviation

Variance: $\frac{\sum(x_i-\bar{x})^2}{11}\approx231.36$. Std dev $s\approx15.21$.

Step3: Find t-critical value

df=11, 90% confidence: $t_{0.05,11}=1.796$.

Step4: Compute margin of error

$E=1.796\times\frac{15.21}{\sqrt{12}}\approx8.13$.

Step5: Construct confidence interval

$\bar{x}\pm E\approx25.17\pm8.13=(17.04,33.30)\approx(17.1,33.3)$.

Answer:

C. We are 90% confident that the mean commute time for a Cypress College student will lie between 17.1 and 33.3 minutes.