A nationwide survey of college students was conducted and found that students spend two hours per class hour studying. A professor at your school wants to determine whether the time students spend at your school is significantly different from the two hours. A random sample of fifteen statistics students is carried out and the findings indicate an average of 1.75 hours with a standard deviation of 0.24 hours. Test at the 5% level of significance.
A) The critical value of t is -4.03. The calculated value of t is $\pm$2.145.
B) The critical value of t is $\pm$2.145. The calculated value of t is -4.03.
C) The critical value of t is 1.761. The calculated value of t is -4.03.
D) The critical value of t is $\pm$1.761. The calculated value of t is -1.041.
E) The t-test should not be used. Rather, use the z-test.

Question

A nationwide survey of college students was conducted and found that students spend two hours per class hour studying. A professor at your school wants to determine whether the time students spend at your school is significantly different from the two hours. A random sample of fifteen statistics students is carried out and the findings indicate an average of 1.75 hours with a standard deviation of 0.24 hours. Test at the 5% level of significance.
A) The critical value of t is -4.03. The calculated value of t is  $\pm$2.145.
B) The critical value of t is  $\pm$2.145. The calculated value of t is -4.03.
C) The critical value of t is 1.761. The calculated value of t is -4.03.
D) The critical value of t is  $\pm$1.761. The calculated value of t is -1.041.
E) The t-test should not be used. Rather, use the z-test.

Quizplus · Accepted Answer

Since we are comparing a sample mean to a population mean and our sample size is less than 30, we should use a t-test. Our null hypothesis is that the average time spent studying at our school is not significantly different from two hours per class hour; thus, we have a two-tailed test. 
Using a t-table with 14 degrees of freedom (n-1), we find the critical value for a 5% level of significance to be approximately 2.145. 
Our calculated t-value is (1.75-2)/(0.24/sqrt(15)) = -4.03. 
Since our calculated t-value (-4.03) is less than the absolute value of our critical t-value (2.145), we reject the null hypothesis that the mean time spent studying at our school is not significantly different from two hours per class hour. Therefore, we can conclude that the average time students spend studying at our school is significantly different from two hours per class hour.

A Nationwide Survey of College Students Was Conducted and Found ±\pm±

A Nationwide Survey of College Students Was Conducted and Found $\pm$