Question

A student group claims that first-year students at a university should study 2.5 hours (150 minutes) per night during the school week. A skeptic suspects that they study less than that on the average. A survey of 51 randomly selected students finds that on average students study 138 minutes per night with a standard deviation of 32 minutes. What conclusion can be made from this data? Select one:

A) The p-value is greater than .05, therefore we do not have enough evidence to conclude that students study less than 150 minutes per night.

B) The p-value is less than .05, therefore we conclude that students study greater than 150 minutes per night.

C) The p-value is less than .05, therefore we conclude that students study less than 150 minutes per night.

D) We do not have enough information to make a conclusion about this study. The p-value is less than .05, therefore we do not have enough evidence to conclude that students study less than 150 minutes per night.

Answer 1

Solution :

= 150

=138

=32

n = 51

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :   = 150

H_a : < 150

Test statistic = z

= ( - ) / / n

= (138-150) /32 / 51

= −2.68

P(z <−2.68 ) = 0.0037

P-value = 0.0037

= 0.05  

P-value < 0.05

p=0.0037<0.05, it is concluded that the null hypothesis is rejected.

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean \muμ is less than 150, at the 0.05 significance level