Question

A student group claims that first-year students at a university must 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 class survey finds that the average study time claimed by 272 students is xbar= 141 minutes, with a sample standard deviation of 66.
Regard these students as a random sample of all first-year students and suppose we know that the study times follow a Normal distribution.

What is the standard error of the sample mean?

Consider the hypotheses H0: µ = 150 against Ha: µ < 150.

What is the value of the test statistic? Give your answer to two decimal places.

The p-value for the correct test statistic is 0.0126. What do you conclude at the a = 0.05 level?

We do not have enough evidence to say that students are not studying 2.5 hours per night during the school week.
We have strong evidence that, on average, students study less than 2.5 hours per night during the school week.

Answer 1

Answer:

We have strong evidence that on average, students study less than 150 minutes per night during the school week

Step-by-step explanation:

Normal distribution:

mean     μ₀ = 150

Sample:

Sample size    n = 272

Sample mean   x = 141

Sample standard deviation  s  = 66

The standard error of the sample mean  SE = σ /√n

SE = 66/√272

SE = 66 / 16,49

SE = 4

Test Hypothesis:

Null hypothesis                            H₀             x  =   μ₀

Alternative hypothesis                Hₐ            x <    μ₀

z(s)  test statistics is:

z(s)  =  ( x  -  μ₀ ) / s/√n

z(s) = - 9 /4

z(s) =  -  2,25

p-value  for that z(s)      p-value  = 0,0122

Then for α =  0,05 p-value < 0,05

We are in the rejection region we need to reject H₀