Question

A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40. The value of the test statistic is

Answer 1

Step-by-step explanation:

Population Mean (u) = 3.50

Sample (n)= 36

Sample mean (x) = 3.60

Population standard deviation (s)= 0.40

Test statistics:

(Null hypothesis) H0: u= 3.5 (Population mean is equal to 3.5)

(Alternate hypothesis) H1: u> 3.5 (Population mean is greater than 3.5)

Z= $\frac{x-u}{\frac{s}{\sqrt{n} } }$= $\frac{3.60-3.50}{\frac{0.4}{\sqrt{36} } }$= $\frac{0.10}{0.067}$= 1.5

critical value= Z0.05= 1.645 (From Z table)

Since, Z value is less than critical Z value that is Z<1.645

We cannot reject null hypothesis

So, we decide to reject that the mean GPA of graduates exceeds 3.50