Question

Professor Ricahrds wants to estimate the population mean performance for his cybercrime class of 25 students. The average this semester is 84 with a standard deviation of 12.6. In the past 20 semesters that the professor has taught this class, the average performance in the class was a 78.5.

Test the null hypothesis that the current class is the same as the previous classes against the alternative hypothesis that this current semester has students who are genuinely smarter. What do you conclude? Use an alpha level of 0.01. State each step in your hypothesis test

Answer 1

STEP 1

Null hypothesis Ho :- mean is equal to 78.5

Alternate hypothesis Ha:- mean is greater than 78.5

STEP 2

we will reject the null hypothesis when the p value is less than 0.01 level

STEP 3

Given that x(bar) = 84, standard deviation s = 12.6, sample size n = 25 and mean(mu) = 78.5

test statistics t =

degree of fredom = n-1 = 25 - 1 = 24

using t distribution with df(24) and t calculated value(2.18) for a right tailed hypothesis, we get

p value = 0.0196

STEP 4

p value is more than significance level of 0.01. Failed to reject the null hypothesis

We can conclude that there is insufficient evidence to support that the current semester has students who are genuinely smarter