Question

The lecturer claims that the underlying true average mark for this exam is 67. The lecturer wants to test if the new cohort marks (sample mean: 52.222, sample variance: 153.651, n: 130) support this hypothesis. The minimum and maximum marks in the new cohort are 27.421 and 76.607 respectively.

a. Write down the null and alternative hypothesis we would use to test the lecturers claim that the true average mark is 67.

b. What are the assumptions for conducting a hypothesis test around this data? Are these satisfied? You may assume that more than 1300 students take the course each year.

c. Calculate the p-value for your hypothesis.

d. What is the conclusion for your hypothesis test?

Answer 1

a. Write down the null and alternative hypothesis we would use to test the lecturers claim that the true average mark is 67.

Here, we have to use t test for population mean.

Null hypothesis: H₀: The true average mark is 67.

Alternative hypothesis: H_a: The true average mark is not 67.

b. What are the assumptions for conducting a hypothesis test around this data? Are these satisfied? You may assume that more than 1300 students take the course each year.

We assume that the sample data is coming from normally distributed population. Sample size is adequate as compared to population size. That is, 10% of 1300 is 130. Also, from given minimum and maximum values, it is observed that there are no outliers exists in the data.

c. Calculate the p-value for your hypothesis.

Test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

We are given

Xbar = 52.222

S^2 = 153.651

S = 12.3956

n = 130

df = n – 1 = 129

t = (52.222 – 67) /[ 12.3956/sqrt(130)]

t = -13.5931

P-value = 0.00

(by using t-table or excel)

d. What is the conclusion for your hypothesis test?

Here, P-value < α = 0.05

So, we reject the null hypothesis

There is insufficient evidence to conclude that the true average mark is 67.