In: Statistics and Probability
3. The Mathematics & Statistics department at Lancaster University claims that, on average, 25% of students obtain a first class degree. A competitor university is interested in showing that this value is an overestimate. They randomly sample 82 graduates and find that 18 have a host class degree
This is problem of Hypothesis Test for a Proportion
a) To conduct a hypothesis test of a proportion, the following conditions are should be met:
In this context we have,
(sample size)
(no. of success)
First we need to check our assumptions that both np ≥ 10 and n(1−p) ≥ 10
np = 82 × 0.2195 = 17.999 and n(1−p)= 64.001 .Both are greater than 10 so this assumption has been met and we can use the standard normal approximation with this data.
b) Null Hypotheses
Ho: p = 0.25
c) Alternative Hypotheses
Ha: p < 0.25
This corresponds to a left-tailed test, for which a z-test for one population proportion needs to be used.
The z-statistic is computed as follows:
d) We need to find the corresponding level of p from the z value obtained. For this purpose, we need to look at the z table.
The p-value is p=0.2619
e) Since p=0.2619≥0.05, it is concluded that the null hypothesis is not rejected at 95% significant level.
f) NO, we are not agree with the competitor university that the proportion of first-class degrees advertised is an overestimate.