Question

A study was conducted to determine if the students from the public universities
take longer to graduate than the students from the private universities. 100
students from both the public universities and private universities were
surveyed. Suppose that from the years of research, it was known that the
population standard deviations were 1.58 years and 1 year respectively. The
following data were collected. The public and private universities students took
an average of 4.5 and 4.1 years respectively with a standard deviation of 0.3.
Use a 0.01 level of significance to test the claim.
(i) State the null and alternative hypotheses.

(ii) Is there any evidence to support the claim at α =0.01?

MANUAL CALCULATION

Answer 1

The researcher wants to check that whether the students from the public universities
take longer to graduate than the students from the private universities.

Public universities:

Private universities:

(i).

The null and the alternative hypothesis is,

It is a right-tailed test.

(ii).

The test statistic is,

At the significance level 0.01, the right tailed critical value obtained from z-table is 2.33.

Since the calculated value (2.139) is less than the critical value (2.33), so the researcher does not reject the null hypothesis. Hence the result is insignificant for the study.

Therefore, there is insufficient evidence to support that the students from the public universities take longer to graduate than the students from the private universities.