Question

A study is done to determine if students in the California state university system take longer to graduate, on average, than students enrolled in private universities. One hundred students from both the California state university system and private universities are surveyed. Suppose that from years of research, it is known that the population standard deviations are 1.5381 years and 1 year, respectively. The following data are collected. The California state university system students took on average 4.6 years with a standard deviation of 0.5. The private university students took on average 4.2 years with a standard deviation of 0.3. Conduct a hypothesis test at the 5% level. NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

Answer 1

Explanation:

Base on the scenario been described in the question, we can use the following method to solve the given problem

Test the claim at 5% level of significance.

0: − ≤ 0

: − > 0

Since the population standard deviations are known we can use z-distribution.

Test statistic is

=

√

1

2

1

+

2

2

2

=

4.5 − 4.1

√

1.58112

100 +

1

2

100

= 2.14.

Critical value for 5% level of significance:

zcrit = 1.645.

We reject the null hypothesis at 5% level of significance because the test statistic = 2.14 is bigger than

critical value zcrit= 1.645. There is evidence to conclude that students in the California state university

system take on average longer to graduate, than students enrolled in private universities.