Question

According the the U.S. Department of Education, full-time graduate students receive an average salary of $15,000 with a standard deviation of $1,200. The dean of graduate studies at a large state university in PA claims that his graduate students earn more than this. He surveys 100 randomly selected students and finds their average salary is $16,000. Use a significance level of 0.05 to test if there is evidence that the dean's claim is correct. What are the hypotheses

Answer 1

Answer:

Step-by-step explanation:

Given that :

population Mean = 15000

standard deviation= 1200

sample size n = 100

sample mean = 16000

The null and the alternative hypothesis can be computed as follows:

$\mathtt{H_o : \mu = 15000 }\\ \\ \mathtt{H_1 : \mu > 15000}$

Using the standard normal z statistics

$z = \dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}}$

$z = \dfrac{16000 -15000}{\dfrac{1200 }{\sqrt{100}}}$

$z = \dfrac{1000}{\dfrac{1200 }{10}}$

$z = \dfrac{1000\times 10}{1200}$

z = 8.333

degree of freedom = n - 1 = 100 - 1 = 99

level of significance ∝ = 0.05

P - value from the z score = 0.00003

Decision Rule: since the p value is lesser than the level of significance, we reject the null hypothesis

Conclusion: There is sufficient evidence  that the Dean claim for his graduate students earn more than average salary of $15,000