Question

​It's tough to find out how much people​ earn, but in​ 2011, a magazine reported that the average​ lawyer's salary in a country was $64,000. Suppose that today you interview a random sample of 55 lawyers in the country and find that the average salary is $75,275​, with a standard deviation of $82,694.Do you think the average​ lawyer's salary today is higher than that reported by the magazine in​ 2011? For this​ problem, assume alphaαequals=0.05.

Let muμ be the population mean​ lawyer's salary in the country.

Determine the null and alternative hypotheses.

H0 : u = 64,000

HA : u > 64,000

Test statistic is 1.01

What is the P-Value?

Answer 1

Solution :

= 64000

= 75275

= 82694

n = 55

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   = 64000

H_a : > 64000

Test statistic = z

= ( - ) / / n

= (75275 - 64000) / 82694 / 55

= 1.01

p(Z > 1.01 ) = 1-P (Z < 1.01) = 0.1582

P-value = 0.1582

= 0.05  

p=0.1582 ≥ 0.05, it is concluded that the null hypothesis is not rejected.

There is not enough evidence to claim that the population mean μ is greater than 64000, at the 0.05 significance level.