Question

According to an estimate, the mean income of attorneys was $66,271 in 2015. A researcher wanted to check if the current mean income of attorneys is greater than $66, 271. A random sample of 64 attorneys taken by this researcher produced a mean income of $69,484 with a standard deviation of $11,500. Test at the 5 % significant level whether the current mean income of all attorneys is greater than $66,271. Explain your conclusion in words.

Answer 1

Solution :

= 66271

= 69484

s = 11500

n = 64

This is the right tailed test .

The null and alternative hypothesis is

H0 :   = 66271

Ha : > 66271  

Test statistic = t

= ( - ) / s/ n

= (69484 - 66271) / 11500 / 64

= 2.235

p(Z > 2.235 ) = 1-P (Z < 2.235) = 0.0145

P-value = 0.0145

= 0.05  

0.0145 < 0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that