Question

The mean age of Senators in the 109th Congress was 60.35 years. A random sample of 40 senators from various state senates had an average age of 55.4 years, and the population standard deviation is 6.5 years. At α= 0.05, is there sufficient evidence that state senators are on average younger than the Senators in Washington?

We should use

Left- tailed test

Right- Tailed Test

Two- tailed Test

Answer 1

Solution :

= 60.35

= 55.4

= 6.5

n = 40

This is the left tailed test .

The null and alternative hypothesis is

H0 :   = 60.35

Ha : < 60.35

Test statistic = z

= ( - ) / / n

= (55.4 - 60.35) / 6.5 / 40

= -4.816

P (Z < -4.816 ) = 0

P-value = 0.0000

= 0.05  

0< 0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that state senators are on average younger than the Senators in Washington.