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 \alpha α = 0.05, is there sufficient evidence that state senators are on average younger than the Senators in Washington? What is the statistic value? Round your answer to the nearest hundredths.

Answer 1

Solution :

Given that,

Population mean = =

Sample mean = =

Population standard deviation = =

Sample size = n =

Level of significance = = 0.05

This is a left (One) tailed test,

The null and alternative hypothesis is,  

Ho: 60.35

Ha: 60.35

The test statistics,

Z =( - )/ (/n)

= ( 55.4 - 60.35 ) / ( 6.5 / 40 )

= -4.82

P-value = P(Z < z )

= P(Z < -4.82 )

= 0

The p-value is p = 0, and since p = 0 < 0.05, it is concluded that the null hypothesis is rejected.

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