AP Statistics Quiz 10.2 1.

Mrs. Toguchi wants to determine if politicians tend to have higher salaries, on average, than first

responders (specifically emergency medical technicians, EMTs). Independent random samples from each

of these two professions were selected and their salaries were recorded. The data are summarized below.

a) the distribution of salary in each group is skewed right. The use of two-sample t procedures is still justified why?

b) construct and interpret a 99% confidence interval for the difference in the true mean salaries for politicians and EMTs

Hello some data related to your question is missing attached below is the missing data

a) we will reject the null hypothesis hence it can be determined that the salary of politicians is greater than that of EMTs through the use of two-sample t procedures. since ( to > critical value )

b) ( 3.819 , 8.5226 )

Step-by-step explanation:

Applying the Given data:

The test hypothesis :

H0 : μ1 = μ2

Ha : μ1 > 2

A) since ( to > critical value ) we will reject the null hypothesis hence it can be determined that the salary of politicians is greater than that of EMTs through the use of two-sample t procedures

B ) construct and interpret

next calculate the SP value

=

where: S1 = 7524 , n1 = 50 , n2 = 100 , S2 = 5551   ( input values into equation above )

∴ = 39354491.3716

hence : = 6273.32

next calculate the value of test statistic

to = ( X1 - X2 - Δo ) / Sp

where: X1 = 61234 , X2 = 54529 , Sp = 6273.32 , n1 = 50 , n2 = 100  ( input values into equation above )

to = 6705 / 1086.5702 = 6.1708

Df ( degree of freedom ) = n1 + n2 - 2 = 148

critical value at ∝ = 0.01  = ± 2.3518  ( using excel function : T.INV(0.01,148) )

hence the confidence Interval

= ( 6.1708 ± 2.3518 )

= ( 3.819 , 8.5226 )

the answer is 62