Question

How do I find the standard error?

The U.S. Center for Disease Control reports that the mean life expectancy was 47.6 years for whites born in 1900 and 33.0 years for nonwhites. Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span was 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, the mean life span was 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test to see if the mean life spans in the county were the same for whites and nonwhites. (a) State the null and alternative hypotheses. (Let w = white, and nw = nonwhite.) O Ho: Mw€ Inw Ha: Uw = Unw Ho: Mw = Unw Ha: Mw # Unw O Ho: Mw = Unw Ha: Mw< Unw O Ho: Uw = Unw Ha: Mw > Hnw (b) In symbols, what is the random variable of interest for this test? (Let w = white, and nw = nonwhite.) O uw - Unw Xow (c) The standard error of (Ăw – Xnw) equals 0.1736 X (Round to 3 decimal places)

Answer 1

Pooled standard deviation Sp = sqrt [ (n1 -1 ) S²1+ (n2 -1 ) S²2 / n1 + n2 -2 ]

= sqrt [ (124-1) * 12.7² + (82-1) * 15.6² / (124+82-2 )]

= 13.9240

Standard error = sqrt [ Sp ( 1/ n1 + 1/n2) ] sqrt [ 13.9240 * ( 1 / 124 + 1 / 82) ]

= 0.531