Question

A researcher in the social sciences is concerned that a sample of respondents to a mail-out survey may not be representative of the target population under study. Specifically, the researcher is concerned that the sample of respondents are significantly younger than the population average of 37. For the survey, the social scientist obtained a mean age of 22.4 years, and a standard deviation of 6.8 for a sample of 40 respondents. What can the researcher conclude if the probability of a Type I error is to be at most 0.01? Use Microsoft Excel to solve this question (Show all Excel formulas used)

Answer 1

null hypothesis: HO: μ		=	37
Alternate Hypothesis: Ha: μ		<	37

0.01 level with left tail test and n-1= 39 df, critical t=				-2.426 # use formula: -t.inv(0.01,39)
Decision rule :reject Ho if test statistic t<-2.426

population mean μ=	37
sample mean 'x̄=	22.400
sample size   n=	40.00
sample std deviation s=	6.800
std error 'sx=s/√n=6.8/√40 =	1.0752

test stat t ='(x-μ)*√n/sx=(22.40-37)/1.0752 =

-13.579

p value      =

0.0000 # use formula tdist(13.579,39,1)

since p value <0.01 , we reject null hypotheiss and conclude that sample of respondents are significantly younger than the population average of 37.