For the next two questions, PLEASE show your work for all 6 steps of hypothesis

Question

For the next two questions, PLEASE show your work for all 6 steps of hypothesis testing (hypotheses, sampling distribution, critical value/region(s), test statistic, rejection, decision, and standard interpretation including calculating confidence intervals where appropriate). Round the standard error to two decimal places and use alpha = .05. You live in a socially conservative area and suspect that adolescents in your town consume fewer alcoholic beverages than the national average of 8.8 alcoholic beverages per month. Use the following data to conduct an appropriate statistical test of these ideas. n = 128 X = 7.8 drinks s_x = 1.8 drinks

Explanation / Answer

here nulll hypothesis: mean >=8.8

alternate hypothesis: mean <8.8

sapling distribution is t as we do not know std deviation.

critical value =-1.657 ; decision rule : reject Ho if test stat t<-1.657

std error of mean =std deviation/(n)1/2 =0.159

hence test stat t=(X-mean)/strd error =(7.8-8.8)/0.159 =-6.2854

as test stat t is in critical region we reject null hypothesis, and conclude that twon consumtion of alcoholic beverages is less then 8.8.

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