A government agency reports that the mean amount of earnings for full-time worke

Question

A government agency reports that the mean amount of earnings for full-time workers ages 25 to 34 with a master's degree is less than $70,000. In a random sample of 20 full-time workers ages 25 to 34 with a master's degree, the mean amount of earnings is $66, 230 and the sample standard deviation is $5945. At, is there enough evidence to support the agency's claim? Assume the population is normally distributed. (a) State and (b) Specify the level of significance (c) Find the degree, of freedom, the critical value(s) and the rejection region. (d) Find the standardized test statistic/for the mean. Sketch the graph (e) State if you reject or fail to reject. (f) State if the claim can or cannot be supported and why.

Explanation / Answer

a) null hypothesis: mean >=70000

alternate hypothesis:mean<70000

b) level of significance =0.05 (as it is not mentioned)

c)degree of freedom =n-1=20-1=19

critical value =-1.729

rejection region t<-1.729

d)for std error=std deviation/(n)1/2 =1329.342

hence test stat t=(X-mean)/std error =(66230-70000)/1329.342==-2.836

e)as test stat is in rejection region; reject null hypothesis

f)we have sufficient evidence to conclude that mean amount of earning for worker in age group 25-34 with masters degree is less then 70000

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