8.3 #3 Teaching Assistants Stipends A random sample of stipends of teaching assistants in economics is listed. Is there sufficientevidence at the a=0.05 level to conclude that the average stipend differs from $15,000? The stipends listed (in dollars) are forthe academic year. Use the P-value method. Assume the variable normally distributed. Use a TI-83 Plus/TI-84 Plus calculator.12,283 13.185 13.419 14,356 12,00017.604 11,981 14.000 14.000(a) State the hypotheses and identify the claim.HPH-=$ 15000 not claim15000 claimThis hypothesis test is a two-tailedVYP value=#3

Given that The population mean =$15000 Data 12,283,13,185,13419,14356,12,000,17604, 11,981, 14,000, 14,000 we have to test hypothesis for the claim Is there sufficient evidence at the α = 0.05 level to conclude that the average stipend differs from $15,000: Solution: Sample size (n)=9 Sample mean =Σx/n=122828/9=13647.56 Sample standard deviation (s)=√Σ(xi - x̄)2/(n-1) =√24023834.22/(9-1) =√3002979.278 s=1732.91 Since the population standard deviation is unknown we use t test test statistic t=(x̄-μ)/s/√n =(13647.56-15000)/1732.91/√9 t=-2.341 P value can be computed using the excel formula degree of freedom (df)=n-1=9-1=8 =T.DIST(-2.341,8,2) =0.02367 For two tailed =2×0.02367 =0.0474 Decision: Since the p value=0.0474 is less than 0.05 so we reject the null hypothesis... Conclusion: It is concluded that there is sufficient evidence to support the claim that that the average stipend differs from $15,000....