Question

2. (20 pts) Data was collected on weekly food expenditures from a random sample of n=19 urban households (this includes restaurant expenditures). For this data, the sample mean and standard deviation (rounded to the nearest dollar) are $110 and $30 respectively. (a) Suppose that food expenditures in the population from which this data was collected has a Normal distribution. Construct a 95% confidence interval for the population mean food expenditure. (Possible quantiles for this calculation are provided in the table above problem #1.) (b) Write a sentence, in context, interpreting the meaning of the confidence interval you calculated in part (a).

Answer 1

Solution :- Given :- Mean (x) = 110$ st devils) = 30$ Sample size (n = 19 df = n-1 dt = 19-1 dr = 18 a At 95% confidence level 't' is, At a = 1-95% a = 1-0.gs. q=0.05 /= 0.05% = 0.025 tal, df = 2.10 At 95%, confidence interval for population mean is, X I tala,df (slun) 110 7 2.10 (30/Nig) 110 + 14.45 ( 96, 124) At 95% CI for Population mean is (96, 124) Interpretation We are 95 % confident that interval 96 to 124 actually does contain the true value of mean. b) from