Sales in thousands of units of a particular item by quarter

Sales, in thousands of units, of a particular item by quarter are given in order of occurrence for the last 4 years.

3 6 4 7 2 8 3 5 3 6 5 8 2 7 1 6

At an alpha of .05 is there any evidence of a non-random effect in sales? Use chi-squared to solve.

Solution

Ho: there is no evidence of a non random effect in sales. H1: there is a evidence of a non random effect in sales. Given n=16 & observed frequencies, then expected frequency=(total of observed frequency)/16=76/16=4.75, then chi-square cal=summation over i =1 to 16[(Oi-Ei)²/Ei]=15.7893. The table value of chi-square value (n-1)=(16-1)=15 at 0.05% level of significance is 24.996. Chisquare cal<chisquare table value, so we accept null hypothesis. Therefore, there is no evidence of a non random effect in sales.