Question

Think of a problem that you may be interested in that deals with a comparison of two population means. Propose either a confidence interval or a hypothesis test question that compares these two means. Can someone give me an example, please?

Answer 1

Let us we take a example for test of significance for difference of Means:

Consider a survey of buying habits, 400 women shoppers are chosen at random in a super market 'A' located in a certain section of the city. Their average weekly food expenditur is RS 250 with a standard deviation of Rs 40. For 400 women shoppers chosen at random in super market 'B' in another section of the city, the average weekly food expenditure is Rs 220 with a standard deviation of Rs 55. Test at 1% level of significance whether the average weekly food expenditure of the two population of shoppers are equal.

Solution: In the usual notation, we are given that,

n1=400 x1bar=250 s1= 40

n2= 400 x2bar=220 s2=55

H0: mue1=mue2: the average weekly food expenditure of the two populations of shppers are equal.

H1: mue1=(not equal)=mue2

Test statistics: since sample are large, under H0, the test statistic is:

Z= x1bar-x2bar/(square root(sigma^2/n1+sigma^2/n2))

Z = 8.82

Conclusion: Since |Z| is much greater than 2.58, the null hypothesis is rejected at 1% level of significance and we conclude that the average weekly expenditure of two populations of shoppers in markets A and B differ significantly.