Question

In a survey of buying habits, 400 women
shoppers are chosen at random in super
market A. Their average weekly food expenditure
is rs 250 with a S.D of RS 40. for 500 women shoppers
choosen at supermarket B , the average weekly
food expenditure is rs 220 with a S.D. of RS 45. Test
at 1% level of significance whether the average
food expenditures of the two groups are equal

Answer 1

Step-by-step explanation:

Given In a survey of buying habits, 400 women  shoppers are chosen at random in super market A. Their average weekly food expenditure  is rs 250 with a S.D of RS 40. for 500 women shoppers  choosen at supermarket B , the average weekly  food expenditure is rs 220 with a S.D. of RS 45. Test  at 1% level of significance whether the average  food expenditures of the two groups are equal

• Now n1 = 400, X1 = Rs 250 S1 = Rs 40
• Also n2 = 400, X2 = Rs 220, S2 = Rs 55
• The average weekly food expenditure will be Null hypothesis.
• Now the test will be given by t = X1 – X2 / √S1^2 / n1 + S2^2 / n2
• Where X1 and X2 are Mean expenditure of shoppers in supermarket A and B.
• S1 and S2 are SD of shoppers in A and B
• Now t = 250 – 220 / √40^2 / 400 + 55^2 / 400
• Or t = 30 / √4 + 7.5625
•        = 30 / 3.4003
•   t = 8.8228

So t is greater than 3 and the null hypothesis is rejected at 1% level of significance. Therefore the average of two shoppers differ significantly.

Reference link will be

https://brainly.in/question/11976850