7. Retail stores are interested in how they can best sell products to consumers.

Question

7. Retail stores are interested in how they can best sell products to consumers. The more time that consumers spend in stores positively affects how much they spend. A national study has shown that the mean shopping time for a woman acc children in national housewares store is normally distributed with a mean of 7.3 minutes. A research team is interested in shopping habits in the R random sample of 17 women shoppers with children in a large housewares store in the Richmond area found they spend an average of 8.1 minutes in the store, with a standared ompanied by ichmond area. A deviation of 1.4 minutes. Use a 5% level of significance to test the claim that the average shopping time for women with children in the Richmond area is higher than the national average for this type of store. (9 points)

Explanation / Answer

The national mean time spent at a store by a woman is 7.3 min.

For validating this claim we will formulate the following hypothesis test (lower tail test)

Null hypothesis: Ho: u >= 7.3

Alternate hypothesis Ha: u<7.3

Now in the random sample of n=17 women the avg xbar= 8.1 min while std.dev s = 1.4 min

significance level to be used is 0.05

The t statistic t = xbar - u/ (s/SQRT(n)) = (8.1 - 7.3) / (1.4/SQRT(17)) = 2.35

Now since this is a lower tail test, we will find the area to the left of t= -2.35 on the std. normal curve

p = 0.0158 which can be found using technology or the t dist table

Now 0.015<0.05 i.e. p <alpha hence we will reject the null hypothesis

This shows that average shooping time in the Richmod area is not higher than the national average

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