Question

Which factors are relevant to the time a consumer spends looking at a product on the shelf prior to selection? The article "Effects of Base Price Upon Search Behavior of Consumers in a Supermarket" (J. Econ. Psycho., 2003: 637-652) reported the following data on elapsed time (sec) for fabric softener purchasers and washing-up liquid purchasers; the former product is significantly more expensive than the latter. These products were chosen because they are similar with respect to allocated shelf space and number of alternative brands. Calculate a 90% confidence interval for the true difference between the means for the two products.

Answer 1

Shown below.

Step-by-step explanation:

In this case we need to compute a 90% confidence interval for the true difference between the mean elapsed time (sec) for fabric softener purchasers and washing-up liquid purchasers.

It is provided that these products were chosen because they are similar with respect to allocated shelf space and number of alternative brands.

The (1 - α)% confidence interval for the true difference between the means, when the population standard deviations are not known, is given as follows:

`CI=(\bar x_(1)-\bar x_(2))\pm t_{\alpha/2, (n_(1)+n_(2)-2)}* S_(p)*\sqrt{(1)/(n_(1))+(1)/(n_(2))}`

Here,

`\bar x_(1)=\text{sample mean for fabric softener purchasers}\\\bar x_(2)=\text{sample mean for washing-up liquid purchasers}\\S_(p)=\text{pooled standard deviation}`

The formula to compute the value of [pooled standard deviation is:

`S_(p)=\sqrt{((n_(1)-1)s_(1)^(2)+(n_(2)-1)s_(2)^(2))/(n_(1)+n_(2)-2)}`