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

Answer:

Shown below.

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:

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

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:

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