Question

The management of a large hardware store is interested in estimating the difference between the mean dollar amount of purchases made by customers who use the store’s credit card and the mean dollar amount of purchases made by customers who use a different credit card. a random sample of 74 customers who used the store’s credit card showed a mean purchase of $107 with a standard deviation of $12. a separate random sample of 58 customers who used a different credit card showed a mean purchase of $132 with a standard deviation of $9. technology was used to calculate that the correct number of degrees of freedom is 129.78.

Answer 1

The margin of error for a confidence interval of 98% that should be used to estimate the difference in the mean purchase is given by $2.355\sqrt{\frac{12^2}{74} +\frac{9^2}{58} }$

What is a confidence interval?

In Statistics, a confidence interval refers to a range of estimated values that defines the probability that a population parameter will lie within it.

This ultimately implies that, a confidence interval is an estimate of a range of estimated values (lower bound and an upper bound) that may contain a population parameter.

For a confidence interval of 98%, we have;

$\alpha =1-0.98\\\\\alpha =0.02$

Therefore, the margin of error for a confidence interval of 98% that should be used by the management to estimate the difference in the mean purchase amount for these credit cards is given by:

$2.355\sqrt{\frac{12^2}{74} +\frac{9^2}{58} }$

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