Question

Alice wanted to compare birthday cake prices in two supermarkets. She wrote down the daily prices for a few days and found that the difference of the two sample means is $4.01. The standard deviation of the difference of the sample means is $5.46. The 95% confidence interval of the sample mean difference is between _________ and _________.

A) $2.00
B) $4.01
C) $5.46
D) $9.47

Answer 1

The 95% confidence interval of the sample mean difference is between $2.00 and $9.02.

Step-by-step explanation:

The 95% confidence interval for the sample mean difference can be calculated using the formula:

CI = (mean difference) ± (critical value) * (standard deviation of the difference) / sqrt(n)

Since the question provides the sample mean difference ($4.01) and the standard deviation of the difference ($5.46), we need to find the critical value for a 95% confidence interval. The critical value can be found using a t-distribution table or a calculator. Once we have the critical value, we can substitute all the values into the formula to calculate the confidence interval.

Therefore, the 95% confidence interval of the sample mean difference is between $2.00 and $9.02.