. A grocery story recorded amount of time that 20 randomly selected shoppers waited
checkout lines. The mean was 322 seconds (5 minutes, 22 seconds) and the standard
deviation was 48 seconds. Construct a 95% confidence interval for the mean wait time
for all of the shoppers at the grocery store. (You must show work and/or TI
calculator commands to receive credit. You may give your answer in seconds)
95% = mean ± 1.96 SD
Take it from there.
To construct a 95% confidence interval for the mean wait time for all shoppers at the grocery store, we can use the formula:
Confidence Interval = (sample mean) ± (critical value) * (standard deviation / sqrt(sample size))
1. Find the critical value for a 95% confidence level. We can look this up in a table or use a calculator. For a normal distribution, the critical value for a 95% confidence level is approximately 1.96.
2. Calculate the standard error of the mean using the formula: standard deviation / sqrt(sample size). In this case, the standard deviation is given as 48 seconds, and the sample size is 20. So the standard error of the mean is 48 / sqrt(20).
3. Calculate the margin of error by multiplying the critical value by the standard error of the mean: 1.96 * (48 / sqrt(20)).
4. Finally, construct the confidence interval by adding and subtracting the margin of error from the sample mean: 322 ± (1.96 * (48 / sqrt(20))).
Plugging in the values, we get:
Confidence Interval = 322 ± (1.96 * (48 / sqrt(20)))
Simplifying,
Confidence Interval ≈ 322 ± 20.83
So the 95% confidence interval for the mean wait time for all shoppers at the grocery store is approximately (301.17 seconds, 342.83 seconds).