Question

When 1370 subjects were​ asked, "On how many days in the past 7 days have you felt​ lonely?" the mean was 1.5 and the standard deviation was 2.16. The margin of error for a​ 95% confidence interval for the population mean is 0.12. Construct that confidence​ interval, and interpret it. The confidence interval goes from nothing to nothing. ​(Round to two decimal places as​ needed.)

Answer 1

Confidence Interval = (1.41, 1.59)

Explanation:

To construct a confidence interval for the population mean, we can use the following formula:

Confidence Interval = sample mean ± (margin of error * standard error)

where the standard error is equal to the standard deviation divided by the square root of the sample size.

Given the information provided, we can calculate the standard error as:

standard error = 2.16 / sqrt(1370) = 0.058

Then, we can calculate the margin of error as 0.12.

Substituting these values into the formula, we get:

Confidence Interval = 1.5 ± (0.12 * 0.058)

Confidence Interval = (1.41, 1.59)

Therefore, we can interpret the 95% confidence interval as follows: we are 95% confident that the true population mean of the number of days that people feel lonely in the past 7 days is between 1.41 and 1.59. This means that if we were to take many samples of 1370 subjects and compute the confidence intervals for each sample using the same method, we would expect about 95% of the intervals to contain the true population mean.