Question

A research council wants to estimate the mean length of time (in minutes) that the average U.S. adult spends watching television using digital video recorders (DVR’s) each day. To determine the estimate, the research council takes random samples of 35 U.S. adults and obtains the following times in minutes.

24 27 26 29 33 21 18 24 23 34 17 15 19 23 25 29 36 19 18 22 16 45 32 12 24 35 14 40 30 19 14 28 32 15 39

From past studies, the research council has found that the standard deviation time is 4.3 minutes and that the population of times is normally distributed.
a. Construct a 90% confidence interval for the population mean.

Answer 1

To construct a 90% confidence interval for the population mean, use the formula and given values to calculate the interval.

Step-by-step explanation:

To construct a 90% confidence interval for the population mean, we can use the formula:

Confidence interval = X ± Z * (σ / sqrt(n))

Where:

1. X is the sample mean
2. Z is the Z-value for the desired level of confidence (in this case, 90%)
3. σ is the standard deviation of the population
4. n is the sample size

Given that X = 25.7, Z = 1.645 (Z-value for a 90% confidence level), σ = 4.3, and n = 35, we can substitute these values into the formula:

Confidence interval = 25.7 ± 1.645 * (4.3 / sqrt(35))

Simplifying the expression, we get:

Confidence interval ≈ 25.7 ± 1.645 * 0.729

Confidence interval ≈ 25.7 ± 1.197

Therefore, the 90% confidence interval for the population mean is approximately (24.503, 26.897).