Question

To investigate the youth use of the Internet, a sample of 10 adults was asked to report the number of hours they spent on the Internet during the last month. The results are listed below: 0,7,12,5,44,14,8,0,9,56 The researchers claim that the number of hours the adults spent on the Internet exceeds 20 hours per month. 1. Find the point estimator of the mean ( (μ) for the number of hours the adults spent on the Internet per month. 2. Construct a 99% confidence interval for the population mean "and interpret your findings. 3. State and conduct a 5 -step test of hypotheses to investigate the researchers claim, assuming that the population standard deviation is 12 . Use a=0.10 B. To investigate the youth use of the Internet, a sample of 8 adults was asked to report the number of hours they spent on the Internet during the last month. The results are listed below: 40,52,87,60,39,42,50,30 The researchers claim that the number of hours the adults spent on the Internet exceeds 52 hours per month. 1. Find the point estimator of the mean (") for the number of hours the adults spent on the Internet per month. 2. Find the point estimator of the standard deviation (s) of the number of hours the adults spent on the Internet per month. 3. Construct a 95% confidence interval for the population mean " and interpret your findings. 4. State and conduct a 5 -step test of hypotheses to investigate the researchers claim. Use a=0.10

Answer 1

1. The point estimator of the mean (μ) for the number of hours the adults spent on the Internet per month is 15.5 hours. 2. The 99% confidence interval for the population mean is approximately -0.47 to 31.47. 3. To conduct a 5-step test of hypotheses, the null hypothesis is that the number of hours the adults spent on the Internet does not exceed 20 hours per month (H0: μ <= 20) and the alternative hypothesis is that the number of hours exceeds 20 (Ha: μ > 20).

Step-by-step explanation:

The mean (μ) estimator for the monthly hours adults spend on the Internet involves averaging the sample data.

In this instance, with 8 adults totaling 400 hours, the mean estimator is 50 hours.

The standard deviation (s) estimator is determined by taking the square root of the variance, calculated as the sum of squared deviations from the mean divided by the sample size minus 1.

For this data, with a variance of 150 hours^2, the standard deviation estimator is sqrt(150) = 12.25 hours.

To establish a 95% confidence interval for the population mean, the standard error, derived by dividing the standard deviation by the square root of the sample size, is calculated as 4.335.

The margin of error for a 95% confidence interval is 1.96 times the standard error, resulting in a margin of error of 8.49. Consequently, the confidence interval spans from 41.51 to 58.49.

In conducting a 5-step test of hypotheses, the null hypothesis (H0) posits that Internet usage does not surpass 52 hours monthly (H0: μ <= 52), while the alternative hypothesis (Ha) contends that it exceeds 52 (Ha: μ > 52).

The testing process involves stating hypotheses, formulating an analysis plan, analyzing sample data, interpreting results, and making a decision.