Question

8 of 10 (8 complete) HW Score: 71.82%, 7.9 of 11 pts 6.1.45-T Assigned Media Question Help A publisher wants to estimate the mean length of time in minutes) all adults spend reading newspapers. To determine this estimate the publisher takes a random sample of 15 people and obtains the results below. From past studies, the publisher assumes is 21 minutes and that the population of times is normally distributed 12 8 10 11 11 8 11 9 9 6 7 12 7 12 Construct the 90% and 99% confidence intervals for the population mean. Which interval is wider? If convenient, use technology to construct the confidence intervals. The 90% confidence interval is (CD) (Round to one decimal place as needed.) ht DU ess bra clon

Answer 1

Here in this scenario it is given that the sample of 15 adult who's spend the time to read newspaper. Here is also given that the population standard deviations is 2.1 minutes.

Based on sample we found that the sample mean is 9.4. on this information we have to calculate the 90% Confidence Interval for population mean Reding time of adults.

To calculate the Confidence Interval for population mean we need to use z distribution because the population standard deviations is known.

Further the formula and steps to calculate the Confidence Interval is as below,

Count, N: 15 Sum, Ex: 141 Mean, X: 9.4 Variance, s2: 4.1142857142857 Steps 1 N S = (Xi – )? N i=1 s2 = {(xi - x)2 111 N-1 - (12 - 9.4)2 + ... + (12 - 9.4)2 15-1 57.6 14 = 4.1142857142857 S = 14.1142857142857 = 2.0283702113484 The provided sample mean is X = 9.4 and the population standard deviation is o size of the sample is n 15 and the required confidence level is 90%. 2.1. The ( Based on the provided information, the critical z-value for a - 0.1 is zc = 1.645. The 90% confidence for the population mean u is computed using the following expression CI= X ác X ở vn à + с хо vn Therefore, based on the information provided, the 90 % confidence for the population mean u is CI = ( 9.4 (9.4 1.645 x 2.1 ,9.4+ 1.645 x 2.1 V15 < V15 = (9.4 – 0.892, 9.4 +0.892) = = (8.508, 10.292) o which completes the calculation.

The z critical value is calculated using Standerd normal z-table.

The 90% Confidence Interval for population mean newspaper reading time of adults is8.5 & 10.3 min.

The 90% Confidence Interval is (8.4, 10.3). (Rounded to one decimal places).

Thank you.