8. 3.4. Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation: 22, 18, 14, 25, 17, 28, 15, 21. Use Table 2. a. Calculate the sample mean and the sample standard deviation. (Round intermediate calculations to 4 decimal places. Round "sample mean" to 3 decimal places and "Sample Standard deviation" answer to 2 decimal places.) Sample mean _________ Sample standard deviation _________ b. Construct the 80% confidence interval for the population mean. (Round "t" value to 3 decimal places and final answers to 2 decimal places.) Confidence interval ______to______ c. Construct the 90% confidence interval for the population mean. (Round "t" value to 3 decimal places and final answers to 2 decimal places.) Confidence interval ______to_______ d. What happens to the margin of error as the confidence level increases from 80% to 90%? Pick the best choice from the following: As the confidence level increases, the interval becomes wider. As the confidence level increases, the margin of error becomes wider. **************************************************************************** For decades, people have believed that boys are innately more capable than girls in math. In other words, due to the intrinsic differences in brains, boys are better suited for doing math than girls. Recent research challenges this stereotype, arguing that gender differences in math performance have more to do with culture than innate aptitude. Others argue, however, that while the average may be the same, there is more variability in math ability for boys than girls, resulting in some boys with soaring math skills. A portion of the data on math scores of boys and girls is shown in the accompanying table. Use Table 2. Boys 74 89 92 84 68 88 84 96 100 62 99 77 84 58 100 48 88 94 86 66 90 66 Girls 83 76 89 84 99 88 96 68 82 81 77 94 74 69 84 89 76 66 62 98 88 74 picture Click here for the Excel Data File a. Use Excel to construct 95% confidence intervals for the mean scores of boys and the mean scores of girls. (Do not round intermediate calculations. Round "t" value to 3 decimal places and final answers to 2 decimal places.) Confidence intervals Mean scores of boys _____to_____ Mean scores of girls ______to_____ b. Explain why the widths of the two intervals are different. Pick the best choice from the following: The sample standard errors of the scores of boys and girls are different. The population standard errors of the scores of boys and girls are different. The population variance of the scores of boys and girls are different