We are 95% confident that the true mean reasoning score after 6 monthsof piano lessons is between 2.5783 and 4.6577 higher than the true mean reasoning score before 6 months of piano lessons.

Question

asked 2021-06-17

Do piano lessons improve the spatial-temporal reasoning of preschool children? A study designed to investigate this question measured the spatial-temporal reasoning of a random sample of 34 preschool children before and after 6 months of piano lessons. The difference (After - Before) in the reasoning scores for each student has mean 3.618 and standard deviation 3.055. Construct and interpret a 90% confidence interval for the true mean difference.

asked 2021-06-24

State whether the investigation in question is an observational study or a designed experiment. Justify your answer in each case. The National Association of Colleges and Employers (NACE) compiles information on salary offers to new college graduates and publishes the results in Salary Survey.

asked 2021-06-22

A bank wants to know which of two incentive plans will most increase the use of its credit cards. It offers each incentive to a group of current credit card customers, determined at random, and compares the amount charged during the following six months. What type of study design is being used to produce data?

asked 2021-01-27

\(\begin{array}{|c|c|} \hline & Housework Hours \\ \hline Gender & Sample\ Size & Mean & Standard\ Deviation \\ \hline Women & 473473 & 33.133.1 & 14.214.2 \\ \hline Men & 488488 & 18.618.6 & 15.715.7 \\ \end{array}\)

a. Based on this study, calculate how many more hours per week, on the average, women spend on housework than men.

b. Find the standard error for comparing the means. What factor causes the standard error to be small compared to the sample standard deviations for the two groups? The cause the standard error to be small compared to the sample standard deviations for the two groups.

c. Calculate the 95% confidence interval comparing the population means for women Interpret the result including the relevance of 0 being within the interval or not. The 95% confidence interval for \(\displaystyle{\left(\mu_{{W}}-\mu_{{M}}\right)}\) is: (Round to two decimal places as needed.) The values in the 95% confidence interval are less than 0, are greater than 0, include 0, which implies that the population mean for women could be the same as is less than is greater than the population mean for men.

d. State the assumptions upon which the interval in part c is based. Upon which assumptions below is the interval based? Select all that apply.

A.The standard deviations of the two populations are approximately equal.

B.The population distribution for each group is approximately normal.

C.The samples from the two groups are independent.

D.The samples from the two groups are random.