Travel Time to School A random sample of 50 12th-grade students was asked how long it took to get to school. The sample mean was 16.2 minutes, and the sample standard deviation was 12.3 minutes. (Source: AMSTAT Census at School) a. Find a 95 % confidence interval for the population mean time it takes 12th-grade students to get to school. b. Would a 90 % confidence interval based on this sample data be wider or narrower than the 95 % confidence interval? Explain. Check your answer by constructing a 90 % confidence interval and comparing this width of the interval with the width of the 95 % confidence interval you found in part a.
Travel Time to School A random sample of 50 12th-grade students was asked how long it took to get to school. The sample mean was 16.2 minutes, and the sample standard deviation was 12.3 minutes. (Source: AMSTAT Census at School) a. Find a 95 % confidence interval for the population mean time it takes 12th-grade students to get to school. b. Would a 90 % confidence interval based on this sample data be wider or narrower than the 95 % confidence interval? Explain. Check your answer by constructing a 90 % confidence interval and comparing this width of the interval with the width of the 95 % confidence interval you found in part a.
Solution Summary: The author calculates the 95% confidence interval for the population mean for 12th-grade students to reach school, using the MINITAB software.
Travel Time to School A random sample of 50 12th-grade students was asked how long it took to get to school. The sample mean was
16.2
minutes, and the sample standard deviation was
12.3
minutes. (Source: AMSTAT Census at School)
a. Find a
95
%
confidence interval for the population mean time it takes 12th-grade students to get to school.
b. Would a
90
%
confidence interval based on this sample data be wider or narrower than the
95
%
confidence interval? Explain. Check your answer by constructing a
90
%
confidence interval and comparing this width of the interval with the width of the
95
%
confidence interval you found in part a.
Definition Definition Number of subjects or observations included in a study. A large sample size typically provides more reliable results and better representation of the population. As sample size and width of confidence interval are inversely related, if the sample size is increased, the width of the confidence interval decreases.
During busy political seasons, many opinion polls are conducted. In apresidential race, how do you think the participants in polls are generally selected?Discuss any issues regarding simple random, stratified, systematic, cluster, andconvenience sampling in these polls. What about other types of polls, besides political?
Please could you explain why 0.5 was added to each upper limpit of the intervals.Thanks
28. (a) Under what conditions do we say that two random variables X and Y are
independent?
(b) Demonstrate that if X and Y are independent, then it follows that E(XY) =
E(X)E(Y);
(e) Show by a counter example that the converse of (ii) is not necessarily true.
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