Question 1
You want to know how the commuting time of your employees compare to other departments competing for the same staff, so you get some survey data on average commuting times for 25 randomly selected people in your department.
Data: 59, 74,73, 66, 80, 84, 90, 110, 37.2, 50, 101.8, 39, 80, 35, 88, 34, 82, 65, 61, 63, 66, 88, 70, 79, 75
You find that the mean commuting time is 70 minutes, with a standard deviation of 20.
a) Calculate your standard error.
b) Based on this, calculate a 95 percent Confidence Interval for the mean commuting time. Remember, the C.I. is calculated by adding and subtracting from the observed sample mean the product of the standard error and the appropriate t-value (because the sample is less than 30). Use Excel function TINV (probability, degrees_freedom).
Show your work.

Question 2
b) Given the data in the question above about mean commuting time, calculate the 99% Confidence Interval. (Remember, use the TINV function in Excel, show your work.) Which is a bigger range, the 95% or 99% confidence interval? Why?

Question 3
Every 2 years, the National Assessment of Educational Progress (NAEP) assesses nationally representative samples of more than 120,000 students in public and private schools in grades 4, 8, and 12. Scientific sampling procedures are used to ensure reliable national, regional, and state samples
The NAEP sample of 1077 students in grade 8 in public schools had a mean quantitative score = 275. Because the sample size is large, the sample S is close to the population standard deviation, σ, so take σ = 60.
Give a 95% confidence interval for the mean score in the population of all young adults. Remember, we are now
calculating a range of probable values around our estimate, with Confidence Interval = mean +/-z* (σ / sqrt(n) ), where σ / sqrt(n) is the standard error of the sample mean.

Question 4
b) Suppose that the same result from the question above, x-bar= 275, had come from a sample of 250 young adults. Give the 95% confidence interval for . (Use the same formula, with a different sample size.)

Question 5
c) Then suppose that a sample of 7000 students had produced the sample mean x-bar= 280, and again give the 95% confidence interval for .

Question 6
d) What are the margins of error for samples of size 1077, 250, and 4000? How does increasing the sample size affect the margin of error of a confidence interval?

Question 7
Stating the Research and Null Hypotheses.
What you are trying to prove is called the research hypothesis, or alternative hypothesis, and is symbolized by H1 (some books write it as Ha). Research hypotheses are always expressed in terms of population parameters because we are interested in making statements about a population, based on sample statistics. The null
hypothesis, or Ho, contradicts the research hypothesis, and is usually a statement of no difference.
In each of the following situations, state an appropriate null hypothesis Ho and alternative hypothesis H1. Be sure to state it in terms of population parameters.
a) An education researcher believes that among college students there is a correlation between grade point average (GPA) and self-esteem data.
b) The President believes that tax refunds will create jobs.

Question 1 You want to know how the commuting time of your employ...