LAB ACTIVITY 12
Due Friday, Nov. 11 at 11:59pm
(Use ‘ClassData_FA2016.mtw’ dataset)
Activity 1 (Requires Minitab): Constructing a confidence interval for µ1 – µ2
We are going to estimate the difference in time spent studying between STAT 200 students who sit in the front of the class and those that sit in the back.
Let µ1 be the mean study time per week for students who sit in the front and µ2 be the mean study time per week for students who sit in the back.
1. Using the symbols described immediately above, what single parameter are we trying to estimate in this confidence interval?
2. Open the dataset ‘ClassData_FA2016.mtw’ in Minitab. Get basic descriptive statistics for the variable ‘StudHrWk’ by ‘SitPref’. Follow the sequence stat à basic stat à display descriptive statistics à put ‘StudHrWk’ in Variables box à put ‘SitPref’ in By variables box à OK.
Seating / Sample mean (x-bar) / Std. Dev. (s) / Sample size (n)In the front
In the back
3. What is the sample estimate for the difference in two means?
4. What is the standard error for this estimate?
5. For the degrees of freedom for the relevant t* multiplier, use the smaller of n1 – 1 and n2 – 1. How many degrees of freedom is this, and what is the corresponding t* multiplier for a 90% confidence level?
6. Finally, compute the 90% confidence interval for the parameter of interest. Write a sentence interpreting it in terms of the original research question.
Activity 2 (Requires Minitab): Constructing a confidence interval for µd
Since each student in the sample answered two related questions, giving his or her predicted GPA and goal GPA, we can compare these two quantities to learn whether this sample tells us anything about the difference between predicted and goal in the larger population. The measurements come in pairs, one predicted and one goal for each experimental unit. So we will consider the differences and see what we can learn about µd, the population mean of the difference.
1. Create a new variable equal to the value of GPAgoal minus GPApred for each individual. To do this, select Calc à Calculator. Type GoalMinusPred (or some other new column name if you prefer) into the box labeled “Store result in variable”. Then under “Expression,” select GPAgoal, then click the minus sign, then select GPApred. If done correctly, the calculator should clearly be telling Minitab to take GPAgoal minus GPApred and store the result as a new column.
2. Create a simple boxplot of the new variable (use Graph à Boxplot). Which quartile (1st, 2nd, or 3rd) appears to be closest to zero?
3. Use Stat à Basic Statististics à Display Descriptive Statistics to calculate descriptive statistics for the new variable. Use the sample standard deviation together with the sample size and a t* multiplier of 1.97 to calculate the value of the margin of error for a 95% confidence interval for the mean difference.
4. You can check your answer as follows: Use Basic Statistics à Paired t , then select “Each sample is in a column” and choose GPAgoal for Sample 1 and GPApred for Sample 2. A 95% confidence interval for the mean difference will be calculated and it should agree with the one you would calculate as the sample mean in question 3 plus or minus the margin of error from question 3.
Activity 3 (Does not require Minitab): Practice with the z-table
The standard normal table, or z-table, given on the next page is the same as the first page of your midterm #3 exam packet. Use it to answer the following questions:
1. What is P(–1.13 < Z < 0)?
2. What is the correct z* multiplier for an 86% confidence interval?
3. If SAT verbal scores are normally distributed with a mean of 500 and a standard deviation of 100, what is the 70th percentile of SAT verbal scores?