Lab Activity 1: Confidence Intervals
Obtain the data for this activity on the website. When you click the link, the data should open up automatically in Minitab.
(To open it manually, go to Start > All Programs > Spreadsheets and Statistics > Minitab 13 for Windows > Minitab.)
- The first column of the data provides observations on shear strength (lb) of 100 ultrasonic spot welds made on a certain type of alclad sheet.
a)First, obtain a descriptive plot for these data. You might need to review descriptive plots for quantitative data. Attach your plot.
b)Using these data, estimate the mean shear strength of all ultrasonic spot welds on this type of alclad sheet with a 90% confidence interval. Do it by hand!
To obtain the summary statistics that you need, go to Stat > Basic Statistics > Display Descriptive Statistics…. Enter Shear Strength as the variable. Use the summary statistics to compute the confidence interval. SHOW YOUR WORK! Interpret the interval in the context of the question.
c)Now check your work in Minitab. Go to Stat > Basic Statistics > 1 Sample t… (Don’t let the letter “t” throw you off here. Minitab does things a little differently than we are learning to do them by hand.) Enter Shear Strength as the variable. Under ‘Options’, set the confidence level to 90. Record the interval below. (Note: The interval will not match exactly what you calculated by hand (for various reasons) but it should be close.)
- The second column of the data gives observations on shower-flow rate (L/min) for a sample of n = 129 houses in Perth, Australia. Assuming this is a random sample, use Minitab to estimate the mean shower-flow rate for all houses in Perth with a 99% confidence interval. Report the interval below and interpret it in the context of the problem.
- The third column contains data from a poll of over 200 PSU students who were asked, “Do you smoke?”
a)Obtain a pie chart to describe the sample results (Graph > Pie Chart…). Attach your plot.
b)Compute (BY HAND) and interpret a 95% upper confidence bound for the proportion of all PSU students who smoke and interpret the bound. SHOW YOUR WORK! (You can obtain the info you need from the pie chart or by selecting Stat > Tables > Tally….)
c)Now check your work in Minitab. Go to Stat > Basic Statistics > 1 – Proportion…and enter Smoke as the variable. Under ‘Options’, make sure to choose the appropriate confidence level. Set the alternative to “less than” and check the box next to “Use test and interval based on normal distribution”. Report the bound.