ACTIVITY

Many public polling agencies conduct surveys to determine the current consumer sentiment concerning the state of the economy. For example, the Bureau of Economic and Business Research (BEBR) at the University of Florida conducts quarterly surveys to gauge consumer sentiment in the Sunshine State. Suppose that BEBR randomly samples 484 consumers and finds that 257 are optimistic about the state of the economy.

a. Find a 95% confidence interval to estimate the proportion of all consumers in Florida who are optimistic about the state of the economy by following the steps given below:

• Step 1: Make sure that "Input" menu option is selected.
• Step 2: Type "Optimistic" in the "Data label" box.
• Step 3: Type "484" in the "Sample size" box.
• Step 4: Type "0.531" in the "Sample proportion" box. (Note that sample proportion is 257/484=0.531.)
• Step 5: Select the "Hypothesis test" from menu options.

The output will include: Sample size and proportion followed by a 95% confidence interval for the population proportion.

b. Find a 99% confidence interval by following the steps given below:

• Step 1: Make sure that "Input" menu option is selected.
• Step 2: Type "Optimistic" in the "Data label" box.
• Step 3: Type "484" in the "Sample size" box.
• Step 4: Type "0.531" in the "Sample proportion" box. (Note that sample proportion is 257/484=0.531.)
• Step 5: Select the "Hypothesis test" from menu options
• Step 6: Click on the "Options" button on the upper right hand side of the window.
• Step 7: Change only Alpha from 5.0 to 1.0.
• Step 8: Click on the "OK" button.

The output will include: Sample size, Mean, and Standard deviation followed by 99% confidence interval for the population mean.

c. Compare the length of the confidence intervals that you have found in a and b. Which one is shorter?