ACTIVITY 1

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.

Test the hypothesis that majority of consumers in the Sunshine State are optimistic about the state economy. Use the significance level 0.05.

• 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. Caution: Do not use the output yet.
• Step 6: Click on the "Options" button on the upper right hand side of the window.
• Step 7: On the window that pops up, type the value of the proportion specified in you null hypothesis. That is 0.5 in this case.
• Step 8: Select your alternative hypothesis. For this question the alternative hypothesis is one sided, right-tailed. Therefore select "Greater than".
• Step 9: Type the significance level of the test. In this case it is "5.0"
• Step 10: Click on the "OK" button.

The output will include: Sample size, sample proportion, one-sided 95% confidence interval for the population proportion, and the result of the test. Please report the p-value of the test and interpret. What is your conclusion?

ACTIVITY 2

The reputation (and hence sales) of many businesses can be severely damaged by shipments of manufactured items that contain a large percentage of defectives. For example, a manufacturer of alkaline batteries may want to be reasonably certain that fewer than 5% of its batteries are defective. Suppose 300 batteries are randomly selected from a very large shipment; each is tested and 10 defective batteries are found.

Does this provide sufficient evidence for the manufacturer to conclude that the fraction defective in the entire shipment is less than .05? Use significance level 0.01.

• Step 1: Make sure that "Input" menu option is selected.
• Step 2: Type "Defective" in the "Data label" box.
• Step 3: Type "300" in the "Sample size" box.
• Step 4: Type "0.033" in the "Sample proportion" box. (Note that sample proportion is 10/300=0.033.)
• Step 5: Select the "Hypothesis test" from menu options. Caution: Do not use the output yet.
• Step 6: Click on the "Options" button on the upper right hand side of the window.
• Step 7: On the window that pops up, type the value of the proportion specified in you null hypothesis. That is 0.05 in this case.
• Step 8: Select your alternative hypothesis. For this question the alternative hypothesis is one sided, left-tailed. Therefore select "Less than".
• Step 9: Type the significance level of the test. In this case it is "1.0"
• Step 10: Click on the "OK" button.

The output will include: Sample size, sample proportion, one-sided 95% confidence interval for the population proportion, and the result of the test. Please report the p-value of the test and interpret. What is your conclusion?