A team of researchers (Singer et al., 2000) used the Survey of Consumer Attitude

Question

A team of researchers (Singer et al., 2000) used the Survey of Consumer Attitudes to investigate whether incentives would improve the response rates on telephone surveys. A national sample of 735 households was randomly selected, and all 735 of the households were sent an “advance letter” explaining that the household would be contacted shortly for a telephone survey. However, 368 households were randomly assigned to receive a monetary incentive along with the advance letter, and the other 367 households were assigned to receive only the advance letter. Here are the data on how many households responded to the telephone survey.

d. Null: The population proportion of all American families that would answer the survey when given a monetary incentive is the same as the population proportion of all American families that would answer the survey when not offered a monetary incentive.
??Alternative: The population proportion of all American families that would answer the survey when given a monetary incentive is greater than the population proportion of all American families that would answer the survey when not offered a monetary incentive.

3. State the null and alternative hypotheses in symbols.

d. H0: ?incentive = ?no incentive
Ha: ?incentive < ?no incentive

4. Why would it be okay to use the theory-based method (that is, the normal distribution based method) to find a p-value and confidence interval for this study?

d. All four values in the two-way table (286, 245, 82, and 122) are larger than 10, so the theory-based approach should be valid.

5. Use three decimal places when entering your answers.
?Calculate the appropriate 95% confidence interval for the following statement:
?
? "We are 95% confident that the population proportion of all American households that would respond to the survey when given a monetary incentive is between _________ and _________ higher than the population proportion of all American households that would respond to the survey when not offered a monetary incentive."

a. Null: The population proportion of all American families that would answer the survey when given a monetary incentive is greater than the population proportion of all American families that would answer the survey when not offered a monetary incentive.
Alternative: The population proportion of all American families that would answer the survey when given a monetary incentive is the same as the population proportion of all American families that would answer the survey when not offered a monetary incentive. Received an Incentive? Responded to the Yes telephone survev? No Total Yes 286 82 368 No 245 122 367 Total 531 204 735 Identify both the correct symbol and interpretation for the parameters of interest. Choose all that apply. : The population proportion of all American households that would respond to the survey when given a monetary ?incentive incentive : The population proportion of all American households that would respond to the survey when not offered a monetary incentive ??? incentive : The population proportion of all American households that would respond to the survey when not offered a monetary incentive ??? incentive : The number of American households that would respond to the survey when not offered a monetary incentive ??ncentive nno incentive ?.ncentive : The population proportion of all American households that would respond to the survey when given a monetary : The number of American households that would respond to the survey when given a monetary incentive : The number of American households that would respond to the survey when not offered a monetary incentive incentive ?.ncentive : The number of American households that would respond to the survey when given a monetary incentive

Explanation / Answer

Question1

The parameter of interest is nincentive and nno incentive

Initial two are the correct notation of parameter of interest.

Question 2

Option d is correct here

Null: The population proportion of all American families that would answer the survey when given a monetary incentive is the same as the population proportion of all American families that would answer the survey when not offered a monetary incentive.
Alternative: The population proportion of all American families that would answer the survey when given a monetary incentive is greater than the population proportion of all American families that would answer the survey when not offered a monetary incentive.

Question 3

H0 : pincentive = pno incentive

Ha : pincentive > pno incentive

Option b is correct.

Question 4

All four values in the two-way table (286, 245, 82, and 122) are larger than 10, so the theory-based approach should be valid. Option 4 is correct.

Question 5

sample proportion p^ = 286/368 = 0.7772

Here 95% confidence interval for population proportion of all American households = p^incentive +- Z95% sqrt [p^ * (1-p^)/N}  

= 0.7772 +- 1.96 * sqrt [0.7772 * 0.2228/368]

= 0.7772 + 1.96 * 0.0217

= (0.735, 0.820)

We are 95% confident that the population proportion of all American households that would respond to the survey when given a monetary incentive is between 0.735 and 0.820 higher than the population proportion of all American households that would respond to the survey when not offered a monetary incentive.

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