A researcher was interested in determining whether incentives, and how they were offered, affected the response rate in surveys. A simple random sample of 50 adult residents of a large city was selected. All were mailed a survey. In half of the mailings a check was included as a token of appreciation (in advance) for completing the survey. Five of these checks were for $1.00, five were for $5.00, five were for $10.00, five were for $25.00, and five were for $50.00. In the other half, people were promised a check upon returning a completed survey. Five were promised a check for $1.00, five were promised a check for $5.00, five were promised a check for $10.00, five were promised a check for $25.00, and five were promised a check for $50.00. Which method of payment (check enclosed or check to be sent upon return of a completed survey) and the amount ($1.00, $5.00, $10.00, $25.00, or $50.00) each person received was determined by randomization. For each person who was sent one of the surveys, the researcher recorded whether or not a completed survey was returned.
Let x be the amount of the check (either enclosed or promised) and z be the indicator variable
We wish to fit a logistic regression model
where p is the binomial probability of returning a completed survey, and log is the natural logarithm. The multiple logistic regression output from fitting this model is given below.
A test of the hypotheses H0:β2 = 0 Ha:β2 ≠ 0 has P-value
A. less than 0.05.
B. between 0.05 and 0.10.
C. greater than 0.10.