Question

Response rates to web surveys are typically low, partially due to users starting but not finishing the survey. The factors that influence response rates were investigated. A survey company designed a study to verify this information. Web users were directed to participate in one of several surveys with different formats. One format utilized a welcome screen with a white background and the other one with a blue background. Data of the survey are given in OnlineHW.xlsx. Use three digits whenever necessary.

1. [25 pts.] The survey company assumes when a welcome screen with a blue background is used the rate of break off will be less than 0.25. Test the claim with a =0.07.

2. [10 pts.] Estimate the true population proportion of web users who complete the survey when a welcome screen with a white background is used using 90 % confidence.

3. [30 pts.] Test if there is a difference in the break off rate when different color welcome screens are used. a =0.01.

4. [10 pts.] Suppose one of the executives would like to estimate the response rate for another welcome screen format. How many web users should be selected for the survey if the executive wishes to estimate the response rate with a probability of 0.90 that the error estimation is less than 0.06?

Answer 1

The hypothesis being tested is:

H0: p = 0.25

Ha: p < 0.25

Reject Ho if p-value < 0.05.

p̂ = 37/(141 + 146 + 49 + 37) = 0.10

The test statistic, z = (p̂ - p)/√p(1-p)/n

z = (0.10 - 0.25)/√0.25(1-0.25)/373 = -6.73

The p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.07), we can reject the null hypothesis.

Therefore, we can conclude that a welcome screen with a blue background is used the rate of break off will be less than 0.25.