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.

	white	blue
completed	141	146
breakoff	49	37

1) 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.

a. State the hypothesis

b. What is the decision rule?

c. Test statistic

d. Decision and managerial decision

e.Calculate the p-value

f. Interpret hypothesis using p-value

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 (0.05), 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.

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