Web survey response rates. 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 in Survey Methodology $($Dec$.2013).$ In a designed study, Web users were directed to participate in one of several surveys with different formats. For example, one format utilized a welcome screen with a white background, and another format utilized a welcome screen with a red background. The $$break$-$off rates,$$ i$.$e$.,$ the proportion of sampled users who break off the survey before completing all questions, for the two formats are provided in the table.

White Welcome Screen Red Welcome Screen

Number of Web users $190183$

Number who break off survey $4937$

Break$-$off rate $\mathrm{.}258\mathrm{.}202$

Source: Haer, R$.,$ and Meidert, N$.$Does the first impression count? Examining the effect of the welcome screen design on the response rate.$$ Survey $$Methodology$,$ Vol. $39,$ No$.2,$ Dec. $2013($Table $4\mathrm{.}1).$

Verify the values of the break$-$off rates shown in the table.

The researchers theorize that the true break$-$off rate for Web users of the red welcome screen will be lower than the corresponding break$-$off rate for users of the white welcome screen. Give the null and alternative hypothesis for testing this theory.

Conduct the test, part b$,$ at

$$

$=$

$\mathrm{.}10$

$.$ What do you $$conclude$?$