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

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 following information has been provided:

α=0.10, E=0.06

Since the no estimate of the population proportion p is provided, we use the estimate p = 0.5 (which corresponds to the worst-case scenario).

The critical value for the significance level α=0.10 is

z_c = 1.64

The following formula is used to compute the minimum sample size required to estimate the population proportion p within the required margin of error:

Therefore, the sample size needed to satisfy the condition n≥187.88,

and it must be an integer number,

we conclude that the minimum required sample size is n = 188.

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