Question

Asked Sep 30, 2019

Ouranos Resorts would like to send a survey to its guests asking about their satisfaction with the new website design. It would like to have a margin of error of ±2 percent on responses with 90 percent confidence.

**(a)** Using the conservative approach, what sample size is needed to ensure this level of confidence and margin of error? **(Round up your answer to the next whole number.)**

Sample size _________

**(b)** If Ouranos Resorts wanted the margin of error to be only ±1.0 percent, what would happen to the required sample size? **(Round up your answer to the next whole number.)**

Sample size would (Click to select) increase decrease to .

Step 1

**a.**

The critical value for 90% confidence level is obtained below:

From the given information, Consider, the confidence level is 0.90.

For (1–α) = 0.90

α = 0.10

α/2 = 0.05

From Standard Normal Table, the required *Z*_{0.05} value for 90% confidence level is 1.645.

From the given information, the proportion is unknown so 0.50 can be considered.

The margin of error is 0.02 and the required *Z*_{0.05} value for 90% confidence level is 1.645.

That is, *p* = 0.50, *E* = 0.02 and Z α/2 = 1.645.

The required sample size by using conservative approach is,

Step 2

**b.**

From the given information, the proportion is unknown so 0.50 can be considered.

The margin of error is 0.01 and the required *Z*0.05 value for 90% confidence level is 1.645. That is, *p* = 0.50, *E* = 0.01 and Z &alph...

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