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  .

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  .

check_circleExpert Solution
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 Z0.05 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 Z0.05 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,

n px (1-)x
=0.50(1-0.50) 1645
(0.25)(82)
0.02
=1691.3
1692
help_outline

Image Transcriptionclose

n px (1-)x =0.50(1-0.50) 1645 (0.25)(82) 0.02 =1691.3 1692

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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 Z0.05 value for 90% confidence level is 1.645. That is, p = 0.50, E = 0.01 and Z &alph...

n=[0.50(1-0.50) 1.645
-(0.25)(164.5)
0.01
6765.06
6,766
help_outline

Image Transcriptionclose

n=[0.50(1-0.50) 1.645 -(0.25)(164.5) 0.01 6765.06 6,766

fullscreen

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