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The people at the Cloak soft drink company believe that their brand of drink is favored over their competitor's brand, Pempsi, by the majority of people. A quick survey is conducted to test this belief. Forty people are asked whether they prefer Cloak or Pempsi, and 28 people did prefer Cloak. A statistician at Cloak wishes to construct a 95% confidence interval for the proportion of people that prefer Cloak soft drink. Drag the blue marker from above the words 'lower bound' to the lower bound of the confidence interval on the number line provided. Drag the red marker from above the words 'upper bound' to the upper bound of the confidence interval on the number line provided.

Sagot :

Solution :

[tex]$p = \frac{28}{30}$[/tex]

  = 0.93

Given :

[tex]$a=0.05$[/tex]

[tex]$z(0.025)=$[/tex] [tex]$1.96$[/tex]   (from standard normal table)

So the lower bound is

[tex]$=p+z\times \sqrt{p \times \frac{1-p}{n}}$[/tex]

[tex]$=0.7+0.93\times \sqrt{0.7 \times \frac{1-0.7}{30}}$[/tex]

= 1.63 + 0.083

[tex]$=1.73$[/tex]

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