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A research center project involved a survey of 846 internet users. It provided a variety of statistics on internet users. (a) The sample survey showed that 91% of respondents said the internet has been a good thing for them personally. Develop a 95% confidence interval for the proportion of respondents who say the internet has been a good thing for them personally. (Round your answers to four decimal places.)

Respuesta :

Answer:

95% Confidence interval:  (0.8907,0.9293)

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 846

Proportion of respondents who said the internet has been a good thing for them personally = 91%

[tex]\hat{p} = 0.91[/tex]

95% Confidence interval:

[tex]\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

[tex]z_{critical}\text{ at}~\alpha_{0.05} = 1.96[/tex]

Putting the values, we get:

[tex]0.91\pm 1.96(\sqrt{\dfrac{0.91(1-0.91)}{846}})\\\\ = 0.91\pm 0.0193\\\\=(0.8907,0.9293)[/tex]

(0.8907,0.9293) is the required 95% confidence interval for the proportion of respondents who say the internet has been a good thing for them personally.

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