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Goshia [24]
2 years ago
8

Alice wants to estimate the percentage of people who plan on voting yes for the upcoming school levy. She surveys 380 individual

s and finds that 260 plan on voting yes. Identify the values needed to calculate a confidence interval at the 90% confidence level. Then find the confidence interval.
Mathematics
1 answer:
goblinko [34]2 years ago
3 0

Answer: (0.641, 0.719)

Step-by-step explanation:

The confidence interval for population proportion is given by :-

\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}

Given : Level of significance : 1-\alpha:0.90

Then , significance level : \alpha: 1-0.90=0.10

Since , sample size : n=380 , i.e. a large sample.

Critical value : z_{\alpha/2}=1.645

Also, the proportion of individuals plan on voting yes :-

\hat{p}=\dfrac{260}{380}\approx0.68

Then , the confidence interval at the 90% confidence level will be :-

0.68\pm(1.645)\sqrt{\dfrac{0.68(1-0.68)}{380}}\\\\\approx0.68\pm0.039\\\\=(0.68-0.039, 0.68+0.039=(0.641,\ 0.719)

Hence, the confidence interval at the 90% confidence level= (0.641, 0.719)

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