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7 votes
7 votes
In a survey of 706 parents with kids 4 to 8 years old. 346 say that they know their state booster seat law. Construct a 90% confidence interval for the population proportion.

User Augusto
by
2.7k points

1 Answer

19 votes
19 votes

Answer:

(0.46, 0.52)

Explanation:

The formula for Confidence Interval with Proportion

CI = p ± z × √p(1 - p)/n

Where

p = Proportion = x/n

x = 346

n = 706

p = 346/706

p = 0.49

z = z score of Confidence Interval 90% = 1.645

Therefore:

CI = 0.49 ± 1.645 × √0.49(1 - 0.49)/706

CI = 0.49 ± 1.645 × √0.49 × 0.51/706

CI = 0.49 ± 1.645 × 0.0188139843

CI = 0.49 ± 0.0309490042

Hence:

Confidence Interval is

0.49 - 0.0309490042

= 0.4590509958

≈ 0.46

0.49 + 0.0309490042

= 0.5209490042

≈ 0.52

Therefore , the confidence interval of the population proportion is

(0.46, 0.52)

User Kloarubeek
by
3.5k points
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