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We plan to sample music teachers in order to

construct a 95% confidence interval for the
proportion who believe that listening to hip-hop
music has a positive effect on music education.
We have no value of p available. Estimate the
sample size needed so that a 95% confidence
interval will have a margin of error of 0.03.

User Dotan
by
8.0k points

1 Answer

6 votes

Answer:

1068

Explanation:

95% confidence interval is 1.96

m = 0.03 = margin of error

n= 0.25(confidence interval / margin of error)²

n=0.25 (1.96/0.03)² = 1067.1 round up to 1068

another way:

Sample Size for Confidence Interval.

To estimate the required sample size for constructing a 95% confidence interval with a margin of error of 0.03, we need to use the formula:

n = (z^2 * p * q) / (E^2)

where:

n = sample size

z = z-score for the desired level of confidence (95%)

p = proportion of music teachers who believe that listening to hip-hop music has a positive effect on music education (unknown)

q = 1 - p

E = margin of error (0.03)

Since we do not have an estimate of the proportion p, we can use a conservative value of p = 0.5, which gives us the largest possible sample size.

Plugging in the values, we get:

n = (1.96^2 * 0.5 * 0.5) / (0.03^2)

n = 1067.11

Rounding up to the nearest integer, we need a sample size of at least 1068 music teachers to construct a 95% confidence interval with a margin of error of 0.03 when we have no value of p available.

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elementary statistics william navidi

We plan to sample music teachers in order to construct a 95% confidence interval for-example-1
User David Velasquez
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