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