Your mathematics instructor claims that, over the years, 88% of his students have said that math is their favorite subject. In this year's class, however, only 21 out of 32 students named math as their favorite class. The instructor decides to construct a confidence interval for the true population proportion based on the sample value. What's the correct value for the standard error of SE in this case?
0.045
0.057
0.064
0.088
0.084
To calculate the standard error (SE) for constructing a confidence interval for a proportion, you can use the formula:
SE = sqrt((p_hat * (1 - p_hat)) / n)
Where:
- p_hat is the proportion in the sample (21/32 = 0.65625)
- n is the sample size (32 in this case)
Now, let's calculate the standard error:
SE = sqrt((0.65625 * (1 - 0.65625)) / 32) = sqrt(0.22755625 / 32) ≈ 0.057
Therefore, the correct value for the standard error (SE) in this case is approximately 0.057.
To calculate the standard error (SE) for constructing a confidence interval, you need to use the following formula:
SE = √((p * (1 - p)) / n)
Where:
- p is the sample proportion
- n is the sample size
In this case, the sample proportion is 21 out of 32 students, so p = 21/32 = 0.65625.
The sample size is 32, so n = 32.
Now you can calculate the standard error:
SE = √((0.65625 * (1 - 0.65625)) / 32)
= √((0.65625 * 0.34375) / 32)
= √(0.22509765625 / 32)
= √(0.0070327381)
≈ 0.083848
Rounding to three decimal places, the standard error (SE) is approximately 0.084. Therefore, the correct value for the standard error in this case is 0.084.
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Formula:
Standard error = √(pq/n)
With your data:
p = 21/32 (convert to a decimal); q = 1 - p; and n = 32 (sample size).
Plug the values into the formula and calculate.