A researcher is interested in whether students who attend private high schools have higher average SAT Scores than students in the general population. A random sample of 90 students at a private high school is tested and and a mean SAT score of 1030 is obtained. The average score for public high school student is 1000 (ó= 200). What is the CI?
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Sra
To calculate the confidence interval (CI) for the difference in mean SAT scores, you can use the following formula:
CI = X̄ - E to X̄ + E
Where:
X̄ is the sample mean SAT score for the private high school students (1030),
E is the margin of error, and
X̄ ± E represents the range within which we can be confident that the population mean SAT score lies.
To calculate the margin of error, you need to determine the standard error (SE) of the sample mean. The standard error measures the variability of the sample mean from sample to sample.
SE = σ / sqrt(n)
Where:
σ is the population standard deviation (200),
sqrt represents the square root function, and
n is the sample size (90).
Plugging in the values:
SE = 200 / sqrt(90)
Now, calculate the margin of error (E):
E = t * SE
The t-value refers to the critical value from the t-distribution, which is based on the desired level of confidence. Assuming a 95% confidence level, the critical value for a two-tailed test is approximately 1.96.
E = 1.96 * (200 / sqrt(90))
Now, substitute the values into the CI formula:
CI = 1030 - E to 1030 + E
Calculating it further:
CI = 1030 - (1.96 * (200 / sqrt(90))) to 1030 + (1.96 * (200 / sqrt(90)))
By evaluating this expression, you can find the confidence interval for the mean SAT scores of the private high school students.