Asked by Briana Goins on Jul 20, 2024
Verified
A random sample of 49 statistics examinations was taken.The average score, in the sample, was 84 with a variance of 12.25.The 95% confidence interval for the average examination score of the population of the examinations is
A) 83.45 to 84.55.
B) 80.07 to 87.93.
C) 83.29 to 84.71.
D) 80.5 to 87.5.
Statistics Examinations
Tests or assessments that measure knowledge and understanding of statistical concepts and methods.
Variance
A measure of the spread between numbers in a dataset, indicating how much the individual data points differ from the mean of the data.
- Elucidate and appreciate the idea of interval estimates, which includes the concepts of confidence intervals and margin of error.
- Comprehend the impact of sample size on the breadth of interval estimations.
Verified Answer
MB
Molly BrownJul 23, 2024
Final Answer :
C
Explanation :
We can calculate the standard error of the mean as the square root of the variance divided by the sample size, i.e., sqrt(12.25/49) = 0.7. Then, with a 95% confidence level, we can find the t-value for a two-tailed test with 48 degrees of freedom (n-1), which is approximately 2.01. Therefore, the margin of error is 2.01 times the standard error, i.e., 2.01*0.7 = 1.41. Finally, we can construct the confidence interval as the sample mean plus or minus the margin of error, i.e., 84 +/- 1.41. Thus, the interval is 83.29 to 84.71, which corresponds to choice C.
Learning Objectives
- Elucidate and appreciate the idea of interval estimates, which includes the concepts of confidence intervals and margin of error.
- Comprehend the impact of sample size on the breadth of interval estimations.
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