The 90% confidence interval for the population mean of the considered population from the given sample data is given by: Option C: [130.10, 143.90]
<h3>How to find the confidence interval for population mean from large samples (sample size > 30)?</h3>
Suppose that we have:
- Sample size n > 30
- Sample mean =
- Sample standard deviation = s
- Population standard deviation =
- Level of significance =
Then the confidence interval is obtained as
- Case 1: Population standard deviation is known
- Case 2: Population standard deviation is unknown.
For this case, we're given that:
- Sample size n = 90 > 30
- Sample mean =
= 138
- Sample standard deviation = s = 34
- Level of significance =
= 100% - confidence = 100% - 90% = 10% = 0.1 (converted percent to decimal).
At this level of significance, the critical value of Z is: = ±1.645
Thus, we get:
Thus, the 90% confidence interval for the population mean of the considered population from the given sample data is given by: Option C: [130.10, 143.90]
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