The mean muscular endurance score of a random sample of 60 subjects was found to be 145 with
standard deviation of 40. Construct a 95% confidence interval for the true mean. What is
the formula for the confidence interval?
The formula for the confidence interval is:
Confidence Interval = mean ± (critical value) * (standard deviation / √sample size)
To construct the 95% confidence interval, we need to find the critical value corresponding to a 95% confidence level. This can be found using a z-table or a calculator.
Assuming a normal distribution, the critical value for a 95% confidence level is approximately 1.96.
Substituting the values into the formula:
Confidence Interval = 145 ± (1.96) * (40 / √60)
Calculating the square root of the sample size, we have:
√60 ≈ 7.746
Therefore, the confidence interval becomes:
Confidence Interval = 145 ± (1.96) * (40 / 7.746)
Calculating the standard deviation divided by the square root of the sample size, we have:
40 / 7.746 ≈ 5.165
Finally, the 95% confidence interval is:
Confidence Interval = 145 ± (1.96) * 5.165
Calculating the upper and lower limits of the confidence interval, we have:
Upper Limit = 145 + (1.96) * 5.165 ≈ 155.99
Lower Limit = 145 - (1.96) * 5.165 ≈ 134.01
Therefore, the 95% confidence interval for the true mean is approximately (134.01, 155.99).