A sample of 64 was taken from a population, with the mean of the sample being 42 and the standard deviation of the sample being 5. What is the 95% confidence interval for the mean of the population?
(37.25, 46.75)
(37, 47)
(40.75, 43.25)
(41.375, 42.625)
To calculate the 95% confidence interval for the mean of the population, we can use the formula:
Confidence Interval = sample mean +/- (critical value * standard error)
First, let's determine the critical value for a 95% confidence level with 63 degrees of freedom (since the sample size is 64). Using a t-distribution table or calculator, we find the critical value to be approximately 2.00.
Next, calculate the standard error:
Standard Error = standard deviation / √sample size
Standard Error = 5 / √64
Standard Error = 5 / 8
Standard Error = 0.625
Now, we can calculate the confidence interval:
Lower bound = 42 - (2.00 * 0.625) = 42 - 1.25 = 40.75
Upper bound = 42 + (2.00 * 0.625) = 42 + 1.25 = 43.25
Therefore, the 95% confidence interval for the mean of the population is (40.75, 43.25). The answer is:
(40.75, 43.25)