A sample of 25 men has a mean weight of 65kg with standard deviation of 8kg. Suppose that the weight of men follows normal distribution with a standard deviation of 10kg. Find a 95% confidence interval for the population mean μ.
To find the 95% confidence interval for the population mean μ, we can use the formula:
Confidence Interval = sample mean ± (critical value) * (standard deviation / square root of sample size)
1. Calculate the critical value:
Since we want a 95% confidence interval and the sample size is 25, we can use the t-distribution (since sample size is small) and find the critical value that corresponds to a 95% confidence level with 24 degrees of freedom. From a t-distribution table (or using statistical software), we find the critical value to be approximately 2.064.
2. Calculate the standard error:
The standard error is the standard deviation divided by the square root of the sample size. In this case, the standard error = 10kg / √25 = 2kg.
3. Calculate the confidence interval:
Using the formula mentioned earlier, the confidence interval can be calculated as follows:
Confidence Interval = 65kg ± (2.064) * (2kg)
Now we can calculate the upper and lower limits of the confidence interval:
Upper Limit = 65kg + (2.064) * (2kg)
Lower Limit = 65kg - (2.064) * (2kg)
Calculating these values, we find:
Upper Limit ≈ 65kg + 4.13kg ≈ 69.13kg
Lower Limit ≈ 65kg - 4.13kg ≈ 60.87kg
Therefore, the 95% confidence interval for the population mean μ is approximately 60.87kg to 69.13kg.