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.

# 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.

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1 year ago

1 year ago