Question

Construct a 99% confidence interval to estimate the population mean using the accompanying data. What assumptions need to be made to construct this interval? x=82 o= 16 n= 13 What assumptions need to be made to construct this interval? A. The population is skewed to one side. B. The sample size is less than 30. C. The population must be normally distributed. D. The population mean will be in the confidence interval. and the upper limit of With 99% confidence, when n= 13, the population mean is between the lower limit of (Type an integer or decimal rounded to two decimal places as needed.)

Answer 1

To construct a 99% confidence interval to estimate the population mean, assumptions of normal distribution and a sufficiently large sample size need to be made. The 99% confidence interval for the population mean can be calculated using the formula x ± Margin of Error (ME), where the margin of error depends on the critical value and the standard error of the mean (SEM).

Step-by-step explanation:

To construct a 99% confidence interval to estimate the population mean, the assumptions that need to be made are:

1. The population must be normally distributed.
2. The sample size should be large enough, preferably greater than 30.

Given the data x=82, o=16, and n=13, we can calculate the confidence interval as follows:

1. Calculate the standard error of the mean (SEM) using the formula SEM = o / sqrt(n).

2. Determine the critical value for a 99% confidence interval, which is 2.62 for a two-tailed test.

3. Calculate the margin of error (ME) using the formula ME = critical value * SEM.

4. Calculate the lower limit of the confidence interval by subtracting the margin of error from the sample mean, x - ME.

5. Calculate the upper limit of the confidence interval by adding the margin of error to the sample mean, x + ME.

Thus, the 99% confidence interval for the population mean is (x - ME, x + ME), which can be calculated using the given values.