. The client was hoping for a likability score of at least 5.2. Use your sample mean and standard deviation identified in the answer to question 1 to complete the following table for the margins of error and confidence intervals at different confidence levels. Note: No further calculations are needed for the sample mean. (6 points: 2 points for each completed row) Confidence Level | Margin of error | Center interval | upper interval | Lower interval 68 95 99.7

The 68% confidence interval is (6.3, 6.7).

The 95% confidence interval is (6.1, 6.9).

The 99.7% confidence interval is (5.9, 7.1).

Step-by-step explanation:

The Central Limit Theorem states that if we have a population with mean μ and standard deviation σ and take appropriately huge random-samples (n ≥ 30) from the population with replacement, then the distribution of the sample-means will be approximately normally distributed.

Then, the mean of the sample means is given by,

And the standard deviation of the sample means (also known as the standard error)is given by,

The information provided is:

As n = 400 > 30, the sampling distribution of the sample-means will be approximately normally distributed.

(a)

Compute the 68% confidence interval for population mean as follows:

The 68% confidence interval is (6.3, 6.7).

The margin of error is:

(b)

Compute the 95% confidence interval for population mean as follows:

The 95% confidence interval is (6.1, 6.9).

The margin of error is:

(c)

Compute the 99.7% confidence interval for population mean as follows:

The 99.7% confidence interval is (5.9, 7.1).

The margin of error is:

just sum

10 + 10 = 20