It is known that the population mean for the Full Scale IQ of the WAIS is 100 with a standard

deviation of 15. A researcher assesses a sample of 200 adults and find that they have a
mean Full Scale IQ of 102. The point estimate of the mean for this group is ___________
and the 99% confidence interval for this group is ____________________ .
a. 100; (97.27; 102.73)
b. 102; (97.27, 102.73)
c. 100; (99.27; 104.73)
d. 102; (99.27, 104.73)

To find the point estimate for the mean, we simply use the value of the sample mean, which in this case is 102.

So, the point estimate of the mean for this group is 102.

To find the confidence interval, we can use the formula:

Confidence interval = sample mean ± (critical value * standard error)

First, we need to calculate the standard error:

Standard error = standard deviation / √sample size

The standard deviation is given as 15 and the sample size is 200, so:

Standard error = 15 / √200

Next, we need to find the critical value. Since the confidence level is 99%, the alpha level is 1 - confidence level = 1 - 0.99 = 0.01. Since this is a two-tailed test, we divide the alpha level by 2 to get 0.01 / 2 = 0.005.

Looking up the critical value for an alpha level of 0.005 in a Z-table, we find the value to be approximately 2.57.

Now we can calculate the confidence interval:

Confidence interval = 102 ± (2.57 * (15 / √200))

Confidence interval = 102 ± (2.57 * 1.06)

Confidence interval = 102 ± 2.73

The lower limit of the confidence interval is 102 - 2.73 = 99.27
The upper limit of the confidence interval is 102 + 2.73 = 104.73

So, the 99% confidence interval for this group is (99.27, 104.73).

Therefore, the correct answer is d. 102; (99.27, 104.73).

To calculate the point estimate and the confidence interval, we can use the formula:

Point estimate (x̄) = Mean of the sample
Confidence Interval = Point estimate ± Margin of Error

First, let's calculate the point estimate:
The mean Full Scale IQ for the sample is given as 102.

So, the point estimate (x̄) = 102.

To calculate the confidence interval, we need the margin of error. The margin of error is calculated using the formula:

Margin of Error = (Z)(Standard Deviation / √n)

Where:
Z is the Z-value (also known as the Z-score) for the desired confidence level
Standard Deviation is the population standard deviation
n is the sample size

In this case, the confidence level is 99%. Since it is not specified whether to use a one-tailed or two-tailed test, we will assume a two-tailed test. Therefore, the critical Z-value can be found using a standard normal distribution table, or it can be calculated using statistical software. For a 99% confidence level, the Z-value is approximately 2.58.

Standard Deviation is given as 15, and the sample size is 200.

Plugging in the values:
Margin of Error = (2.58)(15 / √200) ≈ 2.73

Now we can calculate the confidence interval:
Confidence Interval = Point estimate ± Margin of Error

Confidence Interval = 102 ± 2.73 = (99.27, 104.73)

So, the answer is:
The point estimate of the mean for this group is 102, and the 99% confidence interval for this group is (99.27, 104.73).

Therefore, the correct option is d. 102; (99.27, 104.73).