IQ and Lead Exposure: Confidence Interval The data set IQLEAD (found in the lab description) lists full IQ scores for a random sample of subjects selected from a group with low lead levels in their blood and another random sample of subjects selected from a group with high lead levels in their blood. The statistics are for these groups are summarized below. Build 95% Confidence interval to test the claim that the mean IQ score of people with low lead levels is higher than the mean IQ score of people with high lead levels. Low Lead Level: n = 78, x̄= 92.88462, s = 15.34451 High Lead Level: n = 33, x̄ = 86.90476, s = 8.988352 2: Find the 95% confidence interval a) Press STAT & scroll to TESTS & select “2-SampTInt...” (option 0 in TI83Plus) & press Enter (for a hypothesis test of a claim involving two populations b) Enter the following: Inpt: Stats (The statistics are given above) x̄1= sample mean from the low lead level group Sx1 = sample standard deviation from the low lead level group n1 = sample size from the low lead level group x̄2= sample mean from the high lead level group Sx2 = sample standard deviation from the high lead level group n2 = sample size from the high lead level group Pooled: Choose NO c) Highlight “Calculate” and press ENTER & make note of the calculations as you will need them below. Enter the values of confidence interval below here. Round each value to two decimal places. The 95% confidence interval = ( _, _)

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IQ and Lead Exposure: Confidence Interval The data set IQLEAD (found in the lab description) lists full IQ scores for a random sample of subjects selected from a group with low lead levels in their blood and another random sample of subjects selected from a group with high lead levels in their blood. The statistics are for these groups are summarized below. Build 95% Confidence interval to test the claim that the mean IQ score of people with low lead levels is higher than the mean IQ score of people with high lead levels.

Low Lead Level: n = 78, x̄= 92.88462, s = 15.34451

High Lead Level: n = 33, x̄ = 86.90476, s = 8.988352

2: Find the 95% confidence interval

a) Press STAT & scroll to TESTS & select “2-SampTInt...” (option 0 in TI83Plus) & press Enter (for a hypothesis test of a claim involving two populations

b) Enter the following:

Inpt: Stats (The statistics are given above)
x̄1= sample mean from the low lead level group
Sx1 = sample standard deviation from the low lead level group
n1 = sample size from the low lead level group
x̄2= sample mean from the high lead level group
Sx2 = sample standard deviation from the high lead level group
n2 = sample size from the high lead level group
Pooled: Choose NO

c) Highlight “Calculate” and press ENTER & make note of the calculations as you will need them below.

Enter the values of confidence interval below here. Round each value to two decimal places.

The 95% confidence interval = ( _, _)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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