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Dealing with Two Populations

Inferential statistics involves forming conclusions about a population parameter. We do so by constructing confidence intervals and testing claims about a population mean and other statistics. Typically, these methods deal with a sample from one population. We can extend the methods to situations involving two populations (and there are many such applications). This deliverable looks at two scenarios.

Instructions: The following worksheets describe two problems – the first problem is for independent samples and the seco
is for dependent samples. Your job is to demonstrate the solution to each scenario by showing how to work through each p
detail. You are expected to explain all of the steps in your own words.
ndependent samples and the second problem
owing how to work through each problem in
Independent Samples
A researcher conducted a test to learn the effect of lead levels in human bodies. He collected the IQ scores for a ran
low lead levels in their blood and another random sample of subjects with high lead levels in their blood. The summ
Use a 0.05 significance level to test the claim that the mean IQ score of people with low lead levels is higher than t
with high lead levels.
We do not know the values of the population standard deviations.
Low Lead Level
n1
70
High Lead Level
n2
28
94,11
17,45
87,2
9,68
s1
s2
1. Write the hypotheses in symbolic form, determine if the test is right-tailed, left-tailed, or two tailed and explain
2. Calculate the critical value, the test statistic, and p-value. Show calculations below.
Critical Value:
Test Statistic:
p-value:
3. Make a decision about the null hypothesis and explain your reasoning, then make a conclusion about the claim i
He collected the IQ scores for a random sample of subjects with
ad levels in their blood. The summary of finding is listed below.
th low lead levels is higher than the mean IQ score of people
tailed, or two tailed and explain why.
ake a conclusion about the claim in nontechnical terms.
Dependent Samples
The Harry Potter books and movies made a lot of money. A fan wanted to learn which of his favorite movies made
amounts grossed in millions during the first few days of releases of the movies Harry Potter and the Half
Order of the Phoenix. Use a 0.05 significance level to test his claim that the Prince movie did better at the box offic
Use the p-value method to determine whether or not to reject the null hypothesis and state your conclusion.
Days of
Release/B Phoenix
ook
1
44,3
2
18,4
3
25,8
4
28,3
5
22,0
6
10,7
7
9,3
8
8,4
9
7,6
10
10,2
Prince
58,2
22,0
26,8
29,2
21,8
9,9
9,4
7,5
6,9
9,2
4. Write the hypotheses in symbolic form, determine if the test is right-tailed, left-tailed, or two tailed and explain
5. Calculate the critical value, the test statistic, and p-value. Show calculations below.
Critical Value:
Test Statistic:
p-value:
6. Make a decision about the null hypothesis and explain your reasoning, then make a conclusion about the claim i
hich of his favorite movies made more money. He collected the
rry Potter and the Half-Blood Prince and Harry Potter and the
movie did better at the box office.
s and state your conclusion.
tailed, or two tailed and explain why.
ake a conclusion about the claim in nontechnical terms.

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