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 â€“ 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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