in waste em to have an unusually high occurrence of cancer. FBI agent Megan Reeves believes that this might represent a "cancer cluster." Charlie warns her not to jump to this conclusion too quickly. The FBI may have used a statistical technique called a two-proportion test to decide whether the rate of cancer seems to be unusually high in this location. A two-proportion test is a statistical technique that can be used to decide if the rate of cancer seems to be different in different areas of the country. This activity contains an introduction to this test. Consider the following data on cases of cancer, based on a hypothetical random sample of 50,000 people from each of six states in New England. A large sample is used here because the rate of incidence of cancer is quite small. State Connecticut Maine Massachusetts New Hampshire Rhode Island Vermont Cancer Cases 268 291 268 251 281 249

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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Input the data as follows:
x1 represents the number of cases of cancer in the sample from
Maine. x2 represents the number from New Hampshire. n1 and
n2, represent the number of people in each sample (50,000).
Because we are interested in whether the proportion of cases of
cancer is higher in Maine than in New Hampshire, choose >p2.
Then select Calculate to produce the results shown at the right.
2-ProeZTest
x1:291
n1:50000
x2:251
n2:50000
P1:#P2 P2 >PZ
Calculate Draw
If the samples were truly random, the set of all possible differences between the sample
proportions would form a normal distribution. The informal description of a normal distribution is a
"bell shaped curve". The results of the test show whether the difference observed in the data is
typical of most of the differences or if the difference is in fact considerable.
2-PropZTest
P1>P2
z=1.72282231
P=.0424602946
The screen shows a p-value of about 0.042. This value means that if there were no actual
difference between the cancer rates of the two states, the difference observed in these samples
would happen by chance about 4.2% of the time. Many statisticians use 5% (0.05) as a maximum
value to decide if an observation is rare, so they would conclude in this example that it is unlikely to
get such results as these by chance. Statisticians use sampling to make predictions about the
whole population. In this example, it is likely that the actual cancer rate in Maine is higher than that
in New Hampshire, based on the sample data. For a p-value higher than 5%, statisticians would
state that there is not enough information to conclude that one rate was actually higher than the
other. They would not conclude, however, that the there is no difference between the rates.
P1=.00582
P2=.00502
P=.00542
2. Connecticut and Rhode Island are also neighboring states. Compare their cancer data using a
two-proportion test. Choose <p2 or >p2, as appropriate. What is the p-value for this test?
Explain the meaning of this number in the context of this example. Do you have enough
information to conclude that one rate is larger than the other?
O
3. The sample data in this activity indicate that 268 out of 50,000 people in both the Connecticut
and Massachusetts samples were diagnosed with cancer. Does this mean that the actual rates
of incidence of cancer in the total populations of the two states were the same? Compare their
cancer data using a two-proportion test. Choose either <p2 or >p2. What is the p-value for this
test? Explain the meaning of this number in the context of this example.
Ai
4. What is the relationship between the p-value obtained for the <p2 or> p2 test and the value
for the # p2 test?
In
*Snowing now
6
R
4
Transcribed Image Text:Input the data as follows: x1 represents the number of cases of cancer in the sample from Maine. x2 represents the number from New Hampshire. n1 and n2, represent the number of people in each sample (50,000). Because we are interested in whether the proportion of cases of cancer is higher in Maine than in New Hampshire, choose >p2. Then select Calculate to produce the results shown at the right. 2-ProeZTest x1:291 n1:50000 x2:251 n2:50000 P1:#P2 P2 >PZ Calculate Draw If the samples were truly random, the set of all possible differences between the sample proportions would form a normal distribution. The informal description of a normal distribution is a "bell shaped curve". The results of the test show whether the difference observed in the data is typical of most of the differences or if the difference is in fact considerable. 2-PropZTest P1>P2 z=1.72282231 P=.0424602946 The screen shows a p-value of about 0.042. This value means that if there were no actual difference between the cancer rates of the two states, the difference observed in these samples would happen by chance about 4.2% of the time. Many statisticians use 5% (0.05) as a maximum value to decide if an observation is rare, so they would conclude in this example that it is unlikely to get such results as these by chance. Statisticians use sampling to make predictions about the whole population. In this example, it is likely that the actual cancer rate in Maine is higher than that in New Hampshire, based on the sample data. For a p-value higher than 5%, statisticians would state that there is not enough information to conclude that one rate was actually higher than the other. They would not conclude, however, that the there is no difference between the rates. P1=.00582 P2=.00502 P=.00542 2. Connecticut and Rhode Island are also neighboring states. Compare their cancer data using a two-proportion test. Choose <p2 or >p2, as appropriate. What is the p-value for this test? Explain the meaning of this number in the context of this example. Do you have enough information to conclude that one rate is larger than the other? O 3. The sample data in this activity indicate that 268 out of 50,000 people in both the Connecticut and Massachusetts samples were diagnosed with cancer. Does this mean that the actual rates of incidence of cancer in the total populations of the two states were the same? Compare their cancer data using a two-proportion test. Choose either <p2 or >p2. What is the p-value for this test? Explain the meaning of this number in the context of this example. Ai 4. What is the relationship between the p-value obtained for the <p2 or> p2 test and the value for the # p2 test? In *Snowing now 6 R 4
In "Waste Not," the FBI discovers that the children in the area of a sinkhole seem to have an
unusually high occurrence of cancer. FBI agent Megan Reeves believes that this might represent a
"cancer cluster." Charlie warns her not to jump to this conclusion too quickly. The FBI may have
used a statistical technique called a two-proportion test to decide whether the rate of cancer seems
to be unusually high in this location. A two-proportion test is a statistical technique that can be used
to decide if the rate of cancer seems to be different in different areas of the country. This activity
contains an introduction to this test.
Consider the following data on cases of cancer, based on a hypothetical random sample of
50,000 people from each of six states in New England. A large sample is used here because the
rate of incidence of cancer is quite small.
State
Connecticut
Maine
Massachusetts
New Hampshire
Rhode Island
Vermont
Cancer Cases
268
291
268
251
281
249
Based on these data, does there seem to be an association between location and incidence of
cancer? One way of attempting to answer this question is to perform a statistical procedure called
a two-proportion test. This is one of many procedures for testing hypotheses that are studied in
statistics classes.
1. Maine and New Hampshire are neighboring states. What percent of the Maine sample had
cancer? What percent of the New Hampshire sample had cancer? Do you think that the
difference between these two percentages is considerable?
E
The data shows that the proportion of cancer cases in the sample from Maine is higher than the
proportion of cancer cases in the sample from New Hampshire. If the samples involved are
randomly chosen, a two-proportion test can determine if it is likely that the proportion of cases for
the entire state's population is higher in Maine than New Hampshire. A hypothesis test assumes
that there is no difference and inspects the data to see if they in fact do not support this
assumption. In this case, the hypothesis is that there is no difference in the cancer rates for the
states. The alternative hypothesis is that the cancer rate is higher in Maine than in New
Hampshire. A two-proportion test can indicate that the initial hypothesis should be questioned.
To perform this test on your calculator, press [STAT] and go to the
TESTS menu. Then select 6:2-PropZTest....
EDIT CALC TESTS
1:2-Test...
2: T-Test
3:2-Samp2Test....
4:2-SamPTTest....
5:1-PropZTest.....
582-ProPZTest...
IZIZInterval
***Snowing now
Transcribed Image Text:In "Waste Not," the FBI discovers that the children in the area of a sinkhole seem to have an unusually high occurrence of cancer. FBI agent Megan Reeves believes that this might represent a "cancer cluster." Charlie warns her not to jump to this conclusion too quickly. The FBI may have used a statistical technique called a two-proportion test to decide whether the rate of cancer seems to be unusually high in this location. A two-proportion test is a statistical technique that can be used to decide if the rate of cancer seems to be different in different areas of the country. This activity contains an introduction to this test. Consider the following data on cases of cancer, based on a hypothetical random sample of 50,000 people from each of six states in New England. A large sample is used here because the rate of incidence of cancer is quite small. State Connecticut Maine Massachusetts New Hampshire Rhode Island Vermont Cancer Cases 268 291 268 251 281 249 Based on these data, does there seem to be an association between location and incidence of cancer? One way of attempting to answer this question is to perform a statistical procedure called a two-proportion test. This is one of many procedures for testing hypotheses that are studied in statistics classes. 1. Maine and New Hampshire are neighboring states. What percent of the Maine sample had cancer? What percent of the New Hampshire sample had cancer? Do you think that the difference between these two percentages is considerable? E The data shows that the proportion of cancer cases in the sample from Maine is higher than the proportion of cancer cases in the sample from New Hampshire. If the samples involved are randomly chosen, a two-proportion test can determine if it is likely that the proportion of cases for the entire state's population is higher in Maine than New Hampshire. A hypothesis test assumes that there is no difference and inspects the data to see if they in fact do not support this assumption. In this case, the hypothesis is that there is no difference in the cancer rates for the states. The alternative hypothesis is that the cancer rate is higher in Maine than in New Hampshire. A two-proportion test can indicate that the initial hypothesis should be questioned. To perform this test on your calculator, press [STAT] and go to the TESTS menu. Then select 6:2-PropZTest.... EDIT CALC TESTS 1:2-Test... 2: T-Test 3:2-Samp2Test.... 4:2-SamPTTest.... 5:1-PropZTest..... 582-ProPZTest... IZIZInterval ***Snowing now
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