Smoking and cancer deaths ~In 2010, it was reported that an estimated 28.7 percent of all cancer deaths in U.S. adults 35 and older could be attributed to cigarette smoking.Researchers from the American Cancer Society want to update this information and are particularly interested in determining if there is a difference in the proportion of cancer deaths that are attributable to smoking between the two US states, West Virginia and Hawaii.The researchers obtain a sample of 235 people from West Virginia who died from cancer. Using medical records they determine that 77 of these cancer deaths are attributable to smoking. In a sample of 230 people from Hawaii who died from cancer, 60 of the deaths were attributable to smoking. This information is summarized in the table below.StateSmokingNot smokingTotalPopulation 1: West Virginia77158235Population 2: Hawaii60170230Total137328465Round all calculated answers to four decimal places.1.Calculate the observed difference in the proportion of cancer deaths that are attributable to smoking between West Virginia and Hawaii.

1

2

=

p^1p^2=

2.Express the research question in terms of a null and an alternative hypothesis suitable for a randomization-based test.

0

H0: The proportion of cancer deaths that are attributable to smoking in West Virginia is

?

is less than

is more than

is the same as

is different from

the proportion of cancer deaths that are attributable to smoking in Hawaii.

HA: The proportion of cancer deaths that are attributable to smoking in West Virginia is

?

is less than

is more than

is the same as

is different from

the proportion of cancer deaths that are attributable to smoking in Hawaii.

3.To set up a randomization procedure using colored cards, how many cards would we need?a.How many of these cards should be green to represent cancer deaths in West Virginia?b.How many of these cards should be white to represent cancer deaths in Hawaii?

After we shuffle the cards:4.How many should be placed in a pile representing cancer deaths attributable to smoking?5.How many should be place in a pile representing cancer deathsnotattributable to smoking?We then calculate the difference between the proportion of cards representing cancer deaths attributable to smoking in West Virginia and Hawaii

1,

2,

p^1,simp^2,sim.6.If we repeat the randomization procedure many times, and construct a dotplot of the simulated differences,

1,

2,

p^1,simp^2,sim, where would you expect the distribution to be centered?7.To estimate a p-value for this test you would calculate the proportion of simulated differences that were

?

less than

greater than

beyond

the observed difference.8.Suppose you use computer technology to simulate results under the null hypothesis. After 3000 simulations, you find that 208 of the 3000 simulations produced a difference of more than our observed difference,|

1

2

|

|p^1p^2|, and 186 of the 3000 simulations produced a difference less than the opposite of our observed difference,|

1

2

|

|p^1p^2|.Use the results of the simulation to calculate the p-value.p-value =

9.Researchers in Canada replicate the research described in this problem using sample data from the two Canadian provinces of British Columbia and Quebec. Using a randomization-based hypothesis test, they obtain a p-value of 0.062. Based on this p-value, how much evidence do the Candadian researchers have against the null model?A. Little

B. Some

C. Strong

D. Very Strong

E. Extremely Strong