Can proximity (closeness) to a power line cause cancer? The 145 employees 3. at
ID: 3179466 • Letter: C
Question
Can proximity (closeness) to a power line cause cancer? The 145 employees 3. at the slater school in Fresno, located 100 ft from a power line, surfaced 8 cancers when the expected number, based on national statistics, was 4.2 whether this is variation from the overall national or if is example other explanation (e.g., radiation from the power line). What assumptions would justify modeling the probability of cancers in this group X where chance in this (145 theta) where theta is the chance of cancer of for an employee at Slater? Since 4.2/145 almostequalto 0.029, asserting that theta would say that the lying cancer rate at Slater is as the national average. Perform the same the staff at Slater was drawn) was less than or equal to 0.029 vs. the alternative that it was greater. Be sure to provide all the details of our hypothesis testing protocol. continuity correction. Find a 99% confidence interval for the true proportion. Find the power of the test against the alternative 0 0.06 To what population do the results of the test apply (that is, generalize to)?Explanation / Answer
a) Let X be the random variable that number of cancer cases.
Here given that, X ~Binomial(145, 0.029)
Binomial distribution has three basic assumptions :
b) Here we have to test the hypothesis that,
H0 : p = 0.029 vs H1 : p > 0.029
p is population proportion of the number of cancer cases.
Assume alpha = level of significance = 0.01
Given that,
x = 8
n = 145
Here we use z-test for testing single proprotion.
This we can done in MINITAB.
steps :
STAT --> Basic statistics --> 1 Proportion --> Summarized data --> number of trial : 145 --> number of events : 8 --> Options --> Confidence level : 99.0 --> Test proportion : 0.029 --> Alternative : greator than --> click on use test and interval based on normal distribution --> ok --> ok
————— 3/21/2017 10:37:09 AM ————————————————————
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Test and CI for One Proportion
Test of p = 0.029 vs p > 0.029
99%
Lower
Sample X N Sample p Bound Z-Value P-Value
1 8 145 0.055172 0.011063 1.88 0.030
Here Test statistic = 1.88
P-value = 0.030
P-value > alpha (0.01)
Accept H0 at 1% level of significance.
Conclusion : The true proportion may be less than or equal to 0.029
c) 99% confidence interval for true proportion :
99% confidence interval for proportion is,
p^ - E < P < p^ + E
where p^ is the sample proportion
p^ = x/n
E is the margin of error
The confidence interval for proportion also we can done in TI-83 calculator.
steps :
STAT --> TESTS --> A: 1-PropZInt --> ENTER --> Input all the values --> Calculate --> ENTER
99% confidence interval for true proportion is (0.00633, 0.10401).
d) Here we have to find Power for alternative value is 0.06
Power = 1 - P(type II error)
P(type II error) = P(Accept H0/ H1 = p = 0.06)
Power we can find in MINITAB.
steps :
STAT --> Power and sample size --> 1 Proportion --> Specify values for any two of the following --> sample sizes : 145 --> Alternative values of p : 0.06 --> Hypothesized p : 0.029 --> Options --> Alternative hypothesis : greator than --> Significance level : 0.01 --> ok --> ok
————— 3/21/2017 11:00:30 AM ————————————————————
Welcome to Minitab, press F1 for help.
Power and Sample Size
Test for One Proportion
Testing proportion = 0.029 (versus > 0.029)
Alpha = 0.01
Alternative Sample
Proportion Size Power
0.06 145 0.471322
Power = 0.471322