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Answer:
So the p value obtained was a very high value and using the significance level given we have
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that the true proportion not differs significantly from the specified value of 0.00034 or 0.034%.
Step-by-step explanation:
1) Data given and notation
n=420095 represent the random sample taken
X=135 represent the subjects developed cancer of the brain or nervous system (based on data from the Journal of the National Cancer Institute as reported in USA Today)
estimated proportion of subjects developed cancer of the brain or nervous system (based on data from the Journal of the National Cancer Institute as reported in USA Today)
is the value that we want to test
represent the significance level
Confidence=99.5% or 0.995
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
2) Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the brain or nervous system at a rate that is different from the rate of 0.0340% :
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statistic, and the is given by:
(1)
The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value
.
3) Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
4) Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided . The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:
So the p value obtained was a very high value and using the significance level given we have
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that the true proportion not differs significantly from the specified value of 0.00034 or 0.034%.
The unit of measurement is not specified, so for the sake of this problem, we'll assume it's radians (If you need it in degrees, I'll be happy to edit).
Find the compliment of 0.25:
Complementary angles add up to 90 degrees. In radians, this would be π/2. If you're unsure how I got this, check degrees to radian conversions.
The compliment of 0.25 would be
(1/4=0.25)
(This is the simplified form in case you're homework needs it in this form)
That's the compliment. In decimal (rounded to the nearest hundredth), this would be 1.32 radians.
Find the supplement of 7π/8:
Supplementary angles add up to 180 degrees. In radians, this would be π.
The supplement would be the following:
Thus, the supplement is π/8 radians. If any of this struck you as confusing, comment and I'd be happy to clarify.
Find the compliment of 0.25:
Complementary angles add up to 90 degrees. In radians, this would be π/2. If you're unsure how I got this, check degrees to radian conversions.
The compliment of 0.25 would be
(This is the simplified form in case you're homework needs it in this form)
That's the compliment. In decimal (rounded to the nearest hundredth), this would be 1.32 radians.
Find the supplement of 7π/8:
Supplementary angles add up to 180 degrees. In radians, this would be π.
The supplement would be the following:
Thus, the supplement is π/8 radians. If any of this struck you as confusing, comment and I'd be happy to clarify.