What is the degree measure for one sixth of a right angle
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Answer:
The 95% confidence interval for the difference in the proportion of cancer diagnoses between the two groups is (0.3834, 0.5166).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction between normal variables.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
The randomly sampled 400 dogs from homes where an herbicide was used on a regular basis, diagnosing lymphoma in 230 of them.
This means that:
Of 200 dogs randomly sampled from homes where no herbicides were used, only 25 were found to have lymphoma.
This means that:
Distribution of the difference:
Confidence interval:
The confidence interval is:
In which
z is the zscore that has a pvalue of .
95% confidence level
So , z is the value of Z that has a pvalue of
, so
.
The lower bound is
The upper bound is
The 95% confidence interval for the difference in the proportion of cancer diagnoses between the two groups is (0.3834, 0.5166).
The light's coverage area is given mathematically as i.e. Area=
Given that a lighthouse casts a revolving beam of light as far as they peir and asked the area is covered.
The revolving beam of light covers the whole space i.e entirely 360°
I.e. it forms a circle-like region
Area of circle = { where r is the radius of circle}
Let's assume the distance traveled by light as "d"
as it forms a circular region, it forms a circle of radius "d"
Mathematical connection i.e. area of the region
⇒area of circular region= {where d is the radius of region}
Learn more about area here:
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