What is the sum? 2/x^2+4/x2
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Answer:
The 99% confidence interval for the difference in the two proportions is (-0.0247, 0.2833).
Step-by-step explanation:
Before building the confidence interval, we need to understand the Central Limit Theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes 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
A BYU-Idaho professor took a survey of his classes and found that 82 out of 90 people who had served a mission had personally met a member of the quorum of the twelve apostles.
This means that:
Of the non-returned missionaries that were surveyed 86 of 110 had personally met a member of the quorum of the twelve apostles.
This means that:
Distribution of the difference:
Calculate a 99% confidence interval for the difference in the two proportions.
The confidence interval is:
In which
z is the z-score that has a p-value of .
99% confidence level
So , z is the value of Z that has a p-value of
, so
.
The lower bound of the interval is:
The 99% confidence interval for the difference in the two proportions is (-0.0247, 0.2833).