Download Section 7.3 sampling distribution of sample proportion discussion

Section 7.3 Sampling Distribution of the Sample Proportion DISCUSSION
Statistics
In this case, the summary statistics is the proportion of __________________.
In Section 6.2 we looked at the probabilities of the _____________ of successes
in a sample of size ______. For this case, the sampling distribution of the
number of successes _______ is:
It has a mean __________________
It has a standard error _______________________
It will be approximately ________________ as long as _____ is large
enough.
As a general guideline, the “large enough” threshold is that ________
and _____________ should both be at least _______.
Example, the age distribution in the DRC is given below (estimate in 2014):
Age structure: 0-14 years: 43.1% (male 16,810,549/female 16,552,685)
15-24 years: 21.4% (male 8,292,444/female 8,248,326)
25-54 years: 29.4% (male 11,359,385/female 11,405,442)
55-64 years: 3.5% (male 1,287,895/female 1,457,499)
65 years and over: 2.6% (male 849,840/female 1,169,679) (2014 est.)
Notice that there is a 6.1% chance of being 55 or over in the DRC. Is it valid to
consider the probability that in a random sample of 25 Congolese, 5 of them or
more would be 55 years or older? If it is valid, compute the probability.
First, check that the population is large enough to analyze a random
sample of 25:
There is a 6.1% chance of being 55 or over in the DRC. Is it valid to consider
the probability that in a random sample of 200 Congolese, 15 or more of them
would be 55 years or older? If it is valid, compute the probability.
Sampling Distribution of the Sampling ____________________
If we take a sample of 200 Congolese, what is the probability that 7.5% of them
will be 55 years or older? This is the same as the question we have just
answered, because
________
 _______.
________
However, now we are considering the
_________________ of successes instead of the _____________ of successes.
Say we are dealing with a random _____________ of size _____ from a
population where the actual proportion of successes is _______. The
proportion of successes in the sample is represented by _______ (__________).
For each sample, the value of p-hat is computed as:
The formulas for the mean, _______ and standard error, ________ of the
sampling distribution of the sample proportion is found by dividing by ____ to
convert the _________ of successes to the _________________ of successes:
Summary for Properties of the Sampling Distribution of the Sample Proportion
 Mean of the sampling distribution is equal to the mean of the
population: __________________.
 The standard error of the sampling distribution is equal to the
standard deviation of the population:
 pˆ 
____________
___________
Let us now consider our problem:
If we take a sample of 200 Congolese, what is the probability that 7.5% of them
will be 55 years or older?
Would it be unusual to find that more than 12% of 200 Congolese selected
would have an age of 55 years or older?