(a)
To calculate: The mean of the sampling distribution of
(a)
Answer to Problem 29E
The required mean of the sampling distribution
Explanation of Solution
Given information:
Percent of orange candies in the machine = 45%
Number of candies for SRS = 25
Formula used:
The mean of the sampling distribution of a sample proportion
Calculation:
Consider that the sample distribution be p and
So,
And,
Know that the mean of the sampling distribution of a sample proportion
Substitute 0.45 for p in the above formula.
Since, the sampling proportion is an unbiased estimator for the population proportion; so the mean is
Hence, the required mean of the sampling distribution
(b)
To calculate: The standard deviation of the sampling distribution of
(b)
Answer to Problem 29E
The required standard deviation is 0.099487.
Explanation of Solution
Given information:
Percent of orange candies in the machine = 45%
Number of candies for SRS = 25
Formula used:
The standard deviation of the sampling distribution of
Calculation:
Consider that the sample distribution be p and sample size for SRS be n.
So,
And,
Know that the standard deviation of the sampling distribution of
Substitute 0.45 for
Since, the candy machine is large; so it contains more than 250 candies that is the 10% condition is satisfied.
Hence, the required standard deviation is 0.099487.
(c)
Whether the sampling distribution of
(c)
Answer to Problem 29E
The sampling distribution of
Explanation of Solution
Given information:
Percent of orange candies in the machine = 45%
Number of candies for SRS = 25
Formula used:
When the product of sample size and the sampling proportion that is,
Consider that the sample distribution be p and sample size for SRS be n.
So,
And,
Know that the product of sample size and the sampling proportion that is,
Substitute 0.45 for p and 25 for n in the expression
Again, substitute 0.45 for p and 25 for n in the expression
Since, both
Hence, the sampling distribution of
(d)
The change in the sampling distribution of
(d)
Answer to Problem 29E
The standard deviation of the sampling distribution
Explanation of Solution
Given information:
Percent of orange candies in the machine = 45%
Number of candies for SRS = 50
Formula used:
The standard deviation of the sampling distribution of
Calculation:
Consider that the sample distribution be p and sample size for SRS be n.
So,
And,
Know that the standard deviation of the sampling distribution of
Substitute 0.45 for
Thus, the standard deviation is 0.0703562.
Hence, the standard deviation of the sampling distribution
Chapter 7 Solutions
The Practice of Statistics for AP - 4th Edition
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