Concept explainers
(a)
To Explain: the shape, centre and variability of the sampling distribution of
(a)

Answer to Problem 101E
Approximately normal with
Explanation of Solution
Given:
Formula used:
Calculation:
The hypothesis distribution of the sample proportions
The mean of the sampling distribution of the sample proportions
Then 10% condition requires that the sample is less than 10% of the population size. Assuming that the sample of 500 potatoes is less than 10% of the population of all potatoes, the 10% condition is satisfied.
The standard deviation of the sampling distribution of the sample proportion
Therefore the sampling distribution of the sample proportion
(b)
To find: the value of
(b)

Answer to Problem 101E
Explanation of Solution
Given:
From the result part (a) is approximately
Formula used:
Calculation:
If a z-score has probability of 0.05 to the right, so it has a probability of 1-0.05=0.95 to left.
It is observed that the probability of 0.95 lies exactly between 0.9495 and 0.9505. Which associate to the Z-score of 1.64 and 1.65 and then estimate the Z-score associating to 0.95 as the Z-score exactly in the middle between 1.64 and 1.65, which is 1.645
The Z-score is
The two found expressions of the Z-score then
Therefore the sample proportion
(c)
To Explain: the shape, centre and variability of the sampling distribution of
(c)

Answer to Problem 101E
Approximately normal with the mean 0.11 and standard deviation 0.01399
Explanation of Solution
Given:
Formula used:
Calculation:
The sampling distribution of the sample proportions
The mean of the sampling distribution of the sample proportions
The standard deviation of the sampling distribution of the sample proportion
Therefore the sampling distribution of the sample proportion
(d)
To find: the probability of getting a sample proportion from the part (c) greater than the value found in part (b).
(d)

Answer to Problem 101E
0.7642=76.42%
Explanation of Solution
Given:
Formula used:
Calculation:
Z-score is
Probability is
Therefore the power of the test is 0.7642 or 76.42%
Chapter 9 Solutions
PRACTICE OF STATISTICS F/AP EXAM
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