Section 8.3: The Sampling Distribution of a Sample Proportion

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Presentation transcript:

Section 8.3: The Sampling Distribution of a Sample Proportion

Sample proportion of successes:

General Properties of the Sampling Distribution of p Rule 3: When n is large and π is not too near 0 or 1, the sampling distribution of p is approximately normal.

The farther the value of π is from The farther the value of π is from .5, the larger n must be for a normal approximation to the sampling distribution of p to be accurate. Rule of Thumb - If both np ≥ 10 and n(1-p)  10, then it is safe to use a normal approximation.

Example If the true proportion of defectives produced by a certain manufacturing process is 0.08 and a sample of 400 is chosen, what is the probability that the proportion of defectives in the sample is greater than 0.10?

Since n = 400(0.08) = 32 > 10 and n(1-) = 400(0.92) = 368 > 10, it’s reasonable to use the normal approximation.

Example continued

Example Suppose 3% of the people contacted by phone are receptive to a certain sales pitch and buy your product. If your sales staff contacts 2000 people, what is the probability that more than 100 of the people contacted will purchase your product?