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Chapter 8: Q 34. (page 522)

The Large Counts condition When constructing a confidence interval for a population proportion, we check that both np鈭�andn1-p鈭�are at least 10

a. Why is it necessary to check this condition?

b. What happens to the capture rate if this condition is violated?

Short Answer

Expert verified

a. The sample distribution is approximately normal.

b. The chances are less to catch correct population parameter.

Step by step solution

01

Given Information

We check np^andn(1-p^)鈮�10during construction of confidence interval for population proportion.

02

Necessity of Conditions

Large Count condition, np^andn(1-p^)should be at least 10. We require large count condition to be satisfied, so that sampling distribution is normal approximately.

If it is not met, sampling distribution of proportion is skewed. Hence, we can't use normal distribution for estimation of confidence interval.

03

If the above Condition is Violated

If the condition is not satisfied, sampling distribution of sample proportion is skewed, hence normal distribution is not used to estimate confidence interval.

Correct population parameter won't be captured.

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Most popular questions from this chapter

Household income The 2015American Community Survey estimated the median

household income for each state. According to ACS, the 90%confidence interval for the 2015median household income in Arizona is \(51,492卤\)431.

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