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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

The 10%condition When constructing a confidence interval for a population proportion, we check that the sample size is less than 10%of the population size.

a. Why is it necessary to check this condition?

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

Student body totals Use your interval from Exercise 40 to construct and interpret a 99%confidence interval for the total number of students at the school that the student body president can identify by name. Then use your interval to evaluate the president鈥檚 claim.

More cheating Refer to Exercise 36. Calculate and interpret the standard error of p^for these data.

t time When constructing confidence intervals for a population mean, we almost always use critical values from a t distribution rather than the standard Normal distribution.

a. When is it necessary to use a t critical value rather than a z critical value when constructing a confidence interval for a population means?

b. For a particular level of confidence, explain what happens to the t critical values as Page Number: 548 the degrees of freedom increase.

Age and video games Refer to Exercise 41. The study also estimated that 67% of adults aged 18鈥�29play video games, but only 25%of adults aged 65and older play video games.

a. Explain why you do not have enough information to give confidence intervals for these two age groups separately.

b. Do you think a 95% confidence interval for adults aged 18鈥�29 would have a larger or smaller margin of error than the estimate from Exercise 41? Explain your answer.
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