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Chapter 8: Q 31. (page 522)

Check whether each of the conditions is met for calculating a confidence interval for the population proportion

Salty chips A quality control inspector takes a random sample of 25 bags of potato chips from the thousands of bags filled in an hour. Of the bags selected, 3 had too much salt.

Short Answer

Expert verified

The condition which is not met is that of normality.

Step by step solution

01

Given Information

It is given that n=25

Population is thousand of bags of potato.

02

Explanation

  • Condition of Random Selection: As sample is SRS, this condition is satisfied.
  • Less than 10% of population: role="math" localid="1654278677916" 25is less than 10%of population (thousand of population bags)
  • Number of success and failure should be ≥10: No of success are 3<10and failure is 25-3=22≥10. This condition is not met.

All conditions are not met.

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Most popular questions from this chapter

A Gallup poll found that only 28%of American adults expect to inherit money or valuable possessions from a relative. The poll’s margin of error was ±3 percentage points at a 95%confidence level. This means that

a. the poll used a method that gets an answer within 3% of the truth about the population 95%of the time.

b. the percent of all adults who expect an inheritance must be between 25%and 31%.

c. if Gallup takes another poll on this issue, the results of the second poll will lie between 25%and 31%.

d. there’s a 95% chance that the percent of all adults who expect an inheritance is between

25% and 31%.

e. Gallup can be 95% confident that between 25% and 31% of the sample expect an inheritance.

September 11 A recent study asked U.S. adults to name 10historic events that occurred in their lifetime that have had the greatest impact on the country. The most frequently chosen answer was the September 11,2001, terrorist attacks, which was included by 76%of the 2025randomly selected U.S. adults. Construct and interpret a 95%confidence interval for the proportion of all U.S. adults who would include the 9/11attacks on their list of 10historic events.

Fun size candyA candy bar manufacturer sells a “fun size” version that is advertised to weigh 17grams. A hungry teacher selected a random sample of 44fun size bars and found a 95%confidence interval for the true mean weight to be 16.945grams to 17.395grams.

a. Does the confidence interval provide convincing evidence that the true mean weight is different than 17grams? Explain your answer.

b. Does the confidence interval provide convincing evidence that the true mean weight is 17grams? Explain your answer.

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

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?
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