/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q 81. One reason for using a t distrib... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Q 81. (page 543)

One reason for using a t distribution instead of the standard Normal distribution to find critical values when calculating a level C confidence interval for a population mean is that

a. zcan be used only for large samples.

b. zrequires that you know the population standard deviation 蟽.

c. z requires that you can regard your data as an SRS from the population.

d. z requires that the sample size is less than 10% of the population size.

e. a z critical value will lead to a wider interval than a t critical value.

Short Answer

Expert verified

Option (b) is correct.

Step by step solution

01

Given Information

We are given that

a. z can be used only for large samples.

b. z requires that you know the population standard deviation 蟽.

c. z requires that you can regard your data as an SRS from the population.

d. z requires that the sample size is less than 10% of the population size.

e. a z critical value will lead to a wider interval than a t critical value.

02

Explanation

To calculate confidence interval of population mean, zdistribution is used. This is used if standard deviation is known.

If standard deviation is known, tdistribution is used to find critical value.

Option (b) is correct.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Prayer in school Refer to Exercise 5.

a. Explain what would happen to the length of the interval if the confidence level were increased to 99%.

b. How would a 95%confidence interval based on double the sample size compare to the original 95%interval?

c. The news article goes on to say: 鈥淭he theoretical errors do not take into account

additional errors resulting from the various practical difficulties in taking any survey of public opinion.鈥� List some of the 鈥減ractical difficulties鈥� that may cause errors which are not included in the 卤3 percentage point margin of error.

Fun size candyA candy bar manufacturer sells a 鈥渇un size鈥� 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.

School vouchers A small pilot study estimated that 44%of all American

adults agree that parents should be given vouchers that are good for education at any public or private school of their choice.

a. How large a random sample is required to obtain a margin of error of at most 0.03with 99%confidence? Answer this question using the pilot study鈥檚 result as the guessed value for p^

b. Answer the question in part (a) again, but this time use the conservative guessp^=0.5. By how much do the two sample sizes differ?

After deciding on a 95% confidence level, the researcher is deciding between a sample of size n=500 and a sample of size n=1000. Compared with using a sample size of n=500, a confidence interval based on a sample size of n=1000 will be

a. narrower and would involve a larger risk of being incorrect.

b. wider and would involve a smaller risk of being incorrect.

c. narrower and would involve a smaller risk of being incorrect.

d. wider and would involve a larger risk of being incorrect.

e. narrower and would have the same risk of being incorrect.

Catching goldfish for schoolCarly and Maysem plan to be preschool teachers after they graduate from college. To prepare for snack time, they want to know the mean number of goldfish crackers in a bag of original-flavored goldfish. To estimate this value, they randomly selected12 bags of original-flavored goldfish and counted the number of crackers in each bag. Here are their data:

Construct and interpret a 95% confidence interval for the true mean number of crackers in a bag of original- flavored goldfish.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.