Chapter 9: Q.98 (page 553)

Toastmasters International cites a report by Gallop Poll that 40% of Americans fear public speaking. A student believes that less than 40% of students at her school fear public speaking. She randomly surveys 361 schoolmates and finds that 135 report they fear public speaking. Conduct a hypothesis test to determine if the percent at her school is less than 40%.

Short Answer

Expert verified

Confidence Interval: (0.3241, 0.4240)

Step by step solution

Find H0 and Ha: We want to test if American takes less than 40% of the fear in public speaking, on average.

$H_{0} : p = 0.40; H_{a} : p < 0.40$

Determine the distribution needed: In words, CLEARLY state what your random variable P′ represents.Let P′ = the proportion of schoolmates who fear public speaking.

Normal: $N (0.4, \sqrt{\frac{(0.4) (1 - 0.4)}{361}})$

Test Static: $z = - 1.01$

Calculate the p-value using the normal distribution for proportions:

$p - v a l u e = 0.1563$

In one to two complete sentences, explain what the p-value means for this problem. If the null hypothesis is true (the proportion is 0.40), then there is a 0.1563 probability that the sample (estimated) proportion is 0.374 or more.

Compare α and the p-value:Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write an appropriate conclusion, using complete sentences.

alpha	decision	reason for decision
0.05	Do not reject the null hypothesis	$p - v a l u e > 0.05$

Conclusion: There is insufficient evidence to support the claim that less than 40% of students at the school fear public speaking.

Confidence Interval

Confidence Interval: (0.3241, 0.4240): The “plus-4s” confidence interval is (0.3257, 0.4250).

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Short Answer

Step by step solution

Find H0 and Ha: We want to test if American takes less than 40% of the fear in public speaking, on average.

Determine the distribution needed: In words, CLEARLY state what your random variable P′ represents.Let P′ = the proportion of schoolmates who fear public speaking.

Calculate the p-value using the normal distribution for proportions:

Compare α and the p-value:Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write an appropriate conclusion, using complete sentences.

Confidence Interval

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Applied Mathematics

Discrete Mathematics

Probability and Statistics

Logic and Functions

Pure Maths

Study anywhere. Anytime. Across all devices.