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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

01

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

H0:p=0.40;Ha:p<0.40

02

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:N0.4,(0.4)(1-0.4)361

Test Static:z=1.01

03

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

p-value=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.

04

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.

alphadecisionreason for decision
0.05Do not reject the null hypothesis
p-value>0.05

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

05

Confidence Interval

Confidence Interval: (0.3241, 0.4240): The 鈥減lus-4s鈥 confidence interval is (0.3257, 0.4250).

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Scene: The great library of the castle, in which Hamlet does his lessons

Act I

(The day is fair, but the face of Hamlet is clouded. He paces the large room. His tutor, Polonius, is reprimanding Hamlet

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