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Chapter 9: Q 42. (page 582)

Significance tests A test of H0:p=0.65 against Ha:p<0.65

based on a sample of size 400 yields the standardized test statistic z=鈭�1.78 .

a. Find and interpret the P-value.

b. What conclusion would you make at the 伪=0.10 significance level? Would

your conclusion change if you used 伪=0.05 instead? Explain your reasoning.

c. Determine the value of p铃�= the sample proportion of successes.

Short Answer

Expert verified

a. Null hypothesis is rejected.

b. 伪=0.1:fail to reject the null hypothesis.and 伪=0.05:reject the null hypothesis

c.p^=0.6510

Step by step solution

01

Part (a) Step 1: Given Information

It is given that z=1.78

n=400,伪=0.65

H0:p=0.65

Ha:p<0.65

02

Part (a) Step 2: Explanation

Value of zscore, z=1.78is:

P(x<z)=0.96246

P(x>z)=1-0.96246=0.037538

If Pvalue>伪, null hypothesis is rejected.

P=0.037538<0.65, null hypothesis is rejected here.

H0:p=0.65

03

Part (b) Step 1: Given Information

It is given that伪=0.1,伪=0.05

04

Part (b) Step 2: Explanation

As studied above, for 伪=0.65, hypothesis is rejected.

For 伪=0.1,P=0.037538<伪, null hypothesis is rejected. H0:p=0.65

For 伪=0.05,P=0.037538<伪, null hypothesis is rejected. H0:p=0.5

Pvalue changes due to significance level changes.

05

Part (c) Step 1: Given Information

It is given that n=400

p=0.65

z=1.78

06

Part (c) Step 2: Explanation

Test statistic is calculated as:

Z=p^-pp(1-p)n

1.78=p^-0.650.65(1-0.65)400

1.78=p^-0.650.65(0.35)400

1.78=p^-0.655.6875脳10-4

Hence,p^=0.6510

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Most popular questions from this chapter

Ski jump When ski jumpers take off, the distance they fly varies considerably depending on their speed, skill, and wind conditions. Event organizers must position the landing area to allow for differences in the distances that the athletes fly. For a particular competition, the organizers estimate that the variation in distance flown by the athletes will be \(\sigma=10\) \(\sigma=10\) meters. An experienced jumper thinks that the organizers are underestimating the variation.

A significance test allows you to reject a null hypothesis H0H0in favor of an alternative hypothesisHaaat the 5%significance level. What can you say about significance at the1%level?

a.H0H0can be rejected at the1%significance level.

b. There is insufficient evidence to rejectH0H0at the1%significance level.

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d.HaHacan be rejected at the 1%significance level.

e. The answer can't be determined from the information given.

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Stating hypotheses

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b. A researcher suspects that the mean birth weights of babies whose mothers did not see a doctor before delivery is less than 3000 grams. The researcher states the hypotheses as

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Flu vaccine A drug company has developed a new vaccine for preventing the flu. The company claims that fewer than 5% of adults who use its vaccine will get the flu. To test the claim, researchers give the vaccine to a random sample of 1000 adults.

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e. Explain two ways that you could increase the power of the test from part (d).
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