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Chapter 9: Q.40 (page 562)

A test of H0:p=0.65against Ha:p<0.65has test statistic z = -1.78.

(a) What conclusion would you draw at the 5% significance level? At the 1% level?

(b) If the alternative hypothesis were H0:p=0.65, what conclusion would you draw at the 5% significance level? At the 1% level?

Short Answer

Expert verified

a. At 5%the null hypothesis gets rejected and at 1%it is not rejected.

b. At the 5%significance level and at the 1%level the null hypothesis doesn't get rejected.

Step by step solution

01

Introduction

The null hypothesis recommends that no measurable relationship and importance exists in a bunch of given single noticed variables, between two arrangements of noticed information and estimated peculiarities.

02

Explanation Part (a)

The null and alternative hypotheses are,

H0:p=0.65Ha:p<0.65

Test statistic z = -1.78

Calculating the p-value,

=P(Z>|鈭�1.78|)=0.0375

Thus At 5%the null hypothesis gets rejected as the p-value is less and at 1%it is not rejected as p-value is greater.

03

Explanation Part (b)

The null and alternative hypotheses are,

H0:p=0.65Ha:p鈮�0.65

Calculating the p-value,

=2脳P(Z>|Z|)

=2脳0.0375=0.0750

Hence at the 5%significance level and at the 1%level the null hypothesis doesn't get rejected as the p-value is greater.

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Most popular questions from this chapter

Simon reads a newspaper report claiming that 12% of all adults in the United States are left-handed. He wonders if 12% of the students at his large public high school are left-handed. Simon chooses an SRS of 100 students and records whether each student is right- or left-handed.

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Two-sided test The one-sample t statistic from a sample of n=25observations for the two-sided test of H0:渭=64;Ha:渭鈮�64has the value t=-1.12.

(a) Find the P-value for this test using (i) Table Band (ii) your calculator. What conclusion would you draw at the 5%significance level? At the 1%significance level?

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Healthy bones The recommended daily allowance (RDA) of calcium for women between the ages of 18and 24years is 1200milligrams (mg). Researchers who were involved in a large-scale study of women鈥檚 bone health suspected that their participants had significantly lower calcium intakes than the RDA. To test this suspicion, the researchers measured the daily calcium intake of a random sample of 36women from the study who fell in the desired age range. The Minitab output below displays descriptive statistics for these data, along with the results of a significance test.

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