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Chapter 9: Q.12 (page 546)

Refer to Exercise 2. For Yvonne's survey, 96 students in the sample said they rarely or never argue with friends. A significance test yields a P-value of 0.0291.

(a) Interpret this result in context.

(b) Do the data provide convincing evidence against the null hypothesis? Explain.

Short Answer

Expert verified

a. Chance that students in the sample said rarely or never argue with friends is0.0291

b. Yes, the data provide convincing evidence against the null hypothesis

Step by step solution

01

introduction

Given,

sample size is 150

population value is72%

new population value is 0.0291

02

explanation part (a)

Calculating the null and alternative hypotheses,

we get,

Ho:p=0.72Ha:p≠0.72

The chance that students in the sample said rarely or never argue with friends is 0.0291 if the population proportion is0.72.

03

explanation part (b)

The null hypothesis is not accepted as the value of p is less than the significant level of 5%or0.05

But p=0.0291which is less than 0.05.

Yes, the data provide convincing evidence against the null hypothesis

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Most popular questions from this chapter

Study more! A student group claims that first-year students at a university study 2.5hours per night during the school week. A skeptic suspects that they study less than that on average. He takes a random sample of 30first-year students and finds that x=137minutes and sx=45minutes. A graph of the data shows no outliers but some skewness. Carry out an appropriate significance test at the 5%significance level. What conclusion do you draw?

The design of controls and instruments affects how easily people can use them. A student project investigated this effect by asking 25right-handed students to turn a knob (with their right hands) that moved an indicator. There were two identical instruments, one with a right-hand thread (the knob turns clockwise) and the other with a left-hand thread (the knob must be turned counterclockwise). Each of the 25students used both instruments in a random order. The following table gives the times in seconds each subject took to move the indicator a fixed distance:

(a) Explain why it was important to randomly assign the order in which each subject used the two knobs.

(b) The project designers hoped to show that right-handed people find right-hand threads easier to use. Carry out a significance test at the 5%significance level to investigate this claim

An opinion poll asks a random sample of adults whether they favor banning ownership of handguns by private citizens. A commentator believes that more than half of all adults favor such a ban. The null and alternative hypotheses you would use to test this claim are

a).H0:p^=0.5;Ha:p^>0.5

(b) H0:p=0.5;Ha:p>0.5

(c) H0:p=0.5;Ha:p<0.5

(d) H0:p=0.5;Ha:p≠0.5

(e) H0:p>0.5;Ha:p=0.5

Tests and CIs The P-value for a one-sided test of the null hypothesisH0:μ=15is 0.03.

(a) Does the 99%confidence interval for μinclude 15? Why or why not?

(b) Does the 95%confidence interval for μinclude 15? Why or why not?

Two-sided test The one-sample t statistic from a sample of n=25observations for the two-sided test of H0:μ=64;Ha:μ≠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?

(b) Redo part (a) using an alternative hypothesis of Ha:μ<64.
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