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Chapter 9: Q.1.1 Check your understanding (page 555)

According to the National Campaign to Prevent Teen and Unplanned Pregnancy, 20% of teens aged 13 to 19 say that they have electronically sent or posted sexually suggestive images of themselves. 'The counsellor at a large high school worries that the actual figure might be higher at her school. To find out, she gives an anonymous survey to a random sample of 250 of the school's 2800 students. All 250 respond and 63 admit to sending or posting sexual images. Carry out a significance test at the 伪=0.05 significance level. What conclusion should the counsellor draw?

Short Answer

Expert verified

The conclusion is that the actual figure is higher than assumed before

Step by step solution

01

Introduction

Teen pregnancy is the point at which a lady under twenty gets pregnant. It ordinarily alludes to adolescents between the ages of 15-19. However, it can incorporate young ladies as youthful as ten. It's likewise called juvenile pregnancy.

02

Explanation

Given,

Sample size n is 250and Confidence level is 95%

Significance level 伪=0.05and population proportion is 0.20

Calculating the null and alternative hypotheses,

H0:p=0.20Ha:p>0.20

Using,

role="math" localid="1652858782146" z=p^鈭�p0p01鈭�p0n=0.252-0.0190.019(1-0.019)250=2.055

Hence the conclusion is that the actual figure is higher than assumed before

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Most popular questions from this chapter

We want to be rich In a recent year, 73 % of first-year college students responding to a national survey identified "being very well-off financially" as an important personal goal. A state university finds that 132 of an SRS of 200 of its first-year students say that this goal is important. Is there good evidence that the proportion of all first-year students at this university who think being very well-off is important differs from the national value, 73 %? Carry out a test at the 伪=0.05 significance level to help answer this question.

Bullies in middle school A University of Illinois study on aggressive behavior surveyed a random sample of 558 middle school students. When asked to describe their behavior in the last 30 days, 445 students said their behavior included physical aggression, social ridicule, teasing, name-calling, and issuing threats. This behavior was not defined as bullying in the questionnaire. Is this evidence that more than three-quarters of the students at that middle school engage in bullying behavior? To find out, Maurice decides to perform a significance test. Unfortunately, he made a few errors along the way. Your job is to spot the mistakes and correct them.

H0:p=0.75Ha:p->0.797

where p= the true mean proportion of middle school students who engaged in bullying.

- A random sample of 558 middle school students was surveyed.

- 558(0.797)=444.73 is at least 10.

z=0.75鈭�0.7970.797(0.203)445=鈭�2.46;P-value=2(0.0069)=0.0138

The probability that the null hypothesis is true is only 0.0138, so we reject H0. This proves that more than three-quarters of the school engaged in bullying behavior.

One-sided test Suppose you carry out a significance test of H0:渭=5versus Ha:渭>5based on a sample of size n=20and obtain t=1.81.

(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 ofHa:渭鈮�5.

In planning a study of the birth weights of babies whose mothers did not see a

doctor before delivery, a researcher states the hypotheses as

H0:渭<1000gramsHa:渭=900grams

The z statistic for a test of H0 :p = 0.4 versus Ha : p > 0.4 is z = 2.43. This test is

(a) not significant at either 伪=0.05or 伪=0.01.

(b) significant at 伪=0.05but not at 伪=0.01

(c) significant at 伪=0.01but not at 伪=0.05.

(d) significant at both 伪=0.05and 伪=0.01.

(e) inconclusive because we don鈥檛 know the value of 藛p .
See all solutions

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