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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

The health director of a large company is concerned about the effects of stress on the company鈥檚 middle-aged male employees. According to the National Center for Health Statistics, the mean systolic blood pressure for males 35 to 44 years of age is 128. The health director examines the medical records of a random sample of 72 male employees in this age group. The Minitab output below displays the results of a significance test and a confidence interval.

1. Do the results of the significance test allow us to conclude that the mean blood pressure for all the company鈥檚 middle-aged male employees differs from the national average? Justify your answer.

2. Interpret the 95% confidence interval in context. Explain how the confidence interval leads to the same conclusion as in Question 1.

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

For the study of Jordanian children in Exercise 4, the sample mean hemoglobin level was 11.3 g/dl and the sample standard deviation was 1.6 g/dl. A significance test yields a P-value of 0.0016.

(a) Interpret the P-value in context.

(b) What conclusion would you make if 伪= 0.05? 伪= 0.01? Justify your answer.

A 95%confidence interval for a population mean is calculated to be (1.7,3.5). Assume that the conditions for performing inference are met. What conclusion can we draw for a test of role="math" localid="1650275427722" H0:渭=2versus Ha:渭鈮�2at the A=0.05level based on the confidence interval?

(a) None. We cannot carry out the test without the original data.

(b) None. We cannot draw a conclusion at the A=0.05level since this test is connected to the 97.5%confidence interval.

(c) None. Confidence intervals and significance tests are unrelated procedures.

(d) We would reject H0at level A=0.05.

(e) We would fail to reject H0at level A=0.05.

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.
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