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Chapter 9: Q.64 (page 587)

Hemoglobin is a protein in red blood cells that carries oxygen from the lungs to body tissues. People with fewer than 12 grams of hemoglobin per deciliter of blood (g/dl) are anemic. A public health official in Jordan suspects that Jordanian children are at risk of anemia. He measures a random sample of 50 children. Check the conditions for carrying out a significance test of the official鈥檚 suspicion.

Short Answer

Expert verified

The conditions have been mentioned

Step by step solution

01

Introduction

A sampling distribution is a probability distribution of a statistic obtained from a bigger number of tests drawn from a specific population. The sampling distribution of a given population is the distribution of frequencies of the scope of different results that might actually happen for a statistic of a population.

02

Explanation

The conditions for carrying out a significant test of the officer鈥檚 suspicion are-

Random sampling should be done.

The sample size is less than 10%of population size as the number of children is at least500.

The sample size ought to be huge and bigger than30with the goal that we can expect the population is typical. Fifty children are chosen randomly. The test size is 50which is more than 30.

We assume the population is normal.

Hence the conditions for carrying out a significance test of the officials suspicion have been done.

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Most popular questions from this chapter

After checking that conditions are met, you perform a significance test of H0:渭=1versus H伪:渭鈮�1. You obtain a Pvalue of 0.022. Which of the following is true?

(a) A95%confidence interval for 渭will include the value 1

(b) A 95%confidence interval for渭will include the value 0.

(c) A99% confidence interval for渭will include the value 1

(d) A 99%confidence interval for 渭will include the value 0

(e) None of these is necessarily true.

A random sample of 100likely voters in a small city produced 59voters in favor of Candidate A. The observed value of the test statistic for testing the null hypothesis H0:p=0.5versus the alternative hypothesis Ha:p=0.5is

(a)z=0.59-0.50.59(0.41)100

(b). z=0.59-0.50.5(0.5)100

(c). z=0.5-0.590.59(0.41)100

(d). z=0.5-0.590.5(0.5)100

(e).t=0.59-0.50.5(0.5)100

(a) State hypotheses for a significance test to determine whether first responders are arriving within 8 minutes of the call more often. Be sure to define the parameter of interest.

(b) Describe a Type I error and a Type II error in this setting and explain the consequences of each.

(c) Which is more serious in this setting: a Type I error or a Type II error? Justify your answer.

(d) If you sustain a life-threatening injury due to a vehicle accident, you want to receive medical treatment as quickly as possible. Which of the two significance tests鈥�H0:渭=6.7versusHa:渭<6.7 or the one from part (a) of this exercise鈥攚ould you be

more interested in? Justify your answer.

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.

The most important condition for sound conclusions from statistical inference is that

(a) the data come from a well-designed random sample or randomized experiment

(b) the population distribution be exactly Normal.

(c) the data contain no outliers.

(d) the sample size be no more than 10%of the population size.

(c) the sample size be at least 30.
See all solutions

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