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The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset Vaia Explanations$ Math

4th Edition · 809 pages

ISBN: 9781319113339

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’s 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’s suspicion are-

Random sampling should be done.

The sample size is less than $10 %$ of population size as the number of children is at least $500$ .

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

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). $H_{0} : \hat{p} = 0.5; H_{a} : \hat{p} > 0.5$

(b) $H_{0} : p = 0.5; H_{a} : p > 0.5$

(c) $H_{0} : p = 0.5; H_{a} : p < 0.5$

(d) $H_{0} : p = 0.5; H_{a} : p \neq 0.5$

(e) $H_{0} : p > 0.5; H_{a} : p = 0.5$

(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— $H_{0} : μ = 6.7 versus H_{a} : μ < 6.7$ or the one from part (a) of this exercise—would you be

more interested in? Justify your answer.

Eye black Athletes performing in bright sunlight often smear black grease under their eyes to reduce glare. Does cye black work? In one experiment, 16 randomly selected student subjects took a test of sensitivity to contrast after 3 hours facing into bright sun, both with and without eye black. Here are the differences in sensitivity, with eye black mines without eye black:

0.07	0.64	-0.12	-0.05	-0.18	0.14	-0.16	0.03
0.05	0.02	0.43	0.24	-0.11	0.28	0.05	0.29

We want to know whether cye black increases sensitivity an the average.

(a) State hypotheses, Be sure to define the parameter.

(b) Check conditions for carrying out a significance test.

(c) The $P v a l u e$ of the test is $0.047$ . Interpet this value in context.

- Interpret a Type l error and a Type ll error in context, and give the consequences of each.

- Understand the relationsonship between the significance level at a test P(Type li error), and power.

Which of the following 95% confidence intervals would lead us to reject $H 0 : p = 0.30$ in favor of $H a : p \neq 0.30$ at the 5% significance level?

(a) (0.29, 0.38) (c) (0.27, 0.31) (e) None of these

(b) (0.19, 0.27) (d) (0.24, 0.30)

Haemoglobin is a protein in red blood cells that carries oxygen from the lungs to body tissues. People with less than 12 grams of haemoglobin per deciliter of blood (g/dl) are anaemic. A public health official in Jordan suspects that Jordanian children are at risk of anaemia. He measures a random sample of 50 children.

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