/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q1E For each of the following assert... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Q1E (page 325)

For each of the following assertions, state whether it is a legitimate statistical hypothesis and why:

\(\begin{array}{l}{\rm{a}}{\rm{. H: \sigma > 100}}\\{\rm{c}}{\rm{. H: s }} \le {\rm{.20}}\\{\rm{e}}{\rm{. H:}}\overline {{\rm{ X}}} {\rm{ - }}\overline {\rm{Y}} {\rm{ = 5}}\end{array}\) \(\begin{array}{l}{\rm{b}}{\rm{. H: }}\widetilde {\rm{x}}{\rm{ = 45}}\\{\rm{d}}{\rm{. H: }}{{\rm{\sigma }}_{\rm{1}}}{\rm{/}}{{\rm{\sigma }}_{\rm{2}}}{\rm{ < 1}}\end{array}\)

\({\rm{f}}{\rm{. H: \lambda }} \le {\rm{.01}}\), where \({\rm{\lambda }}\) is the parameter of an exponential distribution used to model component lifetime

Short Answer

Expert verified

a)Yes , b) No, c) No, d) Yes, e) No, f) Yes.

Step by step solution

01

Step 1:Statistical hypothesis.

A statistical hypothesis, or just hypothesis, is a claim or assertion either about the value of a single parameter (population characteristic or characteristic of a probability distribution), about the values of several parameters, or about the form of an entire

probability distribution.

02

Step 2:Solution for part a), b) and c).

a)Yes, it is legitimate. It is a claim about the value of a parameter.

b)No, it is not legitimate. It is not a claim about the value of a parameter(the sample median is not a parameter).

c)No, it is not legitimate. It is not a claim about the value of a parameter(the same standard deviation is not a parameter).

03

Step 3:Solution for part d), e) and f).

d)Yes, it is legitimate. It is a claim that the standard deviation of the one population exceeds other.

e)No, it is not legitimate. It is not a claim about the value of a parameter(the \(\overline X \)and\(\overline Y \) are statistics not a parameter).

f)Yes, it is legitimate. It is a claim about the value of a parameter.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Automatic identification of the boundaries of significant structures within a medical image is an area of ongoing research. The paper 鈥淎utomatic Segmentation of Medical Images Using Image Registration: Diagnostic and

Simulation Applications鈥� (J. of Medical Engr. and Tech., 2005: 53鈥�63)discussed a new technique for such identification. A measure of the accuracy of the automatic region is the average linear displacement (ALD). The paper gave the following ALD observations for a sample of 49 kidneys (units of pixel dimensions).

1.38 0.44 1.09 0.75 0.66 1.28 0.51

0.39 0.70 0.46 0.54 0.83 0.58 0.64

1.30 0.57 0.43 0.62 1.00 1.05 0.82

1.10 0.65 0.99 0.56 0.56 0.64 0.45

0.82 1.06 0.41 0.58 0.66 0.54 0.83

0.59 0.51 1.04 0.85 0.45 0.52 0.58

1.11 0.34 1.25 0.38 1.44 1.28 0.51

a.Summarize/describe the data.

b.Is it plausible that ALD is at least approximately normally distributed? Must normality be assumed prior to calculating a CI for true average ALD or testing hypotheses about true average ALD? Explain.

c.The authors commented that in most cases the ALD is better than or of the order of 1.0. Does the data in fact provide strong evidence for concluding that true average ALD under these circumstances is less than 1.0? Carry out an appropriate test of hypotheses.

d.Calculate an upper confidence bound for true average ALD using a confidence level of 95%, and interpret this bound.

Pairs of P-values and significance levels, 伪, are given.

For each pair, state whether the observed P-value would lead to rejection of H0 at the given significance level.

a.P颅-value = .084, 伪= .05

b.P颅-value = .003, 伪= .001

c.P-颅value = .498, 伪= .05

d.P-颅value = .084, 伪= .10

e.P-颅value = .039, 伪= .01

f.P-颅value = .218, 伪 = .10

A sample of n sludge specimens is selected and the pH of each one is determined. The one-sample t test will then be used to see if there is compelling evidence for concluding that true average pH is less than 7.0. What conclusion is appropriate in each of the following situations?

a.n= 6, t= -2.3, 伪= .05

b.n= 15, t= -3.1伪=.01

c.n= 12, t= -1.3, 伪= .05

d.n= 6, t = .7, 伪 = .05

e.n= 6, \(\overline x = 6.68,s/\sqrt n = .0820\)

A common characterization of obese individuals is that their body mass index is at least \(30\) (BMI 5 weighty(height)2, where height is in meters and weight is in kilograms). The article 鈥淭he Impact of Obesity on Illness Absence and Productivity in an Industrial Population of Petrochemical Workers鈥� (Annals of Epidemiology, 2008: 8鈥�14) reported that in a sample of female workers, \(262\) had BMIs of less than \(25,159\) had BMIs that were at least \(25\) but less than \(30\), and \(120\) had BMIs exceeding \(30\). Is there compelling evidence for concluding that more than \(20\% \) of the individuals in the sampled population are obese? a. State and test appropriate hypotheses with a significance level of \(.05\). b. Explain in the context of this scenario what constitutes type I and II errors. c. What is the probability of not concluding that more than \(20\% \) of the population is obese when the actual percentage of obese individuals is \(25\% \)?

The calibration of a scale is to be checked by weighing a 10-kg test specimen 25 times. Suppose that the results of different weightings are independent of one another and that the weight on each trial is normally distributed with 蟽 = .200 kg. Let 碌 denote the true average weight reading

on the scale.

a.What hypotheses should be tested?

b.With the sample mean itself as the test statistic, what is the P-value when \(\overline x = 9.85\), and what would you conclude at significance level .01?

c.For a test with 伪 =.01, what is the probability that recalibration is judged unnecessary when in fact 碌=10.1? When 碌= 9.8?
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.