/*! 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} Q2E For the following pairs of asser... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Q2E (page 325)

For the following pairs of assertions, indicate which with our rules for setting up hypotheses and why (the subscripts 1 and 2 differentiate between quantities for two different populations or samples):

a. H0: 碌= 100, Ha: 碌 > 100

b.H0: 蟽= 20, Ha: \(\sigma \le 20\)

c.H0: p鈮� .25, Ha: p= .25

d.H0: 碌1 - 碌2 = 25, Ha: 碌1 - 碌2 > 100

e.H0: \(S_1^2 = S_2^2\) , Ha: \(S_1^2 \ne S_2^2\)

f.H0: 碌= 120, Ha: 碌= 150

g.H0: 蟽1,/蟽2 =1,Ha: 蟽1,/ 蟽2 鈮�1

h.H0p1 鈥� p2 = -.1, Ha: p1 鈥� p2 < -.1

Short Answer

Expert verified

a)Yes , b) No, c) No, d) No, e) No, f) No, g) Yes, h) 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)This is a valid hypotheses. It complies with the rules.

b)This is not a valid hypotheses. Both \({H_0}\) and \({H_a}\) contain equality \((\sigma = 20)\), therefore it does not comply with the rules.

c)The hypotheses \({H_0}\) should be the equality claim, and in this case the hypotheses \({H_a}\) contains the equality claim, therefore it does not comply with the rules.

03

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

d)Both hypotheses \({H_0}\) and \({H_a}\) should contain same values in order for the hypotheses to comply. First asserted value of \({\mu _1} - {\mu _2}\) is \(25\), whereas the other \(100\), therefore it does not comply with the rules.

e)The statistics can not belong to the test hypothesis. Therefore it does not comply with the rules because \({S_i}\) are statistics.

04

 Step 4:Solution for part  f) ,g) and h).

f)It is not allowed for both hypotheses to have an equality claims, therefore it does not comply with the rules. (it is allowed in some more complicated hypothesis testing).

g)This is a valid hypotheses. It complies with the rules.

h)This is a valid hypotheses. It complies with the rules.

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

Before agreeing to purchase a large order of polyethylene sheaths for a particular type of high-pressure oil filled submarine power cable, a company wants to see conclusive evidence that the true standard deviation of

sheath thickness is less than .05 mm. What hypotheses should be tested, and why? In this context, what are the type I and type II errors?

A new design for the braking system on a certain type of car has been proposed. For the current system, the true average braking distance at 40 mph under specified conditions is known to be 120 ft. It is proposed that the new design be implemented only if sample data strongly indicates a reduction in true average braking distance for the new design.

a.Define the parameter of interest and state the relevant hypotheses.

b.Suppose braking distance for the new system is normally distributed with 蟽= 10. Let \(\overline X \) denote the sample average braking distance for a random sample of 36 observations. Which values of \(\overline x \) are more contradictory to H0 than 117.2, what is the P-value in this case, and what conclusion is appropriate if 伪 = .10?

c.What is the probability that the new design is not implemented when its true average braking distance is actually 115 ft and the test from part (b) is used?

Reconsider the paint-drying situation of Example 8.5, in which drying time for a test specimen is normally distributed with 蟽 = 9. The hypotheses H0: 碌 =75 versus Ha: 碌 <75 are to be tested using a random sample of n= 25 observations.

a.How many standard deviations (of X) below the null value is \(\overline x = 72.3\)?

b.If \(\overline x = 72.3\), what is the conclusion using 伪 =.002?

c.For the test procedure with 伪 =.002, what is 尾(70)?

d.If the test procedure with 伪 =.002 is used, what n is necessary to ensure that 尾(70) = .01?

e.If a level .01 test is used with n5 100, what is the probability of a type I error when m5 76?Answer the following questions for the tire problem in Example 8.7.

a.If \(\overline x = 30,960\) 30,960 and a level 伪=.01 test is used, what is the decision?

b.If a level .01 test is used, what is 尾(30,500)?

c.If a level .01 test is used and it is also required that 尾(30,500) = .05, what sample size n is necessary?

d.If \(\overline x = 30,960\), what is the smallest 伪 at which H0 can be rejected (based on n = 16)?

A manufacturer of plumbing fixtures has developed a new type of washer less faucet. Let \(p = P\) (a randomly selected faucet of this type will develop a leak within \(2\) years under normal use). The manufacturer has decided to proceed with production unless it can be determined that \(p\) is too large; the borderline acceptable value of \(p\) is specified as \(.10\). The manufacturer decides to subject \(n\) of these faucets to accelerated testing (approximating \(2\) years of normal use). With \(X = \) the number among the \(n\) faucets that leak before the test concludes, production will commence unless the observed X is too large. It is decided that if \(p = .10\), the probability of not proceeding should be at most \(.10\), whereas if \(p = .30\) the probability of proceeding should be at most \(.10\). Can \(n = 10\) be used? \(n = 20\)? \(n = 25\)? What are the actual error probabilities for the chosen n?

Newly purchased tires of a particular type are supposed to be filled to a pressure of 30 psi. Let 碌 denote the true average pressure. A test is to be carried out to decide whether 碌 differs from the target value. Determine the P-value for each of the following z test statistic values.

a.2.10 b. -1.75 c. -.55 d. 1.41 e. -5.3
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

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.