Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 14: Q14.123 (page 585)

For each exercise, decide at 10% significance level, whether the data provide sufficient evidence to reject the null hypothesis in favour of alternate hypothesis.

Ha: p≠0

Short Answer

Expert verified

We reject the null hypothesis Ha: p≠0, the variables are not linearly correlated.

Step by step solution

01

Correlation Coefficient 

Sample correlation coefficient is calculated by

r=∑zxzy/( n-1) 

where zxn=(xn-xmean)/standarddeviation, and same for zyn

Using excel and above, r=-0.6325

02

Hypothesis Testing 

r≠0for sample needs to be tested using hypothesis testing, to ensure that the population correlation parameterp (rho) ≠0

t=r/(1-r2) /(n-2)=-0.6325/0.599/3=-0.6325/0.4468t=-1.415

As t value is smaller and p value is greater at two sided 0.10 significance level, so we accept the null hypothesis [H0: p=0]

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

In this Exercise 14.58, we repeat the information from Exercises 14.22. Presuming that the assumptions for regression inferences are met, decide at the specified significance level whether the data provide sufficient evidence to conclude that the predictor variable is useful for predicting the response variable.

Following are the data on the percentage of investments in energy securities and tax efficiency from Exercise 14.22. Use α=0.05.

In Exercises 14.98-14.108, use the technology of your choice to do the following tasks.
a. Decide whether you can reasonably apply the conditional mean and predicted value t-interval procedures to the data. If so, then also do parts (b)-(f)
b. Determine and interpret a point estimate for the conditional mean of the response variable corresponding to the specified value of the predictor variable.
c. Find and interpret a 95%confidence interval for the conditional mean of the response variable corresponding to the specified value of the predictor variable.
d. Determine and interpret the predicted value of the response variable corresponding to the specified value of the predictor variable.
e. Find and interpret a 95% prediction interval for the value of the response variable corresponding to the specified value of the predictor variable.
f. Compare and discuss the differences between the confidence inter. val that you obtained in part (c) and the prediction interval that you obtained in part (e).

14.99 U.S. Presidents. The data from Exercise 14.35 for the ages at inauguration and of death of the presidents of the United States are on the WeissStats site. Specified value of the predictor variable: 53 years.

Fill in the blanks.

a. The line y=β0+β1xis called the ____

b. The common conditional standard deviation of the response variable is denoted _____

c. For x=6, the conditional distribution of the response variable is a____ distribution having mean___ and standard deviation____.

In Exercises 14.48-14.57, we repeat the information from Exercises 14.12-14.21.

a. Decide, at the 10%significance level, whether the data provide sufficient evidence lo conclude that a is useful for predicting y:

b. Find a 90%confidences interval for the slope of the population regression line.

y=1.75+0.25x

Acreage and Value. The document Arizona Residential Property Valuation System, published by the Arizona Department of Revenue, describes how county assessors use computerized systems to value single-family residential properties for property tax purposes. On the WeissStats site are data on lot size (in acres) and assessed value (in thousands of dollars) for a sample of homes in a particular area.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Discrete 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.

Sign-up for free