BuyFind

Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836
BuyFind

Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836

Solutions

Chapter
Section
Chapter 7, Problem 7.10P
Textbook Problem

S O C Nationally, the per capita monthly fuel oil bill is $ 110 . A random sample of 36 cities in the South-east average $ 78 , with a standard deviation of $ 4 . Is the difference significant? Summarize your conclusions in a sentence or two.

Expert Solution
To determine

To find:

The significant difference between the given statements.

Explanation of Solution

Given:

The given information is,

Nationally, the per capita monthly fuel oil bill is $110. A random sample of 36 cities in the South-east average $78, with a standard deviation of $4.

The five step model for hypothesis testing is:

Step 1. Making assumptions and meeting test requirements.

Step 2. Stating the null hypothesis.

Step 3. Selecting the sampling distribution and establishing the critical region.

Step 4. Computing test statistics.

Step 5. Making a decision and interpreting the results of the test.

Formula used:

For small samples with single sample mean and unknown standard deviation, the t value is given by,

t(obtained)=X¯μs/N1

Where, X¯ is the sample mean,

μ is the population mean,

s is the estimate population standard deviation and,

N is the sample size.

Calculation:

From the given information, the sample size is 36, sample mean is $78, population mean is $110 and the sample standard deviation is $4.

Follow the steps for two-tailed hypothesis testing as,

Step 1. Making assumptions and meeting test requirements.

Model:

Random sampling.

Level of measurement is interval ratio.

Sampling distribution is Normal.

Step 2. Stating the null hypothesis.

The statement of the null hypothesis is that there is no significant difference in the per capita monthly fuel oil bill between south east cities and the national average.

Thus, the null and the alternative hypotheses are,

H0:μ=110

H1:μ110

Step 3. Selecting the sampling distribution and establishing the critical region.

Since, the sample is small, t distribution can be used.

Thus, the sampling distribution is t distribution.

The level of significance is α=0.05.

The degree of freedom (df) is,

df=N1=361=35

And area of critical region is t(0

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