Essential Statistics
Essential Statistics
2nd Edition
ISBN: 9781259570643
Author: Navidi
Publisher: MCG
Question
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Chapter 8.2, Problem 3CYU

a.

To determine

Calculate the critical value and the critical region at the significance level of α=0.05.

a.

Expert Solution
Check Mark

Answer to Problem 3CYU

The critical value at α=0.05 is ±1.96_ and the critical region at α=0.05 is z1.96orz1.96_.

Explanation of Solution

It is given that the value of test statistic z as 1.78 and significance level α=0.05.

Denote μ as the true population mean.

The given test hypotheses are:

Null hypothesis: H0:μ=12.

Alternate hypothesis: H1:μ12.

From the given hypotheses, the alternative hypothesis contains the not equal () symbol. Thus, it is clear that the hypotheses follow the two-tailed test.

From Table 8.1 “Table of Critical Values”, the critical value for two-tailed test at α=0.05 level is ±1.96_.

Thus, the critical region is z1.96orz1.96_.

b.

To determine

Decide whether the null hypothesis H0 is rejected at α=0.05 level.

b.

Expert Solution
Check Mark

Answer to Problem 3CYU

The null hypothesis H0 is not rejected at α=0.05 level.

Explanation of Solution

It is given that the test statistic z=1.78 and the significance level α=0.05.

From previous part (a), the critical value is ±1.96.

Decision based on the critical value method:

For left-tailed test: If zzα, reject H0.

For right-tailed test: If zzα, reject H0.

For two-tailed test: If zzα2orzzα2, reject H0.

Conclusion:

The critical values at α=0.05 level are ±1.96 and the test statistic is 1.78.

Here, the test statistic value of 1.78lies within the critical values of ±1.96.

That is, zα2(1.96)<z(=1.78)<zα2(1.96).

Therefore, the null hypothesis is not rejected.

c.

To determine

Obtain the critical value and the critical region for a significance level of α=0.01.

c.

Expert Solution
Check Mark

Answer to Problem 3CYU

The critical value at α=0.01 is ±2.576_ and the critical region at α=0.01 is z2.576_

Explanation of Solution

It is given that the significance level α=0.01.

From Table 8.1 “Table of Critical Values”, the critical value for two-tailed test at α=0.01 level is ±2.576_.

Thus, the critical region is z2.576orz2.576_.

d.

To determine

Decide whether the null hypothesis H0 is rejected at α=0.01 level.

d.

Expert Solution
Check Mark

Answer to Problem 3CYU

The null hypothesis H0 is not rejected at α=0.01 level.

Explanation of Solution

It is given that the test statistic z=1.78 and the significance level α=0.01.

From previous part (c), the critical value is ±2.576.

Decision based on the critical value method:

For left-tailed test: If zzα, reject H0.

For right-tailed test: If zzα, reject H0.

For two-tailed test: If zzα2orzzα2, reject H0.

Conclusion:

The critical value at α=0.01 level is ±2.576 and the test statistic is 1.78.

Here, the test statistic value of 1.78 is lies within the critical values of ±2.576.

That is, zα2(2.576)<z(=1.78)<zα2(2.576).

Therefore, the null hypothesis is not rejected.

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Chapter 8 Solutions

Essential Statistics

Ch. 8.1 - In Exercises 9–12, determine whether the statement...Ch. 8.1 - In Exercises 9–12, determine whether the statement...Ch. 8.1 - Prob. 13ECh. 8.1 - Practicing the Skills In Exercises 13–16,...Ch. 8.1 - Prob. 15ECh. 8.1 - Practicing the Skills In Exercises 13–16,...Ch. 8.1 - Prob. 17ECh. 8.1 - Prob. 18ECh. 8.1 - Prob. 19ECh. 8.1 - Prob. 20ECh. 8.1 - Working with the Concepts 21. Fertilizer: A new...Ch. 8.1 - 22. Big fish: A sample of 100 flounder of a...Ch. 8.1 - Prob. 23ECh. 8.1 - 24. Coffee: The mean caffeine content per cup of...Ch. 8.1 - Prob. 25ECh. 8.1 - Prob. 26ECh. 8.1 - 27. Type I error: A company that manufactures...Ch. 8.1 - Prob. 28ECh. 8.1 - Prob. 29ECh. 8.1 - Prob. 30ECh. 8.2 - Prob. 1CYUCh. 8.2 - Prob. 2CYUCh. 8.2 - Prob. 3CYUCh. 8.2 - Prob. 4CYUCh. 8.2 - Prob. 5CYUCh. 8.2 - Prob. 6CYUCh. 8.2 - Prob. 7CYUCh. 8.2 - Prob. 8CYUCh. 8.2 - Prob. 9CYUCh. 8.2 - Prob. 10CYUCh. 8.2 - Prob. 11CYUCh. 8.2 - Prob. 12CYUCh. 8.2 - 13. For each of the following P-values, state...Ch. 8.2 - Prob. 14CYUCh. 8.2 - Prob. 15CYUCh. 8.2 - Prob. 16CYUCh. 8.2 - Prob. 17CYUCh. 8.2 - Prob. 18CYUCh. 8.2 - Prob. 19CYUCh. 8.2 - Prob. 20CYUCh. 8.2 - Prob. 21CYUCh. 8.2 - A certain type of calculator battery has a mean...Ch. 8.2 - Prob. 23ECh. 8.2 - Prob. 24ECh. 8.2 - Prob. 25ECh. 8.2 - Prob. 26ECh. 8.2 - Prob. 27ECh. 8.2 - Prob. 28ECh. 8.2 - Prob. 29ECh. 8.2 - Prob. 30ECh. 8.2 - Prob. 31ECh. 8.2 - Prob. 32ECh. 8.2 - Prob. 33ECh. 8.2 - In Exercises 29–34, determine whether the...Ch. 8.2 - Prob. 35ECh. 8.2 - Prob. 36ECh. 8.2 - Prob. 37ECh. 8.2 - Prob. 38ECh. 8.2 - Prob. 39ECh. 8.2 - Prob. 40ECh. 8.2 - Prob. 41ECh. 8.2 - Prob. 42ECh. 8.2 - Prob. 43ECh. 8.2 - Prob. 44ECh. 8.2 - Prob. 45ECh. 8.2 - Prob. 46ECh. 8.2 - Prob. 47ECh. 8.2 - Prob. 48ECh. 8.2 - Prob. 49ECh. 8.2 - Prob. 50ECh. 8.2 - Prob. 51ECh. 8.2 - Prob. 52ECh. 8.2 - Prob. 53ECh. 8.2 - Prob. 54ECh. 8.2 - Prob. 55ECh. 8.2 - Prob. 56ECh. 8.2 - Prob. 57ECh. 8.2 - Prob. 58ECh. 8.2 - Prob. 59ECh. 8.2 - Prob. 60ECh. 8.2 - Prob. 61ECh. 8.2 - Prob. 62ECh. 8.2 - Prob. 63ECh. 8.2 - Prob. 64ECh. 8.2 - Prob. 65ECh. 8.2 - Prob. 66ECh. 8.2 - Prob. 67ECh. 8.2 - Prob. 68ECh. 8.2 - Prob. 69ECh. 8.2 - Prob. 70ECh. 8.2 - Prob. 71ECh. 8.2 - Prob. 72ECh. 8.3 - Prob. 1CYUCh. 8.3 - Prob. 2CYUCh. 8.3 - Prob. 3CYUCh. 8.3 - Prob. 4CYUCh. 8.3 - Prob. 5CYUCh. 8.3 - Prob. 6CYUCh. 8.3 - Prob. 7ECh. 8.3 - In Exercises 7 and 8, fill in each blank with the...Ch. 8.3 - Prob. 9ECh. 8.3 - Prob. 10ECh. 8.3 - Prob. 11ECh. 8.3 - Prob. 12ECh. 8.3 - Prob. 13ECh. 8.3 - Prob. 14ECh. 8.3 - Prob. 15ECh. 8.3 - Prob. 16ECh. 8.3 - Prob. 17ECh. 8.3 - Prob. 18ECh. 8.3 - Prob. 19ECh. 8.3 - Prob. 20ECh. 8.3 - Prob. 21ECh. 8.3 - How much is in that can? A machine that fills...Ch. 8.3 - Credit card debt: Following arc outstanding credit...Ch. 8.3 - Prob. 24ECh. 8.3 - Prob. 25ECh. 8.3 - Prob. 26ECh. 8.3 - Prob. 27ECh. 8.3 - Prob. 28ECh. 8.3 - Prob. 29ECh. 8.3 - Prob. 30ECh. 8.3 - Prob. 31ECh. 8.3 - Prob. 32ECh. 8.3 - Prob. 33ECh. 8.3 - Prob. 34ECh. 8.3 - Prob. 35ECh. 8.3 - Prob. 36ECh. 8.3 - Prob. 37ECh. 8.3 - Prob. 38ECh. 8.3 - Prob. 39ECh. 8.3 - Prob. 40ECh. 8.3 - Prob. 41ECh. 8.4 - Prob. 1CYUCh. 8.4 - Prob. 2CYUCh. 8.4 - Prob. 3CYUCh. 8.4 - A Gallup poll taken in December 2009 sampled 1000...Ch. 8.4 - Prob. 5ECh. 8.4 - Prob. 6ECh. 8.4 - Prob. 7ECh. 8.4 - In Exercises 7 and 8, determine whether the...Ch. 8.4 - Prob. 9ECh. 8.4 - Prob. 10ECh. 8.4 - Prob. 11ECh. 8.4 - Prob. 12ECh. 8.4 - Prob. 13ECh. 8.4 - Prob. 14ECh. 8.4 - Prob. 15ECh. 8.4 - Prob. 16ECh. 8.4 - Prob. 17ECh. 8.4 - Prob. 18ECh. 8.4 - Prob. 19ECh. 8.4 - Prob. 20ECh. 8.4 - Prob. 21ECh. 8.4 - Prob. 22ECh. 8.4 - Prob. 23ECh. 8.4 - Prob. 24ECh. 8.4 - Prob. 25ECh. 8.4 - Interpret calculator display: The following...Ch. 8.4 - Prob. 27ECh. 8.4 - Prob. 28ECh. 8.4 - Prob. 29ECh. 8.4 - Who will you vote for? A simple random sample of...Ch. 8.4 - Prob. 31ECh. 8.4 - Prob. 32ECh. 8.4 - Prob. 33ECh. 8.5 - Prob. 1CYUCh. 8.5 - Prob. 2CYUCh. 8.5 - Prob. 3CYUCh. 8.5 - Prob. 4CYUCh. 8.5 - Prob. 5ECh. 8.5 - Prob. 6ECh. 8.5 - Prob. 7ECh. 8.5 - Prob. 8ECh. 8.5 - Prob. 9ECh. 8.5 - Prob. 10ECh. 8.5 - Prob. 11ECh. 8.5 - Prob. 12ECh. 8.5 - Prob. 13ECh. 8.5 - Prob. 14ECh. 8.5 - Mercury pollution: Mercury is a toxic metal that...Ch. 8.5 - Ladies’ shoes: A random sample of 100 pairs of...Ch. 8 - Prob. 1CQCh. 8 - Prob. 2CQCh. 8 - Prob. 3CQCh. 8 - Prob. 4CQCh. 8 - Prob. 5CQCh. 8 - Prob. 6CQCh. 8 - Prob. 7CQCh. 8 - Prob. 8CQCh. 8 - Prob. 9CQCh. 8 - Prob. 10CQCh. 8 - Prob. 11CQCh. 8 - Prob. 12CQCh. 8 - Prob. 13CQCh. 8 - Prob. 14CQCh. 8 - Prob. 15CQCh. 8 - Prob. 1RECh. 8 - Prob. 2RECh. 8 - Prob. 3RECh. 8 - Prob. 4RECh. 8 - Prob. 5RECh. 8 - Prob. 6RECh. 8 - Prob. 7RECh. 8 - Prob. 8RECh. 8 - Prob. 9RECh. 8 - Prob. 10RECh. 8 - Interpret calculator display: The following TI-84...Ch. 8 - Prob. 12RECh. 8 - Prob. 13RECh. 8 - Prob. 14RECh. 8 - Prob. 15RECh. 8 - Prob. 1WAICh. 8 - What does the P-value represent? Ch. 8 - Prob. 3WAICh. 8 - Prob. 4WAICh. 8 - Prob. 5WAICh. 8 - Prob. 1CSCh. 8 - Prob. 2CSCh. 8 - Prob. 3CSCh. 8 - Prob. 4CSCh. 8 - Prob. 5CSCh. 8 - Prob. 6CSCh. 8 - Prob. 7CS
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