Essential Statistics
Essential Statistics
2nd Edition
ISBN: 9781259570643
Author: Navidi
Publisher: MCG
Question
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Chapter 8.1, Problem 30E

a.

To determine

Identify the best among the three given conclusions when H0 is rejected.

a.

Expert Solution
Check Mark

Answer to Problem 30E

The statement that gives the best conclusion of the hypotheses when H0 is rejected is option (i), “The classes are successful.”

Explanation of Solution

A random sample 60 students attended the series of coaching class and had the mean IQ score of 100. It is given that μ be the population mean IQ score.

The given test hypothesis is:

Null hypothesis

 H0:μ=100

That is, the classes are not successful.

Alternate hypothesis

H1:μ>100

That is, the classes are successful.

Three statements regarding the conclusion of the hypothesis for the given study are given.

Reasons for correct answer:

If H0 is rejected, It means that it is evident that the classes are successful.

Hence, the statement that gives the best interpretation of the hypotheses is option (i), “The classes are successful.”

Reasons for incorrect answers:

If the null hypothesis H0 is rejected, then conclude that the alternate H1 is true or null hypothesis H0 is false.

Here, the surveyor rejects the null hypothesis H0. Hence, option (ii) is incorrect.

Moreover, the surveyor rejects the null hypothesis H0. As a result, it is appropriate to reject the null hypothesis H0. Hence, option (ii) is incorrect.

Now, rejecting the null hypothesis H0 means that it is not true. Thus, there is no chance that the classes might be successful. Hence, option (iii) is incorrect.

Statistics Concept Introduction

Conclusion of the hypotheses test:

  • If the null hypothesis H0 is rejected, then conclude that the alternate H1 is true or null hypothesis H0 is false.
  • If the null hypothesis H0 is not rejected, then conclude that the null hypothesis H0 might be true.

b.

To determine

Identify the best among the three given conclusions when H0 is not rejected.

b.

Expert Solution
Check Mark

Answer to Problem 30E

The statement that gives the best conclusion of the hypotheses when H0 is not rejected is option (iii), “The classes might not be successful”

Explanation of Solution

Three statements regarding the interpretation of the hypothesis for the given study are given.

Reasons for correct answer:

If H0 is not rejected, It means that it is evident that the classes might not be successful.

Hence, the statement that gives the best interpretation of the hypotheses is option (iii), “The classes might not be successful.”

Reasons for incorrect answers:

If the null hypothesis H0 is not rejected, then conclude that the alternate H1 is not true or null hypothesis H0 is might be true.

Here, the surveyor failed to reject the null hypothesis H0. However, failure to reject H0 does not necessarily mean that H0 is true. It simply implies that H0 might be true. Hence, option (i) is incorrect.

Now, failing to reject the null hypothesis H0 means that it may be true. Thus, there is chance for the classes might not be successful. Hence, option (ii) is incorrect.

c.

To determine

Identify the type of error.

c.

Expert Solution
Check Mark

Answer to Problem 30E

The error committed is type II error.

Explanation of Solution

It is assumed that the classes are successful, but the conclusion made on the part of surveyor is that the classes might not be successful.

Type I error:

Type I error is defined as the probability of rejecting the null hypothesis, when it is actually true.

If Type I error is committed, the surveyor concludes that the classes are not successful, when in reality, the classes are successful.

Type II error:

Type II error is defined as the probability of failure to reject the null hypothesis when alternate hypothesis is actually true.

If Type II error is committed, the surveyor concludes that the classes are successful, when in reality, the classes might not be successful.

If further analysis reveals that in reality, the conclusion made is that the classes might not be successful, then the surveyor will have committed the Type I error.

The error committed is Type I error by concluding that “classes might not be successful”, when in actual “the classes are successful”.

d.

To determine

Decide whether it is possible to make Type I error when the classes are not successful.

d.

Expert Solution
Check Mark

Answer to Problem 30E

Yes, it is possible to make Type I error.

Explanation of Solution

It is assumed that the classes are not successful.

Possible decisions made with a hypothesis test:

Correct decision:

  • Rejecting H0 when it is false.
  • Failing to reject H0 when it might be true.

Wrong decision:

  • Rejecting H0 when it might be true leads to Type I error.
  • Failing to reject H0 when it is false leads Type II error.

Now, rejecting H0 when it might actually be false leads to Type I error. However when it is already known that H0 is correct, rejecting H0 will be the incorrect decision. As a result, committing a Type I error will also be possible.

Thus, it is possible to make Type I error in this context.

e.

To determine

Decide whether it is possible to make Type II error when the classes are not successful.

e.

Expert Solution
Check Mark

Answer to Problem 30E

No, it is not possible to make Type II error.

Explanation of Solution

It is assumed that the classes are not successful.

Now, failure to reject H0 when it might actually be false leads to Type II error. However when it is already known that H0 is correct, rejecting H0 will be the incorrect decision. As a result, committing a Type II error will also be impossible.

Thus, it is not possible to make Type II error in this context.

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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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