Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 8: Q21BSC (page 356)

Critical Values. In Exercises 21–24, refer to the information in the given exercise and do the following.

a. Find the critical value(s).

b. Using a significance level of \(\alpha \)= 0.05, should we reject \({H_0}\)or should we fail to reject \({H_0}\)?

Short Answer

Expert verified

a.The critical value is equal to 1.645.

b.The decision of the statistical test is to fail to reject \({H_0}\).

Step by step solution

01

Given information

A test statistic value of \(z = 1.00\) is obtained, and the claim to be tested is \(p > 0.3\).

02

Hypotheses and tail of the test

In correspondence with the given claim, the following hypotheses are set up:

Null Hypothesis:\(p = 0.3\)

Alternative Hypothesis:\(p > 0.3\)

Since there is a greater than sign in the alternative hypothesis, the test is right-tailed.

03

Critical value

a.

Referring to the standard normal table, the critical value of z corresponding to the right-tailed test at \(\alpha = 0.05\) is equal to 1.645.

04

Decision about the test

b.

If the test statistic value is greater than the critical value, then the null hypothesis is rejected.

Here, the test statistic value (1.00) is less than the critical value (1.645), so the decision is to fail to reject the null hypothesis.

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

Cans of coke for the sample data from exercise 1, we get “P-value<0.01” when testing the claim that the new filling process results in volumes with the same standard deviation of 0.115 oz.

  1. What should we conclude about the null hypothesis?
  2. What should we conclude about the original claims?
  3. What do these results suggest about the new filling process?

Testing Hypotheses. In Exercises 13–24, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), or critical value(s), and state the final conclusion that addresses the original claim.

Garlic for Reducing Cholesterol In a test of the effectiveness of garlic for lowering cholesterol, 49 subjects were treated with raw garlic. Cholesterol levels were measured before and after the treatment. The changes (before minus after) in their levels of LDL cholesterol (in mg>dL) have a mean of 0.4 and a standard deviation of 21.0 (based on data from “Effect of Raw Garlic vs Commercial Garlic Supplements on Plasma Lipid Concentrations in Adults with Moderate Hypercholesterolemia,” by Gardner et al., Archives of Internal Medicine, Vol. 167, No. 4). Use a 0.05 significance level to test the claim that with garlic treatment, the mean change in LDL cholesterol is greater than 0. What do the results suggest about the effectiveness of the garlic treatment?

In Exercises 1–4, use these results from a USA Today survey in which 510 people chose to respond to this question that was posted on the USA Today website: “Should Americans replace passwords with biometric security (fingerprints, etc)?” Among the respondents, 53% said “yes.” We want to test the claim that more than half of the population believes that passwords should be replaced with biometric security.

Requirements and Conclusions

a. Are any of the three requirements violated? Can the methods of this section be used to test the claim?

b. It was stated that we can easily remember how to interpret P-values with this: “If the P is low, the null must go.” What does this mean?

c. Another memory trick commonly used is this: “If the P is high, the null will fly.” Given that a hypothesis test never results in a conclusion of proving or supporting a null hypothesis, how is this memory trick misleading?

d. Common significance levels are 0.01 and 0.05. Why would it be unwise to use a significance level with a number like 0.0483?

Testing Claims About Proportions. In Exercises 9–32, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section.

Eliquis The drug Eliquis (apixaban) is used to help prevent blood clots in certain patients. In clinical trials, among 5924 patients treated with Eliquis, 153 developed the adverse reaction of nausea (based on data from Bristol-Myers Squibb Co.). Use a 0.05 significance level to test the claim that 3% of Eliquis users develop nausea. Does nausea appear to be a problematic adverse reaction?

In Exercises 9–12, refer to the exercise identified. Make subjective estimates to decide whether results are significantly low or significantly high, then state a conclusion about the original claim. For example, if the claim is that a coin favours heads and sample results consist of 11 heads in 20 flips, conclude that there is not sufficient evidence to support the claim that the coin favours heads (because it is easy to get 11 heads in 20 flips by chance with a fair coin).

Exercise 6 “Cell Phone”
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Calculus

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