/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q4 Confidence interval Assume that ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Q4 (page 396)

Confidence interval Assume that we will use the sample data from Exercise 1 鈥淰ideo Games鈥� with a 0.05 significance level in a test of the claim that the population mean is greater than 90 sec. If we want to construct a confidence interval to be used for testing the claim, what confidence level should be used for the confidence interval? If the confidence interval is found to be 21.1 sec < 渭< 191.4 sec, what should we conclude about the claim?

Short Answer

Expert verified

The 90% confidence interval should be used to test the claim at a 0.05 level of significance.

It can be concluded that there is insufficient evidence to support the claim that the population mean is greater than 90 seconds.

Step by step solution

01

Given information

Refer to Exercise 1 for the duration times of alcohol use for 12 different video games. The claim tested at the 0.05 level of significance indicates that the population mean is greater than 90 sec.

The confidence interval is 21.1sec<渭<191.4sec.

02

State the hypotheses

For true population mean , the hypotheses are formulated as follows:

Hence, this is a right-tailed test or a one-tailed test.

03

Determine the confidence level

The relationship between significance level and confidence level is stated below.



Confidence level



Two-tailed test

One-tailed test

Significance level

0.01

99%

98%

0.05

95%

90%

0.10

90%

80%

For a one-tailed test with a significance level 伪=0.05, a 90% confidence interval would be used.

04

State the decision using confidence interval

The 90% confidence interval is 21.1 sec to 191.4 sec.

The hypothesized value of 90 sec lies within the confidence interval. Thus, there is insufficient evidence to reject the null hypothesis.

Thus, it is concluded that we fail to reject the null hypothesis.

Therefore, it is concluded that there is insufficient evidence to support the claim that the population mean is greater than 90 seconds.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

Using Confidence Intervals to Test Hypotheseswhen analyzing the last digits of telephone numbers in Port Jefferson, it is found that among 1000 randomly selected digits, 119 are zeros. If the digits are randomly selected, the proportion of zeros should be 0.1.

a.Use the critical value method with a 0.05 significance level to test the claim that the proportion of zeros equals 0.1.

b.Use the P-value method with a 0.05 significance level to test the claim that the proportion of zeros equals 0.1.

c.Use the sample data to construct a 95% confidence interval estimate of the proportion of zeros. What does the confidence interval suggest about the claim that the proportion of zeros equals 0.1?

d.Compare the results from the critical value method, the P-value method, and the confidence interval method. Do they all lead to the same conclusion?

Grey-Seal Nursing. The average lactation (nursing) period of all earless seals is 23 days. Grey seals are one of several types of earless seals. The length of time that a female grey seal nurses her pup are studied by S. Twiss et al. in the article "Variation in Female Grey Seal (Halichoerus grypus) Reproductive Performance Correlates to Proactive-Reactive Behavioural Types" (PLOS ONE 7(11): e49598. doi:10.1371/journal. pone.0049598). A sample of 14 female grey seals had the following lactation periods, in days.

20.2

20.9

20.6

23.6

19.6

15.9

19.8

15.4

21.4

19.5

17.4

21.9

22.3

16.4

At the significance level, do the data provide sufficient evidence to conclude that the mean lactation period of grey seals differs from 23 days? Assume that the population standard deviation is days. (Note: The sum of the data is days.)

Testing Claims About Variation. In Exercises 5鈥�16, 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. Assume that a simple random sample is selected from a normally distributed population.

Mint Specs Listed below are weights (grams) from a simple random sample of 鈥渨heat鈥� pennies (from Data Set 29 鈥淐oin Weights鈥� in Appendix B). U.S. Mint specifications now require a standard deviation of 0.0230 g for weights of pennies. Use a 0.01 significance level to test the claim that wheat pennies are manufactured so that their weights have a standard deviation equal to 0.0230 g. Does the Mint specification appear to be met?

2.5024 2.5298 2.4998 2.4823 2.5163 2.5222 2.4900 2.4907 2.5017

Testing Claims About Proportions. In Exercises 9鈥�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.

OxyContin The drug OxyContin (oxycodone) is used to treat pain, but it is dangerous because it is addictive and can be lethal. In clinical trials, 227 subjects were treated with OxyContin and 52 of them developed nausea (based on data from Purdue Pharma L.P.). Use a 0.05 significance level to test the claim that more than 20% of OxyContin users develop nausea. Does the rate of nausea appear to be too high?

Got a Minute? Students of the author estimated the length of one minute without reference to a watch or clock, and the times (seconds) are listed below. Use a 0.05 significance level to test the claim that these times are from a population with a mean equal to 60 seconds. Does it appear that students are reasonably good at estimating one minute?

69 81 39 65 42 21 60 63 66 48 64 70 96 91 65
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

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.