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Chapter 9: Q.66 (page 588)

The composition of the earth’s atmosphere may have changed over time. To try to discover the nature of the atmosphere long ago, we can examine the gas in bubbles inside ancient amber. Amber is tree resin that has hardened and been trapped in rocks. The gas in bubbles within amber should be a sample of the atmosphere at the time the amber was formed. Measurements on 9 specimens of amber from the late Cretaceous era (75 to 95 million years ago) give these percent of nitrogen:

63.4 65.0 64.4 63.3 54.8 64.5 60.8 49.1 51.0

Explain why we should not carry out a one-sample t test in this setting.

Short Answer

Expert verified

The selection of the sample is done through a simple random technique hence we should not carry out a one-sample t test in this setting.

Step by step solution

01

Introduction

A test statistic is a statistic utilized in statistical hypothesis testing. A hypothesis test is typically specified as far as a test statistic, considered as a numerical synopsis of an informational collection that decreases the information to one worth that can be utilized to play out the hypothesis test.

02

Explanation

Given,

63.4    65.0    64.4    63.3    54.8    64.5    60.8    49.1    51.0

We cannot carry out a one-sample t-test in this setting as a selection of the sample is done through a simple random technique and the sample size is 9which is less than 30. Hence the normality assumption is not satisfied.

Hence the selection of the sample is done through a simple random technique and we should not carry out a one-sample t test in this setting.

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Most popular questions from this chapter

You are thinking about opening a restaurant and are searching for a good location. From the research you have done, you know that the mean income of those living near the restaurant must be over $85,000 to support the type of upscale restaurant you wish to open. You decide to take a simple random sample of 50 people living near one potential location. Based on the mean income of this sample, you will decide whether to open a restaurant there.8

(a) State appropriate null and alternative hypotheses. Be sure to define your parameter.

(b) Describe a Type I and a Type II error, and explain the consequences of each.

(c) If you had to choose one of the “standard” significance levels for your significance test, would you choose α=0.01, 0.05, or 0.10? Justify your choice.

Improving health A large company's medical director launches a health promotion campaign to encourage employees to exercise more and eat better foods. One measure of the effectiveness of such a program is a drop in blood pressure. The director chooses a random sample of 50employees and compares their blood pressures from physical cams given before the campaign and again a year later. The mean change (after - before) in systolic blood pressure for these 50employees is -6and the standard deviation is 19.8.

(a) Do these data provide convincing evidence of an average decrease in blood pressure among all of the company's employees during this year? Carry out a test at the α=0.05significance level.

(b) Can we conclude that the health campaign caused a decrease in blood pressure? Why or why not?

You are testing HO:μ=10Hα:μ<10against based on an SRS of 20observations from a Normal population. The tstatistic is . t=-2.25The P-value

(a) falls between 0.01and0.02

(b) falls between0.02and0.04

(c) falls between0.04and0.05

(d) falls between .05and0.25.

(c) is greater than0.25.

The z statistic for a test of H0 :p = 0.4 versus Ha : p > 0.4 is z = 2.43. This test is

(a) not significant at either α=0.05or α=0.01.

(b) significant at α=0.05but not at α=0.01

(c) significant at α=0.01but not at α=0.05.

(d) significant at both α=0.05and α=0.01.

(e) inconclusive because we don’t know the value of ˆp .

Healthy bones The recommended daily allowance (RDA) of calcium for women between the ages of 18and 24years is 1200milligrams (mg). Researchers who were involved in a large-scale study of women’s bone health suspected that their participants had significantly lower calcium intakes than the RDA. To test this suspicion, the researchers measured the daily calcium intake of a random sample of 36women from the study who fell in the desired age range. The Minitab output below displays descriptive statistics for these data, along with the results of a significance test.

(a) Determine whether there are any outliers. Show your work.

(b) Interpret the P-value in context.

(c) Do these data give convincing evidence to support the researchers’ suspicion? Carry out a test pg 571to help you answer this question.
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