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Chapter 9: Q.6 (page 546)

When ski jumpers take off, the distance they fly varies considerably depending on their speed, skill, and wind conditions. Event organizers must position the landing area to allow for differences in the distances that the athletes fly. For a particular competition, the organizers estimate that the variation in distance flown by the athletes will be

σ= 10meters. An experienced jumper thinks that the organizers are underestimating the variation.

Short Answer

Expert verified

Standard deviation is 10as per null hypothesis and is greater than10as per alternative hypothesis.

Step by step solution

01

introduction

Given,

For a particular competition, the organizers estimate that the variation in distance flown by the athletes will be σ=10meters.

The null and alternative hypotheses are calculated.

02

explanation

Standard devitaion is σ=10

Standard deviation is10as per null hypothesis

⇒H0:σ=10

Standard deviation is greater than 10as per alternative hypothesis

⇒Ha:σ>10

Standard deviation is 10 as per null hypothesis and is greater than10 as per alternative hypothesis.

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Most popular questions from this chapter

One-sided test Suppose you carry out a significance test of H0:μ=5versus Ha:μ>5based on a sample of size n=20and obtain t=1.81.

(a) Find the P-value for this test using (i) Table Band (ii) your calculator. What conclusion would you draw at the 5%significance level? At the 1%significance level?

(b) Redo part (a) using an alternative hypothesis ofHa:μ≠5.

Tests and CIs The P-value for a one-sided test of the null hypothesisH0:μ=15is 0.03.

(a) Does the 99%confidence interval for μinclude 15? Why or why not?

(b) Does the 95%confidence interval for μinclude 15? Why or why not?

Your company markets a computerized device for detecting high blood pressure. The device measures an individual’s blood pressure once per hour at a randomly selected time throughout a 12-hour period. Then it calculates the mean systolic (top number) pressure for the sample of measurements. Based on the sample results, the device determines whether there is significant evidence that the individual’s actual mean systolic pressure is greater than 130. If so, it recommends that the person seek medical attention.

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

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

(c) The blood pressure device can be adjusted to decrease one error probability at the cost of an increase in the other error probability. Which error probability would you choose to make smaller, and why?

Describe a Type II error in this setting.

What is significance good for? Which of the following questions does a significance test answer? Justify your answer.

(a) Is the sample or experiment properly designed?

(b) Is the observed effect due to chance?

(c) Is the observed effect important?
See all solutions

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