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Chapter 9: Q. 59 (page 565)

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 伪=0.05or 伪=0.01.

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

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

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

(e) inconclusive because we don鈥檛 know the value of 藛p .

Short Answer

Expert verified

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

Step by step solution

01

Given information

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

02

Explanation

H0: p=0.4. The claim tested by a significance test.

Ha: p>0.4 can be greater than/less than to the parameter. The claim about the population we're trying to find evidence for mean.

Estimating Z value and the significant test is performed at both伪=0.05and伪=0.01

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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 鈥渟tandard鈥� significance levels for your significance test, would you choose 伪=0.01, 0.05, or 0.10? Justify your choice.

Explain in plain language why a significance test that is significant at the 1% level must always be significant at the 5% level. If a test is significant at the 5% level, what can you say about its significance at the 1% level?

In planning a study of the birth weights of babies whose mothers did not see a

doctor before delivery, a researcher states the hypotheses as

H0:渭<1000gramsHa:渭=900grams

(a) State hypotheses for a significance test to determine whether first responders are arriving within 8 minutes of the call more often. Be sure to define the parameter of interest.

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

(c) Which is more serious in this setting: a Type I error or a Type II error? Justify your answer.

(d) If you sustain a life-threatening injury due to a vehicle accident, you want to receive medical treatment as quickly as possible. Which of the two significance tests鈥�H0:渭=6.7versusHa:渭<6.7 or the one from part (a) of this exercise鈥攚ould you be

more interested in? Justify your answer.

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

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