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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

Bottles of a popular cola are supposed to contain 300milliliters (ml) of cola. There is some variation from bottle to bottle because the filling machinery is not perfectly precise. From experience, the distribution of the contents is approximately Normal. An inspector measures the contents of six randomly selected bottles from a single day鈥檚 production. The results are 299.4297.7301.0298.9300.2297.0Do these data provide convincing evidence that the mean amount of cola in all the bottles filled that day differs from the target value of 300ml? Carry out an appropriate test to support your answer

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(a) Interpret the P-value in context.

(b) What conclusion would you make if 伪= 0.05? 伪= 0.01? Justify your answer.

A local high school makes a change that should improve student satisfaction with the parking situation. Before the change, 37% of the school鈥檚 students approved of the parking that was provided. After the change, the principal surveys an SRS of 200 of the over 2500 students at the school. In all, 83 students say that they approve of the new parking arrangement. The principal cites this as evidence that the change was effective. Perform a test of the principal鈥檚 claim at the 伪=0.05 significance level.

A researcher claims to have found a drug that causes people to grow taller. The coach of the basketball team at Brandon University has expressed interest but demands evidence. Over 1000 Brandon students volunteer to participate in an experiment to test this new drug. Fifty of the volunteers are randomly selected, their heights are measured, and they are given the drug. Two weeks later, their heights are measured again. The power of the test to detect an average increase in height of one inch could be increased by

(a) using only volunteers from the basketball team in the experiment.

(b) using A=0.01 instead of A=0.05.

(c) using A=0.05 instead of A=0.01.

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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.

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