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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

The French naturalist Count Buffon (1707-1788) tossed a coin 4040 times. He got 2048 heads. That's a bit more than one-half. Is this evidence that Count Buffon's coin was not balanced? To find out, Luisa decides to perform a significance test. Unfortunately, she made a few errors along the way. Your job is to spot the mistakes and correct them.

H0:渭>0.5Ha:x炉=0.5

- Independent 4040(0.5)=2020 and 4040(1-0.5)=2020 are both at least 10 .

- Normal There are at least 40,400 coins in the world.

t=0.5鈭�0.5070.5(0.5)4040=鈭�0.89;P-value=1鈭�0.1867=0.8133

Reject H0because the P-value is so large and conclude that the coin is fair.

Growing tomatoes An agricultural field trial compares the yield of two varieties of tomatoes for commercial use. Researchers randomly selected 10Variety A and 10 Variety B tomato plants. Then the researchers divide in half each 10 small plots of land in different locations. For each plot, a coin toss determines which half of the plot gets a Variety A plant; a Variety B plant goes in the other half. After harvest, they compare the yield in pounds for the plants at each location. The 10differences (VarietyA-VarietyB) give x=0.34andsx=0.83. A graph of the differences looks roughly symmetric and single-peaked with no outliers. Is there convincing evidence that Variety A has a higher mean yield? Perform a significance test using 伪=0.05to answer the question.

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

Are boys more likely? We hear that newborn babies are more likely to be boys than girls. Is this true? A random sample of 25,468 firstborn children included 13,173 boys. Boys do make up more than half of the sample, but of course, we don't expect a perfect 50-50 split in a random sample.

(a) To what population can the results of this study be generalized: all children or all firstborn children? Justify your answer.

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Anemia For the study of Jordanian children in Exercise 64, the sample mean hemoglobin level was 11.3mg/dl and the sample standard deviation was 1.6mg/dl.

(a) Calculate the test statistic.

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more precise P-value from your calculator.
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