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Stating hypotheses

a. A change is made that should improve student satisfaction with the parking situation at a local high school. Before the change, 37%of students approve of the parking that's provided. The null hypothesis H0:p>0.37H0:p>0.37is tested against the alternative Ha: p=0.37Ha:p=0.37

b. A researcher suspects that the mean birth weights of babies whose mothers did not see a doctor before delivery is less than 3000 grams. The researcher states the hypotheses as

H0:x-=3000grams-5H0:x=3000grams

Ha: x-<3000grams Ha:x<3000grams

explain what's wrong with the stated hypotheses. Then give correct hypotheses.

Short Answer

Expert verified

The correct hypotheses are listed as:

Part (a)H0:p=0.37,Ha:p>0.37

Part (b)H0:p=0.3000grams, Ha:p<0.3000grams

Step by step solution

01

Part (a) Step 1:Given information

The null hypothesisH0:p>0.37H0:p>0.37is tested against the alternative

Ha:p=0.37Ha:p=0.37

02

Part (b) Step 2:Explaination

The null hypothesis given by the following expression:

H0:p^=0.37

And the alternate hypothesis is given by the following expression:

Ha:p^0.37

Now, know that the hypotheses always used the population value not the sample value. So the sample values stated in the null hypothesis and alternate hypothesis should be remove and replaced by population value.

The correct hypotheses are listed as:

H0:p=0.37

Ha:p>0.37

Hence, there is use population value not the sample value in hypotheses.

03

Part (b)Step 2:Given information

H0:x-=3000gramsH0:x=3000grams

Ha:x-<3000gramsHa:x<3000grams

04

Part (b) Step 2:Explaination

The null hypothesis given by the following expression:

H0:x=0.3000grams

And the alternate hypothesis is given by the following expression:

Ha:x<0.3000grams

Now, know that the hypotheses always used the population value not the mean value. So the sample values stated in the null hypothesis and alternate hypothesis should be remove and replaced by population value.

The correct hypotheses are listed as:

H0:p=0.3000grams

Ha:p<0.3000grams

Hence, there is use population value not the sample value in hypotheses.

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Most popular questions from this chapter

Flu vaccine A drug company has developed a new vaccine for preventing the flu. The company claims that fewer than 5% of adults who use its vaccine will get the flu. To test the claim, researchers give the vaccine to a random sample of 1000 adults.

a. State appropriate hypotheses for testing the company鈥檚 claim. Be sure to define your parameter.

b. Describe a Type I error and a Type II error in this setting, and give the consequences Page Number: 615 of each.

c. Would you recommend a significance level of 0.01, 0.05, or 0.10 for this test? Justify your choice.

d. The power of the test to detect the fact that only 3% of adults who use this vaccine would develop flu using 伪=0.05 is 0.9437. Interpret this value.

e. Explain two ways that you could increase the power of the test from part (d).

Clean water The Environmental Protection Agency (EPA) has determined that safe

drinking water should contain at most 1.3mg/liter of copper, on average. A water supply company is testing water from a new source and collects water in small bottles at each of30randomly selected locations. The company performs a test at the 伪=0.05 significance level ofH0:=1.3versus Ha:>1.3, where 渭 is the

true mean copper content of the water from the new source.

a. Describe a Type I error and a Type II error in this setting.

b. Which type of error is more serious in this case? Justify your answer.

c. Based on your answer to part (b), do you agree with the company鈥檚 choice of =0.05? Why or why not?

Reporting cheating What proportion of students are willing to report cheating by other students? A student project put this question to an SRS of 172 undergraduates at a large university: 鈥淵ou witness two students cheating on a quiz. Do you go to the professor?鈥 The Minitab output shows the results of a significance test and a 95% confidence interval based on the survey data.13

a. Define the parameter of interest.

b. Check that the conditions for performing the significance test are met in this case.

c. Interpret the P-value.

d. Do these data give convincing evidence that the population proportion differs from 0.15? Justify your answer with appropriate evidence.

In a test ofH0:p=0.4against Ha:p0.4, a random sample of size 100 yields a standardized test statistic of z=1.28. Which of the following is closest to the P-value for this test?

a. 0.90

b. 0.40

c. 0.05

d. 0.20

e. 0.10

How much juice? Refer to Exercises 3 and 11 .

a. What conclusion would you make at the =0.10=0.10level?

b. Would your conclusion from part (a) change if a 5 \% significance level was used instead? Explain your reasoning.

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