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Chapter 9: Q .13. (page 564)

Interpreting a P-value A student performs a test of H0:渭=100H0:渭=100versus Ha: 渭>100Ha:渭>100and gets a P-value of 0.044.The student says, "There is a0.044 probability of getting the sample result I did by chance alone." Explain why the student's explanation is wrong.

Short Answer

Expert verified

- The interpretation is not given that the probability only carries when the null hypothesis is true.

- The interpretation is not given that the sample results can be more extreme (larger) as well.

Step by step solution

01

Step 1:Given information

Interpreting a P-value A student performs a test of $H0:渭=100H0:渭=100versusHa:渭>100Ha:渭>100and gets a P-value of0.044. The student says, "There is a0.044probability of getting the sample result I did by chance alone."

02

Step 2:Explaianation

P=0.044=4.4%

H0:渭=100

Ha:渭>100

The p-value is the probability of getting the value of the test statistic, or a value more extreme, when the null hypothesis is true.

It is observed that there are two issues with the given interpretation of the P-value:

- The interpretation is not given that the probability only carries when the null hypothesis is true.

- The interpretation is not given that the sample results can be more extreme (larger) as well.

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Most popular questions from this chapter

Which of the following is not a condition for performing a significance test about an unknown population proportion p?

(a) The data should come from a random sample or randomized experiment.

(b) Individual measurements should be independent of one another.

(c) The population distribution should be approximately Normal, unless the sample size is large.

(d) Both np and n(1 - p) should be at least 10.

(e) If you are sampling without replacement from a finite population, then you should sample no more than 10% of the population.

According to the Bureau of Labor Statistics, the average age of American workers is 41.9years. The manager of a large technology company believes that the company鈥檚 employees tend to be younger, on average. So she takes a random sample of 12 employees and records their ages.

Here are the data:

27 38 32 24 30 47 42 38 27 43 37 33

a. State appropriate hypotheses for testing the manager鈥檚 belief. Be sure to define the parameter of interest.

b. State the conditions for performing a test of the hypotheses in (a), and determine whether each condition is met.

c. The P-value of the test is0.003. Interpret this value. What conclusion would you make?

Attitudes The Survey of Study Habits and Attitudes (SSHA) is a

psychological test with scores that range from 0to200.. The mean score for U.S. college students is115. A teacher suspects that older students have better attitudes toward school. She gives the SSHA to an SRS of 45students from the more than 1000students at her college who are at least 30years of age. The teacher wants to perform a test at the 伪=0.05significance level of

H0:渭=115Ha:渭>115

where 渭=the mean SSHA score in the population of students at her college who are at least 30years old. Check if the conditions for performing the test are met.

Losing weight A Gallup poll found that 59% of the people in its sample said 鈥淵es鈥� when asked, 鈥淲ould you like to lose weight?鈥� Gallup announced: 鈥淔or results based on the total sample of national adults, one can say with 95% confidence that the margin of (sampling) error is 卤3 卤3percentage points.鈥�12 Based on the confidence interval, is there convincing evidence that the true proportion of U.S. adults who would say they want to lose weight differs from 0.55? Explain your reasoning

Heavy bread? The mean weight of loaves of bread produced at the bakery where you work is supposed to be 1pound. You are the supervisor of quality control at the bakery, and you are concerned that new employees are producing loaves that are too light. Suppose you weigh an SRS of bread loaves and find that the mean weight is 0.975pound.

a. State appropriate hypotheses for performing a significance test. Be sure to define the parameter of interest.

b. Explain why there is some evidence for the alternative hypothesis.

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d. What conclusion would you make at the 伪=0.01 significance level?
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