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Chapter 9: Q 20. (page 565)

Making conclusions A student performs a test of H0:μ=12versus Ha:μ≠12

at the α=0.05significance level and gets a P-value of 0.01. The

student writes: “Because the P-value is small, we reject H0. The data prove that Hais true.” Explain what is wrong with this conclusion.

Short Answer

Expert verified

The data do not show that H1is true, it show that alternative hypothesis H1is true.

Step by step solution

01

Given Information

It is given that p=0.01

α=0.05

H0:μ=12

H1:μ≠12

02

Explanation

As 0.01<0.05⇒RejectH0

There is convincing evidence that null hypothesis is not true.

Issue with statement is:

  • Data do not convince that H1is true.
  • It shows that alternative hypothesisH1is true.

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Most popular questions from this chapter

Battery life A tablet computer manufacturer claims that its batteries last an average of 10.5 hours when playing videos. The quality-control department randomly selects 20 tablets from each day’s production and tests the fully charged batteries by playing a video repeatedly until the battery dies. The quality control department will discard the batteries from that day’s production run if they find convincing evidence that the mean battery life is less than 10.5 hours. Here are a dot plot and summary statistics of the data from one day:

a. State appropriate hypotheses for the quality-control department to test. Be sure to define your parameter.

b. Check if the conditions for performing the test in part (a) are met.

Which of choices (a) through (d) is not a condition for performing a significance test about a population proportion p?

a. The data should come from a random sample from the population of interest.

b. Both np0and n(1-p0)should be at least 10.

c. If you are sampling without replacement from a finite population, then you should sample less than 10%of the population.

d. The population distribution should be approximately Normal unless the sample size is large.

e. All of the above are conditions for performing a significance test about a population proportion.

A random sample of 100 likely voters in a small city produced 59 voters in favor of Candidate A. The observed value of the standardized test statistic for performing a test of H0:p=0.5H0:p=0.5versus Ha:p>0.5Ha:p>0.5

is which of the following?

a)z=0.59-0.50.59(0.41)100

b)z=0.59-0.50.5(0.5)100

c)z=0.5-0.590.59(0.41)100

d)z=0.5-0.590.5(0.5)100

e)z=0.59-0.5100

Opening a restaurant You are thinking about opening a restaurant and are

searching for a good location. From research you have done, you know that the mean income of those living near the restaurant must be over \(85,000to support the type of upscale restaurant you wish to open. You decide to take a simple random sample of 50people living near one potential location. Based on the mean income of this sample, you will perform a test of

H0:μ=\)85,000

Ha:μ>$85,000

where μis the true mean income in the population of people who live near the restaurant. Describe a Type I error and a Type II error in this setting, and give a possible consequence of each.

Walking to school A recent report claimed that 13%of students typically walk to school. DeAnna thinks that the proportion is higher than 0.13at her large elementary school. She surveys a random sample of 100students and finds that 17typically walk to school. DeAnna would like to carry out a test at the α=0.05significance level of H0:p=0.13versus Ha:p>0.13, where p= the true proportion of all students at her elementary school who typically walk to school. Check if the conditions for performing the significance test are met.
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