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Chapter 8: Q1 (page 408)

True/False Characterize each of the following statements as being true or false.

a. In a hypothesis test, a very high P-value indicates strong support of the alternative hypothesis.

b. The Student t distribution can be used to test a claim about a population mean whenever the sample data are randomly selected from a normally distributed population.

c. When using a x2 distribution to test a claim about a population standard deviation, there is a very loose requirement that the sample data are from a population having a normal distribution.

d. When conducting a hypothesis test about the claimed proportion of adults who have current passports, the problems with a convenience sample can be overcome by using a larger sample size.

e. When repeating the same hypothesis test with different random samples of the same size, the conclusions will all be the same.

Short Answer

Expert verified

a. The statement is false.

b. The statement is true.

c. The statement is false.

d. The statement is false.

e. The statement is false.

Step by step solution

01

State the p-value approach in the hypothesis test

a.

The p-value is a probability of getting the values as extreme as the test statistic.

The decision rule is expressed below.

  • If the p-value is lesser than the significance level, the null hypothesis will be rejected.
  • If the p-value is greater than the significance level, the null hypothesis will be failed to be rejected.

Thus, the high p-value will be supportive of the null hypothesis.

Therefore, the statement will be false.

02

State the requirements for the student’s t-distribution test

b.

The requirements for the student鈥檚 t-distribution test for testing the claim of the population mean are stated below.

  • The population is normally distributed, or the sample is larger than 30.
  • The sample is a simple random sample.
  • The population standard deviation is unknown.

Therefore, the statement will be true.

03

State the requirements for the chi-square test for the standard deviation 

c.

The requirements for the chi-square test for the standard deviation are as follows.

  • The population is normally distributed, which is stricter than the other tests.
  • The sample is a simple random sample.

Therefore, the statement is false.

04

State the requirements for the test for proportions

d.

Simple random samples are collected such that each sample is independent of another.

On the other hand, in convenience sampling, the samples are collected as per the convenience of investigators. Thus, the samples are not random selections.

Thus, a larger sample will not solve the problem of applying the test.

Therefore, the statement is false.

05

Analyze the results for the hypothesis test

e.

Different samples of the same sizes are collected for the hypothesis test of the same claim.

Different samples result in varied statistics and hence, varying results of the test statistics and hence, the decision.

Thus, the statement is false.

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Most popular questions from this chapter

Testing Hypotheses. In Exercises 13鈥�24, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), or critical value(s), and state the final conclusion that addresses the original claim.

Cans of Coke Data Set 26 鈥淐ola Weights and Volumes鈥� in Appendix B includes volumes (ounces) of a sample of cans of regular Coke. The summary statistics are n = 36, x = 12.19 oz, s = 0.11 oz. Use a 0.05 significance level to test the claim that cans of Coke have a mean volume of 12.00 ounces. Does it appear that consumers are being cheated?

Using Technology. In Exercises 5鈥�8, identify the indicated values or interpret the given display. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section. Use 伪= 0.05 significance level and answer the following:

a. Is the test two-tailed, left-tailed, or right-tailed?

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Adverse Reactions to Drug The drug Lipitor (atorvastatin) is used to treat high cholesterol. In a clinical trial of Lipitor, 47 of 863 treated subjects experienced headaches (based on data from Pfizer). The accompanying TI@83/84 Plus calculator display shows results from a test of the claim that fewer than 10% of treated subjects experience headaches.

df If we are using the sample data from Exercise 1 for a t-test of the claim that the population mean is greater than 90sec, What does df denote, and what is its value?

Confidence interval Assume that we will use the sample data from Exercise 1 鈥淰ideo Games鈥� with a 0.05 significance level in a test of the claim that the population mean is greater than 90 sec. If we want to construct a confidence interval to be used for testing the claim, what confidence level should be used for the confidence interval? If the confidence interval is found to be 21.1 sec < 渭< 191.4 sec, what should we conclude about the claim?

Final Conclusions. In Exercises 25鈥�28, use a significance level of = 0.05 and use the given information for the following:

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Original claim: More than 58% of adults would erase all of their personal information online if they could. The hypothesis test results in a P-value of 0.3257.
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