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Chapter 7: Q22E (page 403)

In a test of the hypothesis H0:μ=70versusHa:μ>70, a sample of n = 100 observations possessed meanx¯=49.4and standard deviation s = 4.1. Find and interpret the p-value for this test.

Short Answer

Expert verified

The p-value for the test is 0.9279. The p-value indicates the probability of getting the test statistic is more than -1.46 when the claim μ=50is true.

Step by step solution

01

Given information

The hypothesis test is: H0:μ=50versus Ha:μ>50.

A random sample of size 100 is selected.

The sample mean is x¯=49.4.

The sample standard deviation is s=4.1.

02

Computing the value of the test statistic

The test statistic is:

z=x¯-μsn=49.4-504.1100=-0.64.110=-0.60.41=-1.46

The test statistic is z = -1.46.

03

 Step 3: Computing the p-value

The p-value for the right-tailed test is:

p=PZ>-1.46=1-PZ⩽-1.46=1-0.0721=0.9279

The z-table is used to obtain the probability of a z-score less than or equal to -1.46.

Therefore, the p-value is 0.9279.

04

Interpretation of the p-value

The p-value indicates the probability of getting the test statistic is more than -1.46 when the claimμ=50 is true.

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Most popular questions from this chapter

Refer to Exercise 6.44 (p. 356), in which 50 consumers taste-tested a new snack food. Their responses (where 0 = do not like; 1 = like; 2 = indifferent) are reproduced below

  1. Test \({H_0}:p = .5\) against \({H_0}:p > .5\), where p is the proportion of customers who do not like the snack food. Use \(\alpha = 0.10\).
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a. Conduct a test to determine if the true mean amount of dioxide present in water specimens that contained oil was less than 3 milligrams/liter. Use\(\alpha = .10\)

Question: Testing the placebo effect. The placebo effect describes the phenomenon of improvement in the condition of a patient taking a placebo—a pill that looks and tastes real but contains no medically active chemicals. Physicians at a clinic in La Jolla, California, gave what they thought were drugs to 7,000 asthma, ulcer, and herpes patients. Although the doctors later learned that the drugs were really placebos, 70% of the patients reported an improved condition. Use this information to test (at α = 0.05) the placebo effect at the clinic. Assume that if the placebo is ineffective, the probability of a patient’s condition improving is 0.5.

a. List three factors that will increase the power of a test.

b. What is the relationship between b, the probability of committing a Type II error, and the power of a test?

Stability of compounds in new drugs. Refer to the ACS Medicinal Chemistry Letters (Vol. 1, 2010) study of the metabolic stability of drugs, Exercise 2.22 (p. 83). Recall that two important values computed from the testing phase are the fraction of compound unbound to plasma (fup) and the fraction of compound unbound to microsomes (fumic). A key formula for assessing stability assumes that the fup/fumic ratio is 1:1. Pharmacologists at Pfizer Global Research and Development tested 416 drugs and reported the fup/fumic ratio for each. These data are saved in the FUP file, and summary statistics are provided in the accompanying Minitab printout. Suppose the pharmacologists want to determine if the true mean ratio, μ, differs from 1.

a. Specify the null and alternative hypotheses for this test.

b. Descriptive statistics for the sample ratios are provided in the Minitab printout on page 410. Note that the sample mean,\(\overline x = .327\)is less than 1. Consequently, a pharmacologist wants to reject the null hypothesis. What are the problems with using such a decision rule?

c. Locate values of the test statistic and corresponding p-value on the printout.

d. Select a value of\(\alpha \)the probability of a Type I error. Interpret this value in the words of the problem.

e. Give the appropriate conclusion based on the results of parts c and d.

f. What conditions must be satisfied for the test results to be valid?
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