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Chapter 7: Q19E (page 403)

Consider the test of H0:μ=7. For each of the following, find the p-value of the test:

a.Ha:μ>7 ; z=1.20

b.Ha:μ<7 ; z=-1.20

c.Ha:μ≠7 ; z=1.20

Short Answer

Expert verified
  1. The p-value is 0.115.
  2. The p-value is 0.884.
  3. The p-value is 0.230.

Step by step solution

01

 Given Information

The null hypothesis and the alternative hypothesis are given. Z- score is given.

From this, we can easily compute the p-value.

02

(a) Calculate

The hypothesis are given by

H0:μ=7Ha:μ>7

The z-score is 1.20.

The p-value for the right-tailed test is computed as

pz>1.20=1-pz⩽1.20=1-0.884=0.115

Therefore, the p-value is 0.115.

03

(b) Calculate

The hypothesis are given by

H0:μ=7Ha:μ<7

The z-score is -1.20.

The p-value for the left-tailed test is computed as

pz<1.20=pz<-1.20=0.884

Therefore, the p-value is 0.884.

04

(c) Calculation

The hypothesis are given by

H0:μ=7Ha:μ≠7

The z-score is 1.20.

Similarly, the p-value for two-tailed tests is computed as

p value=2×ϕ-zscore=2×ϕ-1.20=0.230

Therefore, the p-value is 0.230.

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Most popular questions from this chapter

A random sample of n observations is selected from a normal population to test the null hypothesis that µ=10.Specify the rejection region for each of the following combinations of \(Ha,\alpha ,\) and n:

a.\(Ha:\)µ\( \ne 10;\alpha = .05.;n = 14\)

b.\(Ha:\)µ\( > 10;\alpha = .01;n = 24\)\(\)

c.\(Ha:\)µ\( > 10;\alpha = .10;n = 9\)

d.\(Ha:\)µ <\(10:\alpha = .01;n = 12\)

e.\(Ha:\)µ\( \ne 10;\alpha = .10;n = 20\)

f. \(Ha:\)µ<\(10;\alpha = .05;n = 4\)

A random sample of 64 observations produced the following summary statistics: \(\bar x = 0.323\) and \({s^2} = 0.034\).

a. Test the null hypothesis that\(\mu = 0.36\)against the alternative hypothesis that\(\mu < 0.36\)using\(\alpha = 0.10\).

b. Test the null hypothesis that \(\mu = 0.36\) against the alternative hypothesis that \(\mu \ne 0.36\) using \(\alpha = 0.10\). Interpret the result.

A sample of five measurements, randomly selected from a normally distributed population, resulted in the following summary statistics: \(\bar x = 4.8\), \(s = 1.3\) \(\) .

a. Test the null hypothesis that the mean of the population is 6 against the alternative hypothesis, µ<6. Use\(\alpha = .05.\)

b. Test the null hypothesis that the mean of the population is 6 against the alternative hypothesis, µ\( \ne 6\). Use\(\alpha = .05.\)

c. Find the observed significance level for each test.

Salaries of postgraduates. The Economics of Education Review (Vol. 21, 2002) published a paper on the relationship between education level and earnings. The data for the research was obtained from the National Adult Literacy Survey of more than 25,000 respondents. The survey revealed that males with a postgraduate degree have a mean salary of \(61,340 (with standard error \(Sx\) = \)2,185), while females with a postgraduate degree have a mean of \(32,227 (with standard error \(Sx\) = \)932).

  1. The article reports that a 95% confidence interval for \[{\bf{\mu }}M\] , the population mean salary of all males with post-graduate degrees, is (\(57,050, \)65,631). Based on this interval, is there evidence to say that \[{\bf{\mu }}M\] differs from \(60,000? Explain.
  2. Use the summary information to test the hypothesis that the true mean salary of males with postgraduate degrees differs from \)60,000. Use \(\alpha \) =.05.
  3. Explain why the inferences in parts a and b agree.
  4. The article reports that a 95% confidence interval for \(\mu F\) , the population mean salary of all females with post-graduate degrees, is (\(30,396, \)34,058). Based on this interval, is there evidence to say that \(\mu F\)differs from \(33,000? Explain.
  5. Use the summary information to test the hypothesis that the true mean salary of females with postgraduate degrees differs from \)33,000. Use \(\alpha \) =.05.
  6. Explain why the inferences in parts d and e agree.

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.
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