# ch09 - Chapter Nine 9.1 a The null hypothesis is a claim...

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Chapter Nine 9.1 a. The null hypothesis is a claim about a population parameter that is assumed to be true until it is declared false. b. An alternative hypothesis is a claim about a population parameter that will be true if the null hypothesis is false. c. The critical point(s) divides the whole area under a distribution curve into rejection and non- rejection regions. d. The significance level, denoted by α, is the probability of making a Type I error, that is, the probability of rejecting the null hypothesis when it is actually true. e. The nonrejection region is the area where the null hypothesis is not rejected. f. The rejection region is the area where the null hypothesis is rejected. g. A hypothesis test is a two-tailed test if the rejection regions are in both tails of the distribution curve; it is a left-tailed test if the rejection region is in the left tail; and it is a right-tailed test if the rejection region is in the right tail. h. Type I error: A type I error occurs when a true null hypothesis is rejected. The probability of committing a Type I error, denoted by α is: α = P ( H 0 is rejected | H 0 is true) Type II error: A Type II error occurs when a false null hypothesis is not rejected. The probability of committing a Type II error, denoted by β, is: β = P ( H 0 is not rejected | H 0 is false) 9.3 A hypothesis test is a two-tailed test if the sign in the alternative hypothesis is "≠ "; it is a left-tailed test if the sign in the alternative hypothesis is " < " (less than); and it is a right-tailed test if the sign in the alternative hypothesis is " > " (greater than). Table 9.3 on page 405 of the text describes these relationships. 9.5 a. Left-tailed test b. Right-tailed test c. Two-tailed test 9.7 a. Type II error b. Type I error 9.9 a. H 0 : μ = 20 hours; H 1 : μ ≠ 20 hours; a two-tailed test b. H 0 : μ = 10 hours; H 1 : μ > 10 hours; a right-tailed test c. H 0 : μ = 3 years; H 1 : μ ≠ 3 years; a two-tailed test 159

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160 Chapter Nine d. H 0 : μ = \$1000; H 1 : μ < \$1000; a left-tailed test e. H 0 : μ = 12 minutes; H 1 : μ > 12 minutes; a right-tailed test 9.11 For a two-tailed test, the p –value is twice the area in the tail of the sampling distribution curve beyond the observed value of the sample test statistic. For a one-tailed test, the p –value is the area in the tail of the sampling distribution curve beyond the observed value of the sample test statistic. 9.13 a. Step 1: H 0 : µ = 46; H 1 : µ ≠ 46; A two-tailed test. Step 2: Since n > 30, use the normal distribution. Step 3: x s = n s / = 9.7 / 40 = 1.53370467 z = ( x μ ) / x s = (49.60–46) / 1.53370467 = 2.35 From the normal distribution table, area to the right of z = 2.35 is .5 – .4906 = .0094 approximately. Hence, p –value = 2(.0094) = .0188 b. Step 1: H 0 : µ = 26; H 1 : µ < 26; A left-tailed test. Step 2: Since n > 30, use the normal distribution. Step 3: x s = n s / = 4.3 / 33 = .74853392 z = ( x μ ) / x s = (24.3–26) / .74853392 = –2.27 From the normal distribution table, area to the left of z = –2.27 is .5 –.4884 = .0116 approximately.
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