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

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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.
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern