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Stats SB Notes 7.3.notebook April 14, 2016 Chapter Outline Chapter • 7.1 Introduction to Hypothesis Testing 7 • 7.2 Hypothesis Testing for the Mean (σ Known) Hypothesis Testing with One Sample • 7.3 Hypothesis Testing for the Mean (σ Unknown) • 7.4 Hypothesis Testing for Proportions • 7.5 Hypothesis Testing for Variance and Standard . Apr 57:58 AM • Deviation Apr 57:58 AM Section 7.3 Objectives • Find critical values in a tdistribution • Use the ttest to test a mean μ when σ is not known Section 7.3 • Use technology to find Pvalues and use them with a ttest to test a mean μ Hypothesis Testing for the Mean (σ Unknown) . . Apr 57:58 AM Apr 57:58 AM Finding Critical Values in a t Distribution • Identify the level of significance α. • Identify the degrees of freedom d.f. = n – 1. • Find the critical value(s) using Table 5 in Appendix B in the row with n – 1 degrees of freedom. If the hypothesis test is Example: Finding Critical Values for t Find the critical value t0 for a lefttailed test given α = 0.05 and n = 21. > lefttailed, use “One Tail, α ” column with a negative sign, > righttailed, use “One Tail, α ” column with a positive sign, > twotailed, use “Two Tails, α ” column with a negative and a positive sign. . . Apr 57:58 AM Apr 57:58 AM Stats SB Notes 7.3.notebook April 14, 2016 Try It Yourself 1, pg 377. Example 2, Finding a Critical Value for a Right-Tailed Test Find the critical value to for a left-tailed test with a = 0.01 and n = 14. Find the critical value to for a right-tailed test with a = 0.01 and n =17. Apr 148:21 AM Apr 148:24 AM Example: Finding Critical Values for t Try It Yourself 2, pg 378. Find the critical value to for a right-tailed test with a = 0.10 and n =9. Find the critical values t0 and t0 for a twotailed test given α = 0.10 and n = 26. . Apr 148:23 AM Apr 57:58 AM tTest for a Mean μ (σ Unknown) Try It Yourself 3, pg 378 Find the critical values -to and to for a two-tailed test with a = 0.05 and n = 16. tTest for a Mean • A statistical test for a population mean. • The ttest can be used when the population is normally distributed, or n ≥ 30. • The test statistic is the sample mean • The standardized test statistic is t. • The degrees of freedom are d.f. = n – 1. . Apr 148:27 AM Apr 57:58 AM Stats SB Notes 7.3.notebook April 14, 2016 Using Pvalues for a zTest for Mean μ (σ Unknown) Using Pvalues for a zTest for Mean μ (σ Unknown) . . Apr 57:58 AM Using Pvalues for a zTest for Mean μ (σ Unknown) Apr 57:58 AM Example: Testing μ with a Small Sample A used car dealer says that the mean price of a twoyearold sedan is at least $20,500. You suspect this claim is incorrect and find that a random sample of 14 similar vehicles has a mean price of $19,850 and a standard deviation of $1084. Is there enough evidence to reject the dealer’s claim at α = 0.05? Assume the population is normally distributed. (Adapted from Kelley Blue Book) . . Apr 57:58 AM Example: Hypothesis Testing An industrial company claims that the mean pH level of the water in a nearby river is 6.8. You randomly select 39 water samples and measure the pH of each. The sample mean and standard deviation are 6.7 and 0.35, respectively. Is there enough evidence to reject the company’s claim at α = 0.05? Assume the population is normally distributed. Apr 57:58 AM Try It Yourself 5, pg 381 The company in Example 5 claims that the mean conductivity of the river is 1890 milligrams per liter. The conductivity of a water sample is a measure of the total dissolved solids in the sample. You randomly select 39 water samples and measure the conductivity of each. The sample mean and standard deviation are 2350 mg per liter and 900 mg per liter, respectively. Is there enough evidence to reject the company's claim at a = 0.01? . Apr 57:58 AM Apr 148:33 AM Stats SB Notes 7.3.notebook Example: Using Pvalues with t Tests, use a calculator A department of motor vehicles office claims that the mean wait time is less than 14 minutes. A random sample of 10 people has a mean wait time of 13 minutes with a standard deviation of 3.5 minutes. At α = 0.10, test the office’s claim. Assume the population is normally distributed. April 14, 2016 Try It Yourself 6, pg 382 Another department of motor vehicles office claims that the mean wait time is at most 18 minutes. A random sample of 12 people has a mean wait time of 15 minutes with a standard deviation of 2.2 minutes. At a = 0.05, test the office's claim. Assume the population is normally distributed. . Apr 57:58 AM Section 7.3 Summary • Found critical values in a tdistribution • Used the ttest to test a mean μ when σ is not known • Used technology to find Pvalues and used them with a t test to test a mean μ when σ is not known Apr 148:36 AM Stats HW Section 7.3 pg 383, 1-14, 16-28 Evens Show work/Check with Calculator . Apr 57:58 AM Apr 148:38 AM
