HW 10 Chap 9 Exemplar

HW 10 Chap 9 Exemplar - α = 0.05 Because this is a...

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Chapter 9, problem 29 (page 358) a. Either the price is $5600 as claimed or it isn’t. So this is a two-tailed test. The pair of mutually exclusive hypotheses are: H 0 : μ = 5600 (the claim) H a : 5600 (the alternative) b. Calculated for the sample of n = 25: xbar = $5835.00 with s = $520.11 259 . 2 = 25 11 . 520 5600 00 . 5835 = = 0 - - n s x t μ Degrees of freedom = n – 1 = 24 Using t table: Search the row df = 24 for a value of 2.259 or close. Reading across the row, the value 2.259 is between 2.064 and 2.492. Reading up the column from 2.064 to the header, the area = 0.025. Reading up from 2.492 to the header, the area = 0.01. So the area in the upper tail is between 0.01 and 0.025. But this is a two-tailed test, so the areas have to be doubled for both tails (upper and the lower tails). Therefore, p -value is between 0.02 (= 2 × 0.01) and 0.05 (= 2 × 0.025). (Exact p -value = 0.0332 from Excel) c. p -value (= 0.0332) α = 0.05; reject H 0 . The mean diamond price in New York City differs. d. Because n = 25, df = 24 Significance level is
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Unformatted text preview: α = 0.05. Because this is a two-tailed test, need the area of the upper tail of α /2; α /2 = 0.025. Find t for upper tail area = 0.025 and for 24 degrees of freedom. t 0.025, 24 = 2.064 from the t table Decision rule: Reject H if t < -2.064 or t > 2.064 Calculated for the sample of n = 25: xbar = $5835.00 with s = $520.11. Some Chap 9 problem solutions 1 © 2010 Harvey A. Singer The t test statistic: 259 . 2 = 25 11 . 520 5600 00 . 5835 = =--n s x t μ 2.259 > 2.064 so reject H ___________________________ New questions: 1. What is the Type I error? In general, a Type I error is to reject a true null. Here, the Type I error is to reject the mean price of $5600 when in fact it is true. 2. What is the chance of making a Type I error? The chance of making the aforementioned Type I error is the given significance level of 5%. Some Chap 9 problem solutions 2 © 2010 Harvey A. Singer...
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This note was uploaded on 02/19/2011 for the course OM 210 taught by Professor Singer during the Spring '08 term at George Mason.

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HW 10 Chap 9 Exemplar - α = 0.05 Because this is a...

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