Prob 9.29

# Prob 9.29 - Significance level is α = 0.05 Because this is...

This preview shows pages 1–2. Sign up to view the full content.

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

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Significance level is 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 Some Chap 9 problem solutions 1 © 2010 Harvey A. Singer 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. 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...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

Prob 9.29 - Significance level is α = 0.05 Because this is...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online