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## Chapter 8

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**Chapter 8**Hypothesis Testing**8.2 Null and Alternative Hypothesis**Hypothesis testing is the process we go through to decide whether or not the conjecture is true.**8.2 Test Value**If the observed (sample) mean is a lot different than the hypothesized population mean, we conclude the hypothesized mean is incorrect.**8.2 Two Tailed vs. One Tailed Test**Bottom pg 394 has English to symbols translations.**8.2 One Tailed Test; α = .01**1 - .01 = .99 Look up .49, what value of z do you get? .5 - .01 = .49 2.33 Critical Value**8.2 One Tailed Test; α = .01**Right-Tail Test Left-Tail Test**8.2 Two Tail Test**If α = .01**8.2 Example 1**.4901 2.33**8.3 Decision Rules for P-Values**If you are not given an α value: X X ? √ 0 .05 .10 .01**8.4 t Test for a Mean**In chapter 7, when n <30 and σ was unknown we used tα/2 values verses z α/2 values for our confidence intervals.**8.4 Example 7**Look at the One tail α heading Use the .01 column Go down to row 22 -2.508 Look at the Two tails α heading Use the .10 column Go down to row 18 -1.734 and +1.734**8.4 Example 9**d.f. = 11 – 1 = 10 Look in row 10 for t-value 2.056 (or the closest two values you can find. For the t-value up to the top of the column; use the One-tail heading.**8.4 Example 9**.025 < p-value < .05 If we were testing at the α = .05 level would we accept or reject H0? Reject because p-value < .05**8.4 Example 10**Look in row 5 for t-value 2.983 Use the Two-tails heading .05 .02 2.571 2.983 3.365 .02 < p-value < .05 If α = .01 level would we accept or reject H0? Do not reject since p-value > .02 > .01**8.6 X2 Test for σ2 or σ**• The areas for Chi-square distribution Table G pg 772 • Left, right and two tailed test • Chi-square distribution different than z and t in that the values are never negative