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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.
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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
