15 Hypothesis Testing Part 1

What does this mean about constructing hypotheses

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What does this mean about constructing hypotheses? What you want to show support for is the alternative hypothesis! Constructing hypotheses: Logic 8
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xample 1: Unknown: avg. cell phone usage of teenagers Want to show: avg. usage is different from 16 hr per week. H0: HA: xample 2: Unknown: proportion of lost bags at PHL airport. Want to show: more than 3% of bags are lost. H0: HA: xample 3: Unknown: Average age of Cadillac drivers Average buyers are younger than 50 years old. H 0: HA: μ = 16 μ ≠ 16 p  0.03 p > 0.03 μ  50 μ < 50 Constructing hypotheses: Examples 9
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Population Want to show that average Cadillac driver is younger than 50 years old. (Null hypothesis H0:  ) (Alt. hypothesis HA:  ) Suppose the sample mean age is 25: x ̅ = 25 Sample Is x ̅ = 25 likely if  = 50? Result If likely, do not reject H0 If not likely, reject H0 (and conclude the alternative) 50 < 50 Select a random sample Constructing hypotheses 10
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Sampling distribution of x̅: z or t-dist  = 50 If H 0 is true 2. It is odd that we would get a sample mean of this value ... 3. Then we reject the null hypothesis that = 50. 25 1. If in fact this were the population mean… x ̅ How odd should the sample mean be to reject H0? Constructing hypotheses 11
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Defines how unwilling we are to give up H0: Tells us how odd is odd enough  is called the “level of significance” for the hypothesis test Typical values are: .05, or .01, or .001 We reject H0 if the probability of getting our sample statistic is less than  Hypothesis testing: 12
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Cadillac example If the probability of getting x̅ < 25 is less than α =.05, then: Reject H0 or Do not reject H0 x ̅ =25 Sampling dist. of x ̅  = 50 If H 0 is true Cadillacs: σx = 30 n = 36 σx = 5 ̅ Hypothesis testing: Using α 13
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The p-value is the smallest  for which H0 can be rejected Called “observed” level of significance Computed from the sample statistic It is the probability of getting your sample statistic or something more “extreme” if the null is true Computed in direction of alternative hypothesis Hypothesis testing: P-Value 14
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The alternative hypothesis defines where we compute the p-value: Lower tail, Upper tail, or Both tails We are trying to refute the null; the alternative tells us how So we are looking for evidence that would be very odd if the null were in fact true and consistent with alternative.
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