15 Hypothesis Testing Part 1

# What does this mean about constructing hypotheses

This preview shows pages 8–16. Sign up to view the full content.

What does this mean about constructing hypotheses? What you want to show support for is the alternative hypothesis! Constructing hypotheses: Logic 8

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

View Full Document
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
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

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

View Full Document
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
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

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

View Full Document
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
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

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

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

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern