1 / 15

Monday, October 21

Monday, October 21. Hypothesis testing using the normal Z-distribution. Student’s t distribution. Confidence intervals. An Example. You draw a sample of 25 adopted children. You are interested in whether they are different from the general population on an IQ test (  = 100,  = 15).

Download Presentation

Monday, October 21

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Monday, October 21 Hypothesis testing using the normal Z-distribution. Student’s t distribution. Confidence intervals.

  2. An Example You draw a sample of 25 adopted children. You are interested in whether they are different from the general population on an IQ test ( = 100,  = 15). The mean from your sample is 108. What is the null hypothesis? H0:  = 100 Test this hypothesis at  = .05 Step 3. Assuming H0 to be correct, find the probability of obtaining a sample mean that differs from  by an amount as large or larger than what was observed. Step 4. Make a decision regarding H0, whether to reject or not to reject it.

  3. Step 1. State the statistical hypothesis H0 to be tested (e.g., H0:  = 100) Step 2. Specify the degree of risk of a type-I error, that is, the risk of incorrectly concluding that H0 is false when it is true. This risk, stated as a probability, is denoted by , the probability of a Type I error. Step 3. Assuming H0 to be correct, find the probability of obtaining a sample mean that differs from  by an amount as large or larger than what was observed. Step 4. Make a decision regarding H0, whether to reject or not to reject it.

  4. Step 1. State the statistical hypothesis H0 to be tested (e.g., H0:  = 100) Step 2. Specify the degree of risk of a type-I error, that is, the risk of incorrectly concluding that H0 is false when it is true. This risk, stated as a probability, is denoted by , the probability of a Type I error. Step 3. Assuming H0 to be correct, find the probability of obtaining a sample mean that differs from  by an amount as large or larger than what was observed, find the critical values of an observed sample mean whose deviation from 0 would be “unlikely”, defined as a probability < . Step 4. Make a decision regarding H0, whether to reject or not to reject it,

  5. GOSSET, William Sealy 1876-1937

  6. X -  X -  _ _ z = t = - - X sX s - sX =  N

  7. The t-distribution is a family of distributions varying by degrees of freedom (d.f., where d.f.=n-1). At d.f. =, but at smaller than that, the tails are fatter.

  8. Degrees of Freedom df = N - 1

  9. Problem Sample: Mean = 54.2 SD = 2.4 N = 16 Do you think that this sample could have been drawn from a population with  = 50?

  10. X -  t = - sX Problem Sample: Mean = 54.2 SD = 2.4 N = 16 Do you think that this sample could have been drawn from a population with  = 50? _

  11. The mean for the sample of 54.2 (sd = 2.4) was significantly different from a hypothesized population mean of 50, t(15) = 7.0, p < .001.

  12. The mean for the sample of 54.2 (sd = 2.4) was significantly reliably different from a hypothesized population mean of 50, t(15) = 7.0, p < .001.

  13. Interval Estimation (a.k.a. confidence interval) Is there a range of possible values for  that you can specify, onto which you can attach a statistical probability?

  14. Confidence Interval _ _ X - tsX   X + tsX Where t = critical value of t for df = N - 1, two-tailed X = observed value of the sample _

More Related