Download presentation

Presentation is loading. Please wait.

1
Hypothesis Tests About With Unknown

2
Hypothesis Testing (Revisited) Five Step Procedure 1.Define Opposing Hypotheses. ( ) 2.Choose a level of risk ( ) for making the mistake of concluding something is true when its not. 3.Set up test (Define Rejection Region). random sample 4.Take a random sample. 5.Calculate statistics and draw a conclusion.

3
t Statistic in Hypothesis Tests for - ( UNKNOWN) When is known we used: When is unknown we use:

4
EXAMPLE Assuming that the ages of MIS managers follow a normal distribution, suppose we wish to draw conclusions about their true mean age (using α =.05) given the following random sample of ages of 5 MIS managers: 25, 30, 32, 38, 25. For this sample:

5
EXAMPLE 1: “> TEST” Is there enough evidence to conclude > 27? 1.H 0 : = 27 H A : > 27 2. =.05 3. Reject H 0 (Accept H A ) if t > t.05,4 = 2.132 4. Take Sample: 25, 30, 32, 38, 25 5. We get: There is not enough evidence to conclude > 27.

6
EXAMPLE 2: “< TEST” Is there enough evidence to conclude < 35? 1.H 0 : = 35 H A : < 35 2. =.10 3. Reject H 0 (Accept H A ) if t < -t.10,4 = -1.533 4. Take Sample: 25, 30, 32, 38, 25 5. We get: There is enough evidence to conclude < 35.

7
EXAMPLE 3: “ TEST” Is there enough evidence to conclude 40? 1.H 0 : = 40 H A : 40 2. =.05 3. Reject H 0 (Accept H A ) if t > t.025,4 = 2.776 or if t < -t.025,4 = -2.776 4. Take Sample: 25, 30, 32, 38, 25 5. We get: There is enough evidence to conclude 40.

8
EXCEL t-TESTS For all hypothesis tests, first get the mean and the standard error (s/ n) as follows: Go to DESCRIPTIVE STATISTICS -- Check –Summary Statistics –Confidence Level for Mean (indicate % confidence)

9
CHECK -- Summary statistics Confidence Level For Mean

10
EXCEL HYPOTHESIS TESTING “> TESTS” Refer to Example 1: H A : >27 Calculate t by: =(Mean-27)/(Standard Error) p-value: if t >0, =TDIST(t,4,1) gives a p <.5 if t.5 Numbers in italics means click on the cell with this value.

11
=(B3-27)/B4 =TDIST(E2,4,1) 1-tail test Degrees of freedom t

12
EXCEL HYPOTHESIS TESTING “< TESTS” Refer to Example 2: H A : <35 Calculate t by: =(Mean-35)/(Standard Error) p-value: if t <0, =TDIST(-t,4,1) gives a p <.5 if t >0, =1-TDIST(t,4,1) gives a p >.5 Numbers in italics means click on the cell with this value.

13
=(B3-35)/B4 =TDIST(-E2,4,1) -t because t < 0 Degrees of freedom 1-tail test

14
EXCEL HYPOTHESIS TESTING “ TESTS” Refer to Example 3: H A : 40 Calculate t by: =(Mean-40)/(Standard Error) p-value:=TDIST(ABS(t),4,2) Numbers in italics means click on the cell with this value.

15
=(B3-40)/B4 =TDIST(ABS(E2),4,2) To make sure the first argument is >0 Degrees of freedom 2-tail test

16
REVIEW t-tests the same as z-tests except: –use s instead of –use t instead of z Excel –Use Descriptive Statistics to get sample mean and standard error –Use of TDIST function

Similar presentations

© 2020 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google