# VCU STAT 210 - Lecture26(3) (1) (122 pages)

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## Lecture26(3) (1)

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## Lecture26(3) (1)

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Pages:
122
School:
Virginia Commonwealth University
Course:
Stat 210 - Basic Practice of Statistics
##### Basic Practice of Statistics Documents
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STAT 210 Lecture 26 Tests of Significance and Sampling Distribution of the Sample Proportion p October 27 2016 Practice Problems Sailboat Pages 252 through 257 Relevant problems IX 1 through IX 7 Recommended problems IX 1 IX 3 and IX 7 Hummingbird Pages 210 through 215 Relevant problems VIII 1 through VIII 7 Recommended problems VIII 1 VIII 3 and VIII 7 Additional Reading and Examples Sailboat Read pages 248 through 251 Pay particular attention to pages 248 249 Hummingbird Read pages 206 through 209 Pay particular attention to pages 206 207 Clicker Tests of Significance The p value is the probability assuming the null hypothesis is true that the test statistic takes a value as extreme or more extreme than the value observed Tests of Significance p value for an upper one sided test p value P Z Zobs or Ha m 110 p value P tdf tobs Note that Zobs and tobs would be some value that we have calculated For example if Zobs 2 76 then p value P Z 2 76 Tests of Significance p value for a lower one sided test p value P Z Zobs or Ha m 110 p value P tdf tobs Note that Zobs and tobs would be some value that we have calculated For example if Zobs 2 76 then p value P Z 2 76 Tests of Significance p value for a two sided test Ha m 110 p value P Z Zobs P Z Zobs 2 P Z Zobs or p value P tdf tobs P tdf tobs 2 P tdf tobs Example 57 a Upper one sided test z 2 65 p value P Z 2 65 1 P Z 2 65 1 9960 0040 Example 57 b Lower one sided test z 1 19 p value P Z 1 19 1170 Example 57 c Two sided test z 2 12 p value 2 P Z 2 12 2 P Z 2 12 2 1 P Z 2 12 2 1 9830 2 0170 0340 Tests of Significance When using the table it is possible for the Zobs value to be off the table With Z if you have a value less than 3 49 use the smallest probability which is 0002 if you have a value greater than 3 49 use the largest probability which is 9998 P value using the t distribution Calculating the p value using the t distribution is very similar to calculating the p value using the Z distribution with the exception being the way the t table is read With the Z distribution we were able to get one number for our p value With the t distribution using the table in the book we can only find two values that the p value would be between Example 58 a Upper one sided test df 8 tobs 2 000 p value Example 58 a Upper one sided test df 8 tobs 2 000 p value P t8 2 000 t 2 000 df 8 Example 58 a Upper one sided test df 8 tobs 2 000 p value P t8 2 000 For p 05 t8 1 860 For p 025 t8 2 306 Example 58 a Upper one sided test df 8 tobs 2 000 p value P t8 2 000 For p 05 t8 1 860 For p 025 t8 2 306 So 025 p value 05 Example 58 a Upper one sided test df 8 tobs 2 000 p value P t8 2 000 For p 05 t8 1 860 For p 025 t8 2 306 So 025 p value 05 NOTE Writing 05 p value 025 is WRONG Example 58 b Lower one sided test df 40 tobs 1 53 p value Example 58 b Lower one sided test df 40 tobs 1 53 p value P t40 1 53 Example 58 b Lower one sided test df 40 tobs 1 53 p value P t40 1 53 P t40 1 53 For p 10 t40 1 303 For p 05 t40 1 684 Example 58 b Lower one sided test df 40 tobs 1 53 p value P t40 1 53 P t40 1 53 For p 10 t40 1 303 For p 05 t40 1 684 So 05 p value 10 Example 58 c Two sided test df 15 tobs 2 680 p value Example 58 c Two sided test df 15 tobs 2 680 p value 2 P t15 2 680 2 P t15 2 680 Example 58 c Two sided test df 15 tobs 2 680 p value 2 P t15 2 680 2 P t15 2 680 For p 01 t15 2 602 For p 005 t15 2 947 Example 58 c Two sided test df 15 tobs 2 680 p value 2 P t15 2 680 2 P t15 2 680 For p 01 t15 2 602 For p 005 t15 2 947 So 2 005 p value 01 Example 58 c Two sided test df 15 tobs 2 680 p value 2 P t15 2 680 2 P t15 2 680 For p 01 t15 2 602 For p 005 t15 2 947 So 2 005 p value 01 So 01 p value 02 Tests of Significance When using the table it is possible for the tobs value to be off the table With t if you have a value off the left edge of the table then the probability is greater than 25 if you have a value off the right edge of the table then the value is less than 0005 Tests of Significance Once the p value is calculated we make a decision about the significance of the test by comparing the p value directly to significance level a If p value a then we reject Ho and hence can conclude that there is sufficient evidence that the alternative hypothesis is true If p value a then we fail to reject Ho and hence can conclude that there is not sufficient evidence that the alternative hypothesis is true Small p values favor the alternative hypothesis Example 59 a 05 a p value 0040 Decision Reject H0 Fail to reject H0 Example 59 a 05 a p value 0040 Since p value 05 we reject H0 Example 59 a 05 b p value 1170 Decision Reject H0 Fail to reject H0 Example 59 a 05 b p value 1170 Since p value 05 we fail to reject H0 Example 59 a 05 c p value 0340 Decision Reject H0 Fail to reject H0 Clicker Example 59 a 05 c p value 0340 Since p value 05 we reject H0 Example 60 a 05 a 025 p value 05 Decision Reject H0 Fail to reject H0 Example 60 a 05 a 025 p value 05 Since p value 05 we reject H0 Example 60 a 05 b 05 p value 10 Decision Reject H0 Fail to reject H0 Example 60 a 05 b 05 p value 10 Since p value 05 we fail to reject H0 Example 60 a 05 c 005 p value 01 Decision Reject H0 Fail to reject H0 Example 60 a 05 c 005 p …

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