WEEK-14-15-STAT-AND-PROB mmmmnmm(1).pptx

WEEK-14-15-STAT-AND-PROB

1. (WEEK 14 - 15) S T A T I S T I C S & P R O B A B I L I T Y

2. S T A T I S T I C S & P R O B A B I L I T Y W E E K 14 - 15 1 If randm smpls of sze n ae dran fro a ppulaton , ten a n beome lager, he smplng ditribuion o the ean aproaces the orma ditribtio , reardlss ofth shpe o th poulatondisribtin HYPOTHESIS TESTING

3. 2 If randm smpls of sze n ae dran fro a ppulaton , ten a n beome lager, he smplng ditribuion o the ean aproaces the orma ditribtio , reardlss ofth shpe o th poulatondisribtin HYPOTHESIS TESTING S T A T I S T I C S & P R O B A B I L I T Y W E E K 14 - 15 HYPOTHESIS TESTING statistical method that is used in making statistical decision using experimental data. HYPOTHESIS is an assumption or conjecture about a population parameter which may or may not be true. Ex. Does the mean height of Grade 11 students differ from 66 inches? Is the proportion of Senor High male student’s height significantly higher than the senior female students?

4. S T A T I S T I C S & P R O B A B I L I T Y W E E K 14 - 15 3 If randm smpls of sze n ae dran fro a ppulaton , ten a n beome lager, he smplng ditribuion o the ean aproaces the orma ditribtio , reardlss ofth shpe o th poulatondisribtin 2 TYPES OF HYPOTHESIS

5. 4 If randm smpls of sze n ae dran fro a ppulaton , ten a n beome lager, he smplng ditribuion o the ean aproaces the orma ditribtio , reardlss ofth shpe o th poulatondisribtin HYPOTHESIS TESTING S T A T I S T I C S & P R O B A B I L I T Y W E E K 14 - 15 2 TYPES OF HYPOTHESIS initial claim contrary to the null hypothesis NULL HYPOTHESIS ALTERNATIVE HYPOTHESIS the independent variable has no effect on the independent variable the independent variable has an effect on the independent variable

6. 5 If randm smpls of sze n ae dran fro a ppulaton , ten a n beome lager, he smplng ditribuion o the ean aproaces the orma ditribtio , reardlss ofth shpe o th poulatondisribtin HYPOTHESIS TESTING S T A T I S T I C S & P R O B A B I L I T Y W E E K 14 - 15 2 TYPES OF HYPOTHESIS NULL HYPOTHESIS ALTERNATIVE HYPOTHESIS

7. 6 If randm smpls of sze n ae dran fro a ppulaton , ten a n beome lager, he smplng ditribuion o the ean aproaces the orma ditribtio , reardlss ofth shpe o th poulatondisribtin 2 TYPES OF HYPOTHESIS S T A T I S T I C S & P R O B A B I L I T Y W E E K 14 - 15 Ex. #1. The average age of Grade 11 students in ACLC Naga is 17.2 years. Ex. #2. A DTI representative wants to test at 99% confidence level whether the average content of Soda X is less than 330 ml as indicated in the label.

8. S T A T I S T I C S & P R O B A B I L I T Y W E E K 14 - 15 7 If randm smpls of sze n ae dran fro a ppulaton , ten a n beome lager, he smplng ditribuion o the ean aproaces the orma ditribtio , reardlss ofth shpe o th poulatondisribtin LEVEL OF SIGNIFICANCE

9. 8 If randm smpls of sze n ae dran fro a ppulaton , ten a n beome lager, he smplng ditribuion o the ean aproaces the orma ditribtio , reardlss ofth shpe o th poulatondisribtin Level of significance S T A T I S T I C S & P R O B A B I L I T Y W E E K 14 - 15 LEVEL OF SIGNIFICANCE - it is denoted by α (alpha) refers to the degree of significance in which we accept or reject the null hypothesis - value that separates the critical region from the non-critical region CRITICAL VALUE

10. 9 If randm smpls of sze n ae dran fro a ppulaton , ten a n beome lager, he smplng ditribuion o the ean aproaces the orma ditribtio , reardlss ofth shpe o th poulatondisribtin Level of significance S T A T I S T I C S & P R O B A B I L I T Y W E E K 14 - 15 LEVEL OF SIGNIFICANCE - it is denoted by α (alpha) refers to the degree of significance in which we accept or reject the null hypothesis CRITICAL REGION - range of the values of the test values that indicates that there is significant difference.

11. 10 If randm smpls of sze n ae dran fro a ppulaton , ten a n beome lager, he smplng ditribuion o the ean aproaces the orma ditribtio , reardlss ofth shpe o th poulatondisribtin Level of significance S T A T I S T I C S & P R O B A B I L I T Y W E E K 14 - 15 LEVEL OF SIGNIFICANCE - it is denoted by α (alpha) refers to the degree of significance in which we accept or reject the null hypothesis - range of the values of the test values that indicates that the difference was probably due to chance. NON-CRITICAL REGION

12. S T A T I S T I C S & P R O B A B I L I T Y W E E K 14 - 15 11 If randm smpls of sze n ae dran fro a ppulaton , ten a n beome lager, he smplng ditribuion o the ean aproaces the orma ditribtio , reardlss ofth shpe o th poulatondisribtin 2 TYPES OF TEST

13. 12 If randm smpls of sze n ae dran fro a ppulaton , ten a n beome lager, he smplng ditribuion o the ean aproaces the orma ditribtio , reardlss ofth shpe o th poulatondisribtin 2 TYPES OF TEST S T A T I S T I C S & P R O B A B I L I T Y W E E K 14 - 15 shows that the null hypothesis may be rejected when the test value is in the critical region on one side of the mean ONE-TAILED TEST RIGHT-TAILED TEST LEFT-TAILED TEST

14. 13 If randm smpls of sze n ae dran fro a ppulaton , ten a n beome lager, he smplng ditribuion o the ean aproaces the orma ditribtio , reardlss ofth shpe o th poulatondisribtin 2 TYPES OF TEST S T A T I S T I C S & P R O B A B I L I T Y W E E K 14 - 15 the null hypothesis should be rejected when the test value is in either of the two critical regions. TWO -TAILED TEST

15. S T A T I S T I C S & P R O B A B I L I T Y W E E K 14 - 15 14 If randm smpls of sze n ae dran fro a ppulaton , ten a n beome lager, he smplng ditribuion o the ean aproaces the orma ditribtio , reardlss ofth shpe o th poulatondisribtin TYPE I and TYPE II ERRORS

16. 15 If randm smpls of sze n ae dran fro a ppulaton , ten a n beome lager, he smplng ditribuion o the ean aproaces the orma ditribtio , reardlss ofth shpe o th poulatondisribtin TYPE I AND TYPE II ERRORS S T A T I S T I C S & P R O B A B I L I T Y W E E K 14 - 15 POSSIBLE OUTCOME OF HYPOTHESIS TEST ACCEPT H O REJECT H O H O (TRUE) H O (FALSE) TYPE I ERROR α TYPE II ERROR β CORRECT DECISION CORRECT DECISION

17. S T A T I S T I C S & P R O B A B I L I T Y W E E K 14 - 15 16 If randm smpls of sze n ae dran fro a ppulaton , ten a n beome lager, he smplng ditribuion o the ean aproaces the orma ditribtio , reardlss ofth shpe o th poulatondisribtin IDENTIFYING APPROPRIATE TEST STATISTICS

18. 17 If randm smpls of sze n ae dran fro a ppulaton , ten a n beome lager, he smplng ditribuion o the ean aproaces the orma ditribtio , reardlss ofth shpe o th poulatondisribtin IDENTIFYING APPROPRIATE TEST STATISTICS S T A T I S T I C S & P R O B A B I L I T Y W E E K 14 - 15 Z-TEST T-TEST - the population standard deviation or variance is known. - the population normally distributed the sample size is greater than or equal to 30. - the population standard deviation or variance is unknown. the sample size is less than to 30.

19. S T A T I S T I C S & P R O B A B I L I T Y W E E K 14 - 15 18 If randm smpls of sze n ae dran fro a ppulaton , ten a n beome lager, he smplng ditribuion o the ean aproaces the orma ditribtio , reardlss ofth shpe o th poulatondisribtin STEPS IN HYPOTHESIS TESTING

20. 19 If randm smpls of sze n ae dran fro a ppulaton , ten a n beome lager, he smplng ditribuion o the ean aproaces the orma ditribtio , reardlss ofth shpe o th poulatondisribtin STEPS IN HYPOTHESIS TESTING S T A T I S T I C S & P R O B A B I L I T Y W E E K 14 - 15 Set up the hypothesis and identify the claim. STEP #1. Set the Level of Significance. STEP #2. Determine the Critical Value of z or t. STEP #3. Calculate the sample z-test or t-test. STEP #4.

21. 20 If randm smpls of sze n ae dran fro a ppulaton , ten a n beome lager, he smplng ditribuion o the ean aproaces the orma ditribtio , reardlss ofth shpe o th poulatondisribtin STEPS IN HYPOTHESIS TESTING S T A T I S T I C S & P R O B A B I L I T Y W E E K 14 - 15 Statistical Decision. STEP #5. State the Conclusion. STEP #6. Accept H o Reject H o Since we reject the null hypothesis, we can conclude that there is enough evidence to support the claim that _________________________. Since we accept the null hypothesis, we can conclude that there is not enough evidence to support the claim that _________________________.

22. 21 If randm smpls of sze n ae dran fro a ppulaton , ten a n beome lager, he smplng ditribuion o the ean aproaces the orma ditribtio , reardlss ofth shpe o th poulatondisribtin STEPS IN HYPOTHESIS TESTING S T A T I S T I C S & P R O B A B I L I T Y W E E K 14 - 15 Ex. #1. A researcher reports that the average salary of company managers is more than ₱63, 000. A sample of 35 company managers has a mean of salary ₱65, 700. At α =0.01, test the claim that the company managers earn more than ₱63, 000 a month. The standard deviation of the population is ₱5, 250 . STEP #1. STEP #2. (claim)

23. 22 If randm smpls of sze n ae dran fro a ppulaton , ten a n beome lager, he smplng ditribuion o the ean aproaces the orma ditribtio , reardlss ofth shpe o th poulatondisribtin STEPS IN HYPOTHESIS TESTING S T A T I S T I C S & P R O B A B I L I T Y W E E K 14 - 15 Ex. #1. A researcher reports that the average salary of company managers is more than ₱63, 000. A sample of 35 company managers has a mean of salary ₱65, 700. At α =0.01, test the claim that the company managers earn more than ₱63, 000 a month. The standard deviation of the population is ₱5, 250 . STEP #2. STEP #3.

24. 23 If randm smpls of sze n ae dran fro a ppulaton , ten a n beome lager, he smplng ditribuion o the ean aproaces the orma ditribtio , reardlss ofth shpe o th poulatondisribtin STEPS IN HYPOTHESIS TESTING S T A T I S T I C S & P R O B A B I L I T Y W E E K 14 - 15 Ex. #1. A researcher reports that the average salary of company managers is more than ₱63, 000. A sample of 35 company managers has a mean of salary ₱65, 700. At α =0.01, test the claim that the company managers earn more than ₱63, 000 a month. The standard deviation of the population is ₱5, 250 . STEP #4.

25. 24 If randm smpls of sze n ae dran fro a ppulaton , ten a n beome lager, he smplng ditribuion o the ean aproaces the orma ditribtio , reardlss ofth shpe o th poulatondisribtin STEPS IN HYPOTHESIS TESTING S T A T I S T I C S & P R O B A B I L I T Y W E E K 14 - 15 Ex. #1. A researcher reports that the average salary of company managers is more than ₱63, 000. A sample of 35 company managers has a mean of salary ₱65, 700. At α =0.01, test the claim that the company managers earn more than ₱63, 000 a month. The standard deviation of the population is ₱5, 250 . STEP #5. Reject H o STEP #6. Since we reject the null hypothesis, we can conclude that there is enough evidence to support the claim that the company managers earn more than ₱63, 000 a month.

26. 25 If randm smpls of sze n ae dran fro a ppulaton , ten a n beome lager, he smplng ditribuion o the ean aproaces the orma ditribtio , reardlss ofth shpe o th poulatondisribtin STEPS IN HYPOTHESIS TESTING S T A T I S T I C S & P R O B A B I L I T Y W E E K 14 - 15 Ex. #2. The average baptismal cost concludes 50 guests. A random sample of 32 baptismals during the past year in the NCR had a mean of 53 guests and a standard deviation of 10. Is there sufficient evidences at the 0.05 level significance that the average number of guests differs from the national average? STEP #1. STEP #2. (claim)

27. 26 If randm smpls of sze n ae dran fro a ppulaton , ten a n beome lager, he smplng ditribuion o the ean aproaces the orma ditribtio , reardlss ofth shpe o th poulatondisribtin STEPS IN HYPOTHESIS TESTING S T A T I S T I C S & P R O B A B I L I T Y W E E K 14 - 15 Ex. #2. The average baptismal cost concludes 50 guests. A random sample of 32 baptismals during the past year in the NCR had a mean of 53 guests and a standard deviation of 10. Is there sufficient evidences at the 0.05 level significance that the average number of guests differs from the national average? STEP #2. STEP #3.

28. 27 If randm smpls of sze n ae dran fro a ppulaton , ten a n beome lager, he smplng ditribuion o the ean aproaces the orma ditribtio , reardlss ofth shpe o th poulatondisribtin STEPS IN HYPOTHESIS TESTING S T A T I S T I C S & P R O B A B I L I T Y W E E K 14 - 15 Ex. #2. The average baptismal cost concludes 50 guests. A random sample of 32 baptismals during the past year in the NCR had a mean of 53 guests and a standard deviation of 10. Is there sufficient evidences at the 0.05 level significance that the average number of guests differs from the national average? STEP #4.

29. 28 If randm smpls of sze n ae dran fro a ppulaton , ten a n beome lager, he smplng ditribuion o the ean aproaces the orma ditribtio , reardlss ofth shpe o th poulatondisribtin STEPS IN HYPOTHESIS TESTING S T A T I S T I C S & P R O B A B I L I T Y W E E K 14 - 15 Ex. #2. The average baptismal cost concludes 50 guests. A random sample of 32 baptismals during the past year in the NCR had a mean of 53 guests and a standard deviation of 10. Is there sufficient evidences at the 0.05 level significance that the average number of guests differs from the national average? STEP #5. Accept H o STEP #6. Since we accept the null hypothesis, we can conclude that there is not enough evidence to support the claim that the average guest in a baptismal is not equal to 50.

30. N A H T K Y O U Hypothesis testing S T A T I S T I C S & P R O B A B I L I T Y W E E K 14 - 15