Hypothesis testing is a statistical method used to make decisions or judgments about populations based on sample data. There are 6 main steps: 1) formulate the null and alternative hypotheses, 2) specify the significance level, 3) determine the critical value, 4) compute the test statistic, 5) make a decision, 6) consider type I and II errors. The p-value is used along with the significance level to determine whether to reject or fail to reject the null hypothesis. Various statistical tests are used depending on the type of data and assumptions. Sample problems demonstrate applications of hypothesis testing across different statistical test formulas.

3. Example :
“ The mean of all bags of pretzels differs from
the advertised weight of 454 grams.”
Null :
“ The mean of all bags of pretzels equals the
advertised weight of 454 grams.”
H0:µ = 454 grams
Alternative :
“ The mean of all bags of pretzels differs from
the advertised weight of 454 grams.”
H1:µ ≠ 454 grams

5. Hypothesis Testing – a method used to make decisions or judgment.
Steps in Hypothesis Testing
1. Formulate the Null Hypothesis
2. Formulate the Alternative Hypothesis
3. Specify the Level of Significance
4. Determine the Critical Value
5. Compute for the test of Statistics
6. Decision or Conclusion

6. • Type I and Type II errors
Our Decision
Truth of H0 If we accept H0. If we reject H0.
If H0 is true Correct decision; Type I error
no error
If H0 is false Type II error Correct decision;
no error
• Conclude a test using the P-value and Level of Significance α.
If P-value ≤ α, we reject the null hypothesis and say the
data are statistically significant at the level α.
If P-value > α, we do not reject the null hypothesis.

8. SAMPLE PROBLEM
A.
A certain task can be done at an average of 40 mins.
w/ standard deviation of 8. A group of 16 workers, given w/
trainings, found the average is only 35 mins. Test the
hypothesis w/ 0.01 level.

9. Statistical Test Formulas…
B. Test for a single mean when variance is unknown & sample is more than 30.

10. SAMPLE PROBLEM
B.
Under the old system, it took an average of 50 minutes/student to
register. If a random sample of 35 students had an average of 42 minutes to
register w/ standard deviation of 11.9 under the use of modern machines.
Test the hypothesis under 0.01 level.

11. Statistical Test Formulas…
C. Test for a single mean when variance is unknown & sample is not more than 30.

12. SAMPLE PROBLEM
C.
In a certain test given under the supervised condition, the mean
score of 25 students is 62 w/ standard deviation of 10. A student who took
under the NS condition turned in mean score of 87 . Test the hypothesis
under 0.01 level.

14. Statistical Test Formulas…
D. Test for the mean of paired observations

15. SAMPLE PROBLEM
D. A team of heart surgeons knows that many patients who undergo corrective
heart surgery have a dangerous buildup of anxiety before their scheduled
operations. The staff psychiatrist at the hospital has started a new counseling
program intended to reduce this anxiety. From the given data, can we conclude
that the counseling sessions reduce anxiety? Use 0.01 level of significance.
B A d=B–A
Patients Score Score After Difference
Before Counseling
Counseling
Jan 121 76 45
Tom 93 93 0
Dianne 105 64 41
Barbara 115 117 -2
Mike 130 82 48
Bill 98 80 18
Frank 142 79 63
Carol 118 67 51
Alice 125 89 36

16. Statistical Test Formulas…
E. Test for the difference of the means from independent samples when variance is
known.

17. SAMPLE PROBLEM
E.
A class of 40 students is taught by method “A” and A class of 36
is taught by method “B”. Both are given same test . The mean scores are 78
and 74 respectively. At standard deviation of 5 & 0.05 level, Test the
hypothesis.

18. Statistical Test Formulas…
F. Test for the difference of the means from independent samples when variance is
unknown and samples are more than 30.

19. SAMPLE PROBLEM
F.
The average grade of 50 senior students in Math is 85 w/ s=10.2,
while a group of 60 senior students got 82 w/ s=8.9. Can the difference in
the mean be attributed to chance using 0.05 level.

20. Statistical Test Formulas…
G. Test for the difference of the means from independent samples when variance is
unknown and samples are not more than 30.

21. SAMPLE PROBLEM
G.
At the beginning of SY, the mean score of 24 students in an
achievement test was 45 w/ s=6. At the end of SY, the mean score of the
same test was 50 w/ s=5. Find if the class has improved. Use 0.05 level of
significance.

22. Statistical Test Formulas…
H. Test about single proportion.

23. SAMPLE PROBLEM
H.
In DLSU, it is estimated that 25% of students have cars on
campus. Does this seem to be valid estimate if random sample of 90
students, 28 are found to have cars? Use alpha 0.05.

24. Statistical Test Formulas…
I. Test of comparing two proportions

25. SAMPLE PROBLEM
I.
In cheating matters among students, 144 or 41.4 % of 348 from
homes of good socio-eco status were found to have cheated in some test.
While 133 or 50.2 % of 265 students of poor socio-eco status also cheated
on same test. Is there a true difference in the incidence of cheating in these
2 groups? Use alpha 0.10

26. Statistical Test Formulas…
J. Test on single variance or standard deviation.

27. SAMPLE PROBLEM
J.
The life of a certain batteries are approximately distributed w/
standard deviation equal to 0.09 yr. If random sample of 10 of these have
s=1.2 years. Is s> 0.9 year? Use alpha 0.05

28. Statistical Test Formulas…
K. Test on two variances or standard deviations

29. SAMPLE PROBLEM
K.
A group of Mass Com students found that 17 incoming calls last
an average of 5.16 minutes w/ variance of 2.12 & 12 outgoings’ last an
average of 4.13 minutes w/ variance of 1.36. Test the Hypothesis that
variances are equal. Use alpha 0.05.

30. In Partial Fulfillment for the Course
Business Statistics – BUS STAT
IA10205
February 2012
***********All rights reserved*************