Objectives: Generate of t-test. Learn about the assumptions of t-test. Calculate t-test. Construct the confidence interval for the population mean. Recall steps for z test: 1. State null and alternative hypothesis. 2. Determine the level of significance 3. Apply test statistics. 4. Identify critical region/ p-value. 5. Interpret the result. Need of t test:  When population standard deviation is known or sample is large enough that sample population deviation will represent population’s standard deviation. We can used z-test or standard normal distribution.  What do we do if population standard deviation is not known and the sample size is less than 30? T distribution: Also known as student’s test. Identified by William Goset. Similarities between z and t distribution: Bell Shaped It is symmetric around the mean. Mean, median, and the mode are plot at zero which is at the center of bell shape curve. The curve does not touch the x-axis. Differences between z and t distribution: T- distribution is associated with degrees of freedom. Degree of freedom is (n-1) and is associated with sample size. Degree of freedom are the number of values that are free to vary after a sample statistics has been computed. It tells the research which t curve to use. With the increase in sample size, the t distribution approaches the standard normal distribution. When to use t test: Standard deviation of population is unknown. Use the s (standard deviation). if sample size less than 30 so normal distribution should be ensured. Steps for hypothesis testing for t test: State null and alternative hypothesis. Determine the level of significance Apply test statistics. Identify critical region/ p-value. Interpret the result.

2. 2
Shakir Rahman
BScN, MScN, MSc Applied Psychology, PhD Nursing (Candidate)
University of Minnesota USA.
Principal & Assistant Professor
Ayub International College of Nursing & AHS Peshawar
Visiting Faculty
Swabi College of Nursing & Health Sciences Swabi
Nowshera College of Nursing & Health Sciences Nowshera

3. By the end of the session, students will be able to:
Generate of t-test.
Learn about the assumptions of t-test.
Calculate t-test.
Construct the confidence interval for the
population mean.
3

4. Descriptive Inferential
Statistics
Estimation Hypothesis testing
Point
Estimate
Interval
Estimate
4

5. 1. State null and alternative hypothesis.
5
2. Determine the level of significance
3. Apply test statistics.
4. Identify critical region/ p-value.
5. Interpret the result
Z-Test

6. Clue: Look at the z test formula.
6

7. When population standard deviation is knownor
sample is large enough that sample population
deviation will represent population’s standard
deviation. Wecan used z-test or standard normal
distribution.
What do we do if population standard deviation is not
known and the sample size is less than 30?
7

8. Also known as student’s test.
Identified by WilliamGoset.
8

9. Bell Shaped
It is symmetric around the mean.
Mean, median, and the mode are plot at
zero which is at the center of bell shape
curve.
The curve does not touch the x-axis.
9

11. T-distribution is associated with degrees of freedom.
Degree of freedom is (n-1) and is associated with
sample size.
Degree of freedom are the number of values that are
free to vary after a sample statistics has been
computed.
It tells the research which t curve to use.
With the increase in sample size, the t distribution
approaches the standard normal distribution.
11

12. 12

13. The average score of 5 individuals is 16 points. The 4out
of 5 values are free to vary. But once the 4 values are
determined, the fifth value must be a specific number to
yield 16 points as mean of all 5 values.
1. 25 points.
2. 15 points.
3. 10 points.
4. 25points.
5. 5 points.
13

14.  Standard deviation of population is unknown. Use thes
(standard deviation).
 If sample size less than 30 so normal distribution
should be ensured.
14

15. 1. State null and alternative hypothesis.
2. Determine the level of significance
3. Apply test statistics.
4. Identify critical region/ p-value.
5. Interpret the result
15

16. Calculate critical value of t with alpha 0.01 and d.f.=
21for left tail.
Calculate value for alpha as 0.1 with d.f. 17 for a two
tailed t-test.
Find the critical value for alpha 0.05 with d.f.= 28 for
right tailed t-test.
16

18. -2.518
+1.740, -1.740
+1.701
18

19. A nurse researcher claims that the mean number of
infections in a week at a hospital in a country is 350
cases. A random sample of 12 weeks had a mean number
of 358 cases. The standard deviation of sample is 16.Test
the claim at alpha 0.05 that the average is higher than
350.
19

20. 20

21. Step 4:
Reject Ho if
t cal > t tabα, d.f.
t cal > t tab 0.05,11.
1.732 < 1.796 (Fail to
reject)
21

23. 1.796
23
1.796

24. Step V:
02-Oct-20 24
Since t cal > t tabα, d.f. and does not fall in
the rejection region, so we fail to reject Ho
at 5 % level of significance and there is not
enough evidence to conclude that mean
infection rate per week is greater than
350.

25. The human resource manager claims that the average
salary of teachers in nursing school in a country is
found to be different from 60$ a day.Arandomsample
from 8 nursing schools were selected, and the daily
salaries (in $) are mentioned below. The value of
sample standard deviation is 5.08. Is this enough
evidence to support the manager’s claim at alpha 0.1?
60 56 60 55
70 55 60 55
25
Bluman(2012)

26. Step 1:
Ho: μ = 60$
Ha: μ ≠ 60$
Step 2:
At alpha: 0.10 and d.f. 7, critical value is 1.895
t tabα, d.f.=t tab 0.1,7= 1.895
26

28. Step 3:
Tocompute test value, the mean and standard
deviation must be found
28

29. 58.88-60/5.08 /√ 8
-0.62
■ Step 4:
■Do not reject null hypothesis since -0.624 does not fall in the
critical region.
■ Rej ect Ho if t cal> t tab or
■ t cal< -t tab
0
-1.895 -0.624
+1.895
29

30. Interpretation:
There is not enough evidence to support manager’s claim
that the average salary of nursing faculty in a country is
different from 60$ a day at 10% level of significance .
30

32. Bluman (2012). Elementary Statistics: A Step by StepApproach
(8th.). McGraw Hill.
Daniel (2014). Biostatistics: Basic Concepts and Methodology
for the Health Sciences. New York: John Wiley &Sons.
32

33. Acknowledgements
Dr Tazeen Saeed Ali
RM, RM, BScN, MSc ( Epidemiology &
Biostatistics), Phd (Medical Sciences), Post
Doctorate (Health Policy & Planning)
Associate Dean School of Nursing & Midwifery
The Aga Khan University Karachi.
Kiran Ramzan Ali Lalani
BScN, MSc Epidemiology & Biostatistics (Candidate)
Registered Nurse (NICU)
Aga Khan University Hospital