A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data.

1. .Confidence Interval
.P-value
.Type 1& 2 Error
.Correlation - Regression
Dr Qurat-Ul-Ain

2. CONFIDENCE INTERVAL
• Parameter and statistic
• A range of values we are fairly sure our true value lies in
• Population value falls within this
• A confidence interval gives an estimated range of values which is
likely to include an unknown population parameter, the estimated
range being calculated from a given set of sample data.

3. CONFIDENCE INTERVAL
• Standard errors are the building blocks of confidence
intervals
• A confidence interval is a statistic plus or minus a
margin of error
• Gives you a lower and upper estimate
• Measures uncertainty

4. CONFIDENCE INTERVAL
• We select a level of a confidence interval that determines the
probability that the interval will contain the true parameter value.
• Common values 0.90, 0.95, and 0.99
• 90% 95% 99%
• We construct a confidence interval to estimate the population
parameter with an estimated level of confidence

5. Steps in Calculating Confidence Interval
• Find the number of observations n, calculate their mean X, and standard
deviation
• Decide what Confidence Interval we want: 95% or 99% are common
choices. Then find the "Z" value for that Confidence Interval from the table
• use that Z in this formula for the Confidence Interval
• X ± Z s/√n
• X is the mean
• Z is the chosen Z-value from the table above
• s is the standard deviation
• n is the number of observations

6. Confidence
Interval
Z
80% 1.282
85% 1.440
90% 1.645
95% 1.960
99% 2.576
99.5% 2.807
99.9% 3.291

7. CONFIDENCE INTERVAL
• Average height of your class 175cm
• SD 20 cm
• At 95% confidence interval
• 175cm+_ 6.2cm
• 175+6.2=181.2cm
• 175-6.2=168.8cm
• So we are95% confident that our true average lies between this range

8. CONFIDENCE INTERVAL
• Martina read that the average graduate student is 33years old. She
wanted to estimate the mean age of graduate students at her large
university, so she took a random sample of 30 graduate students. She
found that their mean age was xˉ=31.8 and the standard deviation
was sx​=4.3. At 95% confidence interval on the mean based on the
data was 30.2, 33.4
• Based on this interval, is it plausible that the mean age of all
graduate students at her university is also 33 years?

9. P-value
• The P value gives the probability of difference occurring due to
chance
• P = 0.5 means that the probability of the difference having happened
by chance is 0.5 in 1, or 50:50.
• P = 0.05 means that the probability of the difference having
happened by chance is 0.05 in 1, i.e. 1 in 20.
• The lower the P value, the less likely it is that the difference happened
by chance and so the higher the significance of the finding

10. LEVEL OF SIGNIFICANCE
•P value
•p > 0.05 accept null hypothesis
•p < 0.05 reject null hypothesis
•P = 0.05 classed as significant
•P = 0.01 highly significant
• P = 0.001 very highly significant

11. ERROR
• No hypothesis test is 100% certain or sure.
• Based on probabilities
• Incorrect conclusion
• TYPE 1 error
• Type 2 error

12. Tests of
significance
Null hypothesis
True
Null hypothesis
False
Accept Null
hypothesis
Correct decision Wrong decision
Type II error
Reject null
hypothesis
Wrong decision `
Type I error
Correct decision

15. CORRELATION
Extent or degree of relation between two variables
Denoted by ‘r’ correlation coefficient
shows how close is the relation between two
variables

16. Define as;
•Correlation is a statistical measure that
indicates the extent to which two or more
variables fluctuate in relation to each other

17. Correlation
Real Life Example
• The more time you spend running on a treadmill, the more
calories you will burn.
• The longer your hair grows, the more shampoo you will
need.
• The more money you save, the more financially secure you
feel.
• As the temperature goes up, ice cream sales also go up.

21. REGRESSION
• A statistical method that helps us to analyze and
understand the relationship between two or more
variables of interest. The process that is adapted to
perform regression analysis helps to understand
which factors are important, which factors can be
ignored, and how they are influencing each other.
• In regression, we normally have one dependent
variable and one or more independent variables.

22. REGRESSION
Estimates relationship among variables
Dependent and independent variable

24. •Thank You
•Any Questions?