HYPOTHESIS TESTINGInferential Statistics

In this session...

What is hypothesis Interpreting and selecting

significance level Type I and Type II error One tailed and Two tailed tests Z-test of One Sample Mean The t-Test of Significance

What is Hypothesis

Hypothesis is a predictive statement, capable of being tested by scientific method, that relates an independent variables to some dependent.

A hypothesis states what we are looking for and it is a proportion which can be put to a test to determine its validity.

e.g. Students who receive counselling will show a greater increase in creativity.

Types of Hypotheses

Null Hypothesis It is an assertion that we hold as true

unless we have sufficient evidence to conclude otherwise.

It is denoted by H0 If a population mean is equal to

hypothesized mean then Null can be written as

H0:µ=µ0

Types of Hypotheses

Alternative Hypothesis The alternative hypothesis is negation of

null hypothesis Also called as the Researcher’s

Hypothesis Denoted by Ha If null is given as

H0:µ=µ0 Then alternative Hypothesis can be

written as Ha=µ≠µ0, H0:µ>µ0, H0:µ<µ0

Example:

Title: The NSAT Scores and Academic Achievement of the Students in Private and Public Schools

Example:

H0: There is no significant relationship between the NSAT performance and the academic achievement among the four learning areas of private schools, public schools and combination of private and public schools

Example:

Ha: There is a significant relationship between the NSAT performance and the academic achievement among the four learning areas of private schools, public schools and combination of private and public schools

Example:Title: A Comparative Study on the

Consumer’s Acceptance of X and Y Toothpastes

Title: A Study on the Relationship of Smoking Habits to Hypertension among employees Of ABC Corporation

Title: Competencies Of Nurses from Government Hospitals and Private Hospitals

Selecting and interpreting significance level Significance means the percentage

risk to reject a null hypothesis when it is true and it is denoted α. Generally taken as 1%, 5% and 10%

The higher the level of significance, the higher the probability of rejecting the null hypothesis when it is true.

(1-α) is the confidence interval in which the null hypothesis will exist when it is true

Type I and Type II Errors

One Tailed Test

A one – sided test is a statistical hypothesis test in which the values for which we can reject the null hypothesis, Ho are located entirely in one tail of the probability distribution.

Left- tailed @5% significance level

Right- tailed @5% significance level

Two tailed test

Two tailed test will reject the null hypothesis if the sample mean is significantly higher or lower than the hypothesized mean.

Two tailed @5% significance level

Procedure for Hypothesis Testing Formulate the null hypothesis, Ho Select an appropriate alternative

Hypothesis, Ha Determine the level of significance to be

used Choose an appropriate test statistic and

determine the critical value of test statistics Find the value of the test statistic using the

sample data Make the decision

Hypothesis Testing of MeansZ-testTest Condition

•Population normal and infinite•Sample size is large or small•Population variance is known•Ha may be one sided or two sided

Hypothesis Testing of MeansT-testTest Condition •Population is infinite and normal•Sample size is small•Population variance is unknown•Ha may be one- sided or two sided

Example:

A certain clinical laboratory set up their quality control standard for the reagents of blood glucose test with an average of 110 mg/dL (milligrams per deciliter) and a standard deviation of 5 mg/dL. In a random sample of 36 runs of the test procedure using the control reagents, the results yielded an average of 113 mg/dL. Is there enough evidence to conclude that the reagents are out of control. Use α=0.05

Example:

Test the hypothesis that the mean of a particular electrophoresis procedure is less than or equal 2.5 hours if a random sample of 16 shows a mean procedure time of 2.6 hours, with a standard deviation of 0.24 hours. Use α=0.01