Question

write a null and alternative hypotheses that demonstrate an understanding of the student t-test. explain your answer.

Answer 1

Dear student here I giving you some more details to understand the concept very well if you satisfied PLEASE THUMBS UP and SUPPORT ME... THANKS IN ADVANCE....

Null Hypothesis

The hypothesis that is tested is called null hypothesis usually denoted as H₀

Alternative Hypothesis

When H₀ is accepted then what would be rejected Or if H₀ is rejected then What would be accepted.. The answer is alternative hypothesis usually denoted as H₁

I will define both in student’s t test.. Let’s look how many t test are there

One sample T test

Two independent sample T test

Paired sample T test

Multiple Comparison T test (But it is generally not used due to uncontrollable increase of type 1 error)

ASSUMPTIONS OF T TEST

• Population is normal
• Standard deviation of population is unknown
• The sample size is small (less than 30)

If these assumptions are held in your problem what you are trying to test, you can go for t test..

Now we look hypothesis of the above mentioned first three student’s t test

(A) ONE SAMPLE T TEST

H₀ : POPULATION MEAN (μ) = SAMPLE MEAN (m₀) i.e, Population Mean - Sample Mean = 0

V/S

H1 : POPULATION MEAN (μ) ≠ SAMPLE MEAN (m₀) OR

H1 : POPULATION MEAN (μ) > SAMPLE MEAN (m₀) OR

H1 : POPULATION MEAN (μ) < SAMPLE MEAN (m₀)

ALTERNATIVE HYPOTHESIS can be chosen based on the problem that you are dealing with. Simply we can write

• H0: μ = m₀
• H1: μ ≠ m₀    (two-tailed)
• H1: μ >m₀  (upper-tailed)
• H1: μ < m₀   (lower-tailed)

Example for two tailed (H1: μ ≠ m₀)

A random sample of size 16 has 53 as the mean and the sum of squares of the deviation taken from mean is 150. Can the sample is from the population with mean 56. In this situation, you can use two-tailed alternative

Example for upper tailed (H1: μ > m₀)

Whether the given data from normal population has mean higher than 50. In this case, you can use upper tail alternative

Similarly, you will understand about lower tail too

(B) TWO INDEPENDENT SAMPLE T TEST

This test is used to check whether the given two normal popultion have same mean

H₀ : POPULATION MEAN (μ₁) = POPULATION MEAN (μ₂) i.e, 1st Population Mean - 2nd Population Mean = 0

V/S

H1 : POPULATION MEAN (μ₁) ≠ POPULATION MEAN (μ₂) OR

H1 : POPULATION MEAN (μ₁) > POPULATION MEAN (μ₂) OR

H1 : POPULATION MEAN (μ₁)) < POPULATION MEAN (μ₂)

(C) Paired sample T test

This test is used to check whether the given population has benefited by applying 2 treatment applied by dividing the population into two groups..

Example: Checking whther there is any difference between the effects of two baby foods.. Divide the population of babies into 2 groups and then each group is treated with the two given baby foods.

H₀ : POPULATION MEAN (μ₁) = POPULATION MEAN (μ₂) i.e, 1st Population Mean - 2nd Population Mean = 0

V/S

H1 : POPULATION MEAN (μ₁) ≠ POPULATION MEAN (μ₂) OR

H1 : POPULATION MEAN (μ₁) > POPULATION MEAN (μ₂) OR

H1 : POPULATION MEAN (μ₁)) < POPULATION MEAN (μ₂)