Question

Describe in detail the steps needed to conduct a significance test. Be sure to address how you write hypotheses, conduct calculations, and write conclusions. Through your response, show me that you know how to complete an entire test.

Answer 1

Answer)

First step is to identify the null and alternate hypothesis.

Null hypothesis means there is no difference.

And alternate hyppthesis is the claim that we are testing.

For example if we are given with the claim that mean is less than 200

So null and alternate hypotheisis would be

Null hyppthesis Ho : u =200 (no difference)

Alternate hypothesis Ha : u < 200 (claim)

Second step is to identity the test

That is if it is left tailed or right tailed or two tailed

(< symbol indicates that it is a left tailed test and > symbol indicates that it is a right tailed test and not equal to sign indicates that it is a two tailed test)

But in our example it is a left tailed test (<)

Third step is to find the test statistics

Test statistics = (obtained mean - claimed mean)/(s.d/√n)

S.d = standard deviation

n = sample size

For example our obtained mean is 198

And population standard deviation is 5

And n = sample size = 25

Then we will use z test statistics (as population standard deviation is given, in case population standard deviation is not given, then we use t test)

Z = (198-200)/(5/√25)

Z = -2

Fourth step is to calculate the p-value

For z test, we will look into the z table

From z table p(z<-2) = 0.0228

Or in case that population standard deviation is unknown and we are provided with sample standard deviation and that is same as 5

So we will use t test

t = -2

From t table for degrees of freedom n-1, 25-1 = 24

And test statistics of -2

P-value would be = 0.025 (one tail)

Step 5

Now we need to compare the p-value with the given significance level

Foe example if given significance level is 0.05

And we can see that p-value in both the cases for t and z test is less than 0.05

So we reject the null hypothesis

And if the given significance level is 0.01

Then in this case, p-value is greater than the given significance level, so here we fail to reject the null hypothesis.

If we reject the null hypothesis

Then the conclusion is

We have enough evidence to support the claim

And if we fail to reject the null hypothesis

Then the conclusion is

We do not have enough evidence to support the claim.