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Hypothesis Testing

Name ID Samia Rahaman 142-15-3676 Md.Mahfuzul Haque 142-15-3747 Md.Masiur Rahman 142-15-4102 Md.Sakib Hossain 142-15-3750 Md.Ashiquzzaman Khondaker 142-15-3706 Md.Samsuzzam 142-15-3737

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What is Hypothesis testing Types of Hypothesis Testing Example of Hypothesis Steps of Hypothesis Testing Probability Distribution Z-test T-test

Contents

A Hypothesis is the statement or an assumption about relationships between variables.

What is Hypothesis Testing?

Types of Hypothesis1.Null Hypothesis (H0) 2.Alternative Hypothesis (Ha or H1)

Example of Hypothesis type

Null Hypothesis (H0) Alternative Hypothesis (Ha or H1)Each of the following statements is an example of a null hypothesis and alternative hypothesis.

Steps in Hypothesis Testing

Establish Critical or Rejection region

Select the Suitable Test of significance or Test Statistic

Whether the test involves one sample, two samples, or samples?

Whether two or more samples used are independent or related?

Is the measurement scale nominal, ordinal, interval, or ratio?

The choice of a probability distribution of a sample statistics is guided but the sample size n and the value of population standard deviation as shown in the table.

Formulate a Decision Rule to Accept Null Hypothesis

Accept H0 if the test statistic value falls within the area of acceptance.Reject otherwise.

Accept H0 if the test statistic value falls within the area of acceptance.Reject otherwise.

Summary of Certain Values for Sample Statistics Z

When we have a large sample, we can get away with substituting the sample standard deviation for the true one and continuing to use the z-distribution. This gives us the following z-score formula:

ns

xz oH

/

But what if you don’t know the true standard deviation and the sample size is small? Then we have to use the t-distribution. We calculate a t-score instead of a z-score:

ns

xt oH

/

And then we find a t-critical value instead of a z-critical value.

ExampleExample: Same example as above, doing a one-tail test. But this time, we don’t know the standard deviation is 2, and our sample size was only 17. Our sample standard deviation turns out to be 1.9, and we use this to find our t-score: 

84.016/9.15.69.6

/

n

xt oH

In the t-table, with df = 16 -1 = 15 and 90% confidence level, t-critical is 1.75. We do not reject the null.

Example: Let’s do the two-tail test on CSUN’s graduation time. Let’s say we know the standard deviation of the population is 2 years, and we sampled 49 CSUN graduates and found a sample mean of 6.9. Then we calculate:

4.149/25.69.6

/

n

xz oH

We need a z-critical value for a significance level of 0.10. Since this is a two-tail test, we want 0.05 in each tail, so find the value of z in Table 3 that gives you an area as close to 0.95 as possible. This turns out to be 1.64. Since 1.4 < 1.64, we do not reject the null. The administration’s claim cannot be rejected.

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