07-23-12 ( JULY 23, 2012); Z- test and T- test for the Mean

On July 23 we III- Gold students were taught a new lesson which is the Z-test and T- test for the Mean.
In our lesson:

•       Hypotheses are tested using a statistical test based on this general formula which is the:

Test value= (observed value-expected value)/ standard error

Observed value: the computed sample

Expected value: the parameter expected when the null hypothesis were true

Standard error: the error of the statistics being tested

• Formula for Z-test and T-test

•  Z-test for the mean is used when (n) is greater or equal to 30 or the population mean is normally distributed and the standard deviation is known.
• T-test for the mean is used when (n) is less than 30 and when the standard deviation is not known.
• Four possible outcomes and the summary statement for each situation:

When Claim is the Null Hypothesis

-          Reject The Null Hypothesis; There is enough evidence to reject the claim

-          Do not Reject the Null Hypothesis; There is not enough evidence to reject the claim

When Claim is the Alternative Hypothesis

-          Reject The Null Hypothesis; There is enough evidence to support the claim

-          Do not Reject the Null Hypothesis; There is not enough evidence to support the claim

•   P-Value Method for the Hypothesis Testing – is the actual area under the standard normal distribution curve, representing the probability of a particular sample statistics or a more extreme sample statistic occurring if the null hypothesis is true.
• Steps in Hypothesis testing  problems in P-Value Method

Step1. State the hypothesis and identify the claim

Step2. Compute the test value

Step3. Find the P-Value

Step 4.Make the decision

Step5. Summarize the Results

•   Decision rule when using a P-Value

If P-Value is less than or equal to alpha, reject the null hypothesis.

If P-Value is greater than the alpha, do not reject the null hypothesis.

By: Carl Joel E. Palma III-Gold