Question

1. Please explain what is P value.

2. Please explain what is the difference and relationship between One-Tailed Test and Two-Tailed Test.

3. Please explain what is the difference between Z-statistic and T-statistic.

Answer 1

(1)

P value is probability of getting a result as or more extreme than the sample result by random chance alone, given the null hypothesis is true.

P value is a number between 0 to 1. A small P value indiccates strong evidence against the null hypothesis. So, we reject the null hypothesis. A high P value indiccates weak evidence against the null hypothesis. So, we fail to reject the null hypothesis.

If P value is less than Significance Level , the difference is significant. Reject null hypothesis.

If P value is greater than Significance Level , the difference is not significant. Fail to reject null hypothesis.

(2)

One Tailed Test is where we are interested in one direction. Two Tailed Test is where we are interested in both directions. One Tailed Test is more powerful than Two Tailed Test.

Suppose we want to test the hypothesis whether the mean is different from 10.

Then,

H0: Null Hypothesis: = 10.

HA: Alternative Hypothesis: 10.

This is a Two Tailed Test because we are testing less than or greater than 10.

Suppose we want to test the hypothesis whether the mean is greater than 10.

Then,

H0: Null Hypothesis: 10.

HA: Alternative Hypothesis: 10.

This is a One Tailed Test because we are testing greater than 10.only.

(3)

Z statistic is used when we have large Sample Size ( n > 30). t statistic is used when we have small Sample Size ( n < 30). Both methods assume a normal distribution.

Z Statistic is obtained by subtracting the population mean from sample man and dividing the result by population standard deviation. t Statistic is obtained by subtracting the population mean from sample man and dividing the result by sample standard deviation.