Question

You are talking to a family member and they are confused. They say, “Of course the store is different: look – it has a rate that is 2% less than the claim!” Explain why you conducted this test. In particular, explain what the p-value means. (Make reference to the following concepts in your explanation: point estimate, sample error, potential errors in the test conclusion, and statistical significance. Make sure to explain clearly so that someone who hasn’t taken statistics can understand.) (4 points)

Answer 1

Here we conduct the test to verify whether the claim of the store is true or the claim of the family menber is true that the store is claiming 2% more than the real rate.

Explanation of the concepts.

• First we need to draw the appropriate sample from the store. Selection of sample will cause sampling error i.e, when the whole population is not taken into consideration.
• The sample data is then used to calculate single value which is the best estimate for the unknown population parameter. This is known as point estimate. Example sample mean is the point estimate of the unknown population mean.
• Then the observed sample value is then used in testing of the hypothesis or in other words it used in a formula (called test-statistic) whose value will determine whether null hypothesis is accepted or rejected. (that is which of the two claims stated will be accepted) There are many types of hypothesis testing like z test, t test, Fishers test etc.
• Standard error of estimate (error in the estimation) is calculated by the variance of the sample mean. This is an important value which is used in different places of hypothesis testing. For example in finding the confidence interval etc
• After the test is done and the conclusions are drawn there may arise two potential error. The potential errors in test conclusion are of two types.
  • Type one error: Probability of rejecting the null hypothesis when it is actually true. That is test rejected the null hypothesis when it was actually true.
  • type two error: Probability of accepting null hypothesis when it is actually false. That is the test conclusion accepted the null hypothesis when the alternative hypothesis was true.
• Statistical significance means a result when it is very unlikely to have occurred given the null hypothesis. Significance level, denoted by , is the probability of the study rejecting the null hypothesis, given that the null hypothesis were assumed to be true and the p-value of a result is statistically significant if p   .

P-Value: The probability of obtaining test results at least as extreme as the results actually observed during the test assuming that the null hypothesis is correct is called p-value.

example: to test the hypothesis H0: =15 v/s H1: 15. let the observered value of test statistic (xbar) be 20, Z test is used for testing the hypothesis. Then the p value is PH0[ Z>20].

[NOTE: The sign inside the bracket of the p value is always in the direction of alternative hypothesis.]