Question

• What is hypothesis testing? How would you explain it to someone who has not had as much statistical experience as you?
• What is the difference between the null and alternate hypotheses?
• What does the p-value tell you? When do you reject the null hypothesis or fail to reject the null hypothesis?
• Explain how collecting data (i.e. convenience sampling, randomly selected sample, etc.) for the samples could impact the ability to generalize your results to the whole population.

Answer 1

Suppose a new product needs to be launched in the market. Before being launched its tested on a sample of the target people whether they like it more than the competitors to see if it will be profitable for a company to launch it.

Here, notice we have a sample, a population at large after the launch, and a test. The test can check the mean value of response of people of their preference and compare it to the mean value of the competitors to check if their mean > competitors mean.

Such a testing is done using a hypothesis test. Here out parameter of interest is the population mean (which is estimated from the sample mean since it is not possible to conduct the tests on the entire population a sample is selected. )

The null hypothesis in this case would be that both the mean values are equal and the alternative hypothesis would be that our mean value > mean value of competitor. Generally alternative hypothesis expresses the condition that we are trying to get through the statistical test.

The p value helps us find the significance of the results. The smaller the p value of the test statistic, the more significant is our result ie we have a stronger evidence to reject the null hypothesis.

When the p-value < significance level of the test which we have considered, then we reject the null hypothesis. When p value > significance level, then we fail to reject the null hypothesis.

Since our conclusion of the test of the whole population depends on the sample that we have collected, so the way of collecting data directly effects our results of the entire population.