Question

• Discuss the five steps in hypothesis testing, citing examples where necessary.
• Define null and research hypotheses.
• Explain how to prepare data for hypothesis testing.
• Describe exploratory data analysis as a prelude to hypothesis testing.
• Distinguish between Type I and II errors. What are the implications of each?

Answer 1

1. State the null hypothesis and the alternate hypothesis. Null Hypothesis - statement about the value of a population parameter. Alternate Hypothesis - statement that is accepted if evidence proves null hypothesis to be false.

2. Select the appropriate test statistic and level of significance. When testing a hypothesis of a proportion, we use the z-statistic or z-test and the formula pd When testing a hypothesis of a mean, we use the z-statistic or we use the t-statistic according to the following conditions. If the population standard deviation, o, is known and either the data is normally distributed or the sample size n > 30, we use the normal eliisiriiblition (х.siai..silc).. When the population standard deviation, σ, is unknown and either the data is normally distributed or the sample size is greater than 30 (n > 30), we use the t-distribution (t-statistic) A traditional guideline for choosing the level of significance is as follows: (a) the 0.10 level for political polling, (b) the 0.05 level for consumer research projects, and (c) the 0.01 level for quality assurance work 3. State the decision rules. The decision rules state the conditions under which the null hypothesis will be accepted or rejected. The critical value for the test-statistic is determined by the level of significance. The critical value is the value that divides the non-reject region from the reject region.

4 When we use the z-statistic, we use the formula Compute the appropriate test statistic and make the decision. When we use the t-statistic, we use the formula r- 8 Compare the computed test statistic with critical value. If the computed value is within the rejection region(s), we reject the null hypothesis; otherwise, we do not reject the null hypothesis. 5 Interpret the decision. Based on the decision in Step 4, we state a conclusion in the context of the original problem.

A hypothesis is a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false. Let's look at an example. Little Susie speculates, or hypothesizes, that the flowers she waters with club soda will grow faster than flowers she waters with plain water. She waters each plant daily for a month (experiment) and proves her hypothesis true! A null hypothesis is a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove. In the example, Susie's null hypothesis would be something like this: There is no statistically significant relationship between the type of water I feed the flowers and growth of the flowers. A researcher is challenged by the null hypothesis and usually wants to disprove it, to demonstrate that there is a statistically-significant relationship between the two ariables in the hypothesis.

An alternative hypothesis simply is the inverse, or opposite, of the null hypothesis. So, if we continue with the above example, the alternative hypothesis would be that there IS indeed a statistically-significant relationship between what type of water the flower plant is fed and growth. More specifically, here would be the null and alternative hypotheses for Susie's study: Null: If one plant is fed club soda for one month and another plant is fed plain water, there will be no difference in growth between the two plants. Alternative: If one plant is fed club soda for one month and another plant is fed plain water, the plant that is fed club soda will grovw better than the plant that is fed plain water

Exploratory data analysis is a set of methods designed to examine and describe the structure of data The exploratory approach, or mode, involves the use of descriptive techniques and the intuition of the analyst to investigate the structure of data. Unlike the confirmatory approach, or mode, which relies on classical statistical analysis and data to confirm and reformulate theory through the vehicles of parameter estimation and hypothesis testing, the exploratory mode uses data to suggest theory through the vehicle of informal data examination. It can be considered, in some sense, a prelude to classical statistical analysis. It is also suggested that the data analyst might consider combining exploratory data analysis and classical statistical analysis into a powerful analytic approach, or mode, which uses both formal statistical inference and informal data exploration The advantages of exploratory data analysis prior to the hypothesis testing is that We can understand the data in a much more dimension. 1. 2. We can able to fix the null and alternative hypothesis. We can also find out some dependent and independent variables. 3. We can also find out which test to be used at different times. 4.

TYPE 1 ERROR AND TYPE 2 ERROR AND ITS IMPLICATIONS type I error (or error of the first kind) is the incorrect rejection of a true null hypothesis. Usually, a type I error leads one to conclude that a supposed effect or relationship exists when in fact it doesn't. Examples of type I errors include a test that shows a patient to have a disease when in fact the patient does not have the disease, a fire alarm going on indicating a fire when in fact there is no fire, or an experiment indicating that a medical treatment should cure a disease when in fact it does not Hypothesis: "Adding water to toothpaste protects against cavities." Null hypothesis: "Adding water does not make the toothpaste more effective in fighting cavities. This null hypothesis is tested against experimental data with a view to nullifying it with evidence to the contrary. A type l error occurs when detecting an effect (adding water to toothpaste protects against cavities) that is not present. The null hypothesis is true (i.e., it is true that adding water to toothpaste does not make it more effective in protecting against cavities), but this null hypothesis is rejected based on bad experimental data or an extreme outcome of chance alone.

This null hypothesis is tested against experimental data with a view to nullifying it with evidence to the contrary A type I error occurs when detecting an effect (adding water to toothpaste protects against cavities) that is not present. The null hypothesis is true (i.e., it is true that adding water to toothpaste does not make it more effective in protecting against cavities), but this null hypothesis is rejected based on bad experimental data or an extreme outcome of chance alone. A type Il error (or error of the second kind) is the failure to reject a false null hypothesis. Examples of type II errors would be a blood test failing to detect the disease it was designed to detect, in a patient who really has the disease; a fire breaking out and the fire alarm does not ring; or a clinical trial of a medical treatment failing to show that the treatment works when really it does Hypothesis: "Adding fluoride to toothpaste protects against cavities." Null hvpothesis: "Adding fluoride to toothpaste has no effect on cavities." This null hypothesis is tested against experimental data with a view to nullifying it with evidence to the contrary. A type Il error occurs when failing to detect an effect (adding fluoride to toothpaste protects against cavities) that is present. The null hypothesis is false (i.e, adding fluoride is actually effective against cavities), but data from the given experiment are such that the null hypothesis cannot be rejected