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Week 3 Group Work

Statistical hypothesis testing is crucial to figuring out and determining if a hypothesis is correct. The process is based on how probable a set of things will occur if the null hypothesis were true. This allows the researcher to use all of the data to answer the hypothesis about the population, rather than looking at individual points. This helps researchers draw conclusions from the sample towards the population being examined. There is a very strict testing process that gives researchers a flow chart and check list to make sure that everything was done correctly to answer the hypothesis.

The first step is to ask a question or state the hypothesis about an unknown population. For this example we will test 25 people wearing cleats to see if they improve athletic mobility. The purpose of this is to start not with any process but with a question that the rest of the steps will attempt to answer. Typically the hypothesis surrounds a population parameter’s value. There are a total of two hypotheses, the null hypothesis and the alternative hypothesis. The null hypothesis is what would occur if the sample wearing cleats did the same as the population without cleats. The alternative hypothesis basically means that wearing cleats did cause an effect. The null hypothesis expects that the untreated population will be able to run a from endzone to endzone and back on average in 25 seconds.

The second step is to use the hypothesis to predict the traits that the sample should contain. When the researcher eventually uses the data from the sample, the researcher will begin to ascertain the details of the hypothesis. This data will allow the researcher to see if the null hypothesis will be wrong. The object of obtaining data is to use the null hypothesis to determine what kind of sample mean should be obtained. This is all done before the data has been collected. The tails of the distribution will hold the extreme values while the middle will contain sample means that will likely be obtained if the null hypothesis is true. These tail areas are the called the test alpha value. Also called the critical region, these unlikely values define outcomes that do not align with the null hypothesis. This region is for very unlikely outcomes if the treatment has no effect. Typically the values will be 0.05 or 0.01. The critical zone for this test is z= +/_1.96

The data is then collected after the hypothesis has been stated as to make sure that the appropriate criteria are what are being tested. The point of this is to make sure that the research and researchers stay objective about their evaluations. After the data is collected, the process really begins. The heart of hypothesis testing is comparing the sample mean with the null hypothesis. In other words, the data itself must be compared with the hypothesis to actually see if there was an effect. First researchers must compute a z-score to show where the sample mean is in relation to the hypothesis population mean from the null hypothesis. The z score is found by subtracting the hypothesized population mean (25) from the sample mean (22) and dividing that by the standard error between the sample mean (5) and hypothesized population mean(25). The top of the formula determines the distance between the data and the hypothesis, while the bottom determines the difference between sample mean and population mean. The z-score is -3.

The final step is to use the z-score obtained in step 3 and compare it with the null hypothesis by the criteria set in step 2. If the sample data is located in the critical region, which would mean the researchers would reject the null hypothesis and saying there was an effect from treatment. If the sample data is not inside the critical region, than the data does not make a strong enough case to suggest that the treatment had an effect. Consequently, the relation and closeness is what ultimately decides how much of an effect a treatment appears to have. If the treated sample looks similar to the untreated sample, there must not have been much of an effect from that treatment. In this example, the sample(-3) did reach the critical area(+/-1.96) of the test, so it rejected the null hypothesis. The cleats the subject wore did increase the running times of the test subjects