Solution :-
About 10% of the human population is left-handed. A researcher at Penn State speculates that students in the College of Arts and Architecture are more likely to be left-handed that people in the general population. A random sample of 100 students in the College of Arts and Architecture is obtained and 18 of these students were found to be left-handed.
Research Question: Are artists more likely to be left-handed than people in the general population?
Step 1: State Null and Alternative Hypotheses
Now that you know the null and alternative hypothesis, did you think about what the type 1 and type 2 errors are? It is important to note that Step 1 is before we even collect data. Identifying these errors helps to improve the design of your research study. Let's write them out:
Type 1 error: Claim artists are more likely to be left-handed than people in the general population, when in truth they are not more likely.
Type 2 error: Fail to claim artists are more likely to be left-handed than people in the general population, when they are in fact more likely.
In this case, the consequences of these two errors are fairly similar (e.g. installing more or fewer left handed desks in classrooms than are needed).
Step 2: Collect and summarize the data so that a test statistic can be calculated.
In the sample of 100 students listed above, the sample proportion is 18 / 100 = 0.18. The hypothesis test will determine whether or not the null hypothesis that p = 0.1 provides a plausible explanation for the data. If not we will see this as evidence that the proportion of left-handed Art & Architecture students is greater than 0.10.
If the null hypothesis is true then the standard error of the sample proportion would be sqrt(0.1(1−0.1)/100) = 03 and the sample proportion would follow the normal curve. Thus, we can use the standard score z = (0.18-0.10) / 0.03 = 2.67 as our test statistic.
Step 3: Use the test statistic to find the p-value.
Using the normal curve table for the Z-value of 2.67 we find the p-value to be about 0.004. Notice that the one-sided alternative hypothesis says to watch out for large values so we look at the percentage of the normal curve above 2.67 to get the p-value.
Interpretation of the p-value. The likelihood of getting our test statistic of 2.67 or any higher value, if in fact the null hypothesis is true, is 0.004.
Step 4: Make a decision using the p-value.
Since the p-value of 0.004 is so small, the null hypothesis provides a very poor explanation of the data. We find good evidence that the population proportion of left-handed students in the College of Art and Architecture exceeds 0.10.
Now that we have made our decision, we are only at risk of making a type 1 error. It is not possible at this point to make a type 2 error because we rejected the null hypothesis......
Objective: The purpose of this project is to provide you with experience in stating and testing a hypothesis of a given data that you have selected Report Guidelines: You should submit a report...
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