Question

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 describing your activities. Your report should contain the exact sections described below. The point vałues that will be assigned to the sections are listed to the right of the section title. Problem Statement (10): In the problem statement, you should introduce the 1. random variable that you are investigating and the data you will be describing. You should then state very precisely the null and alternate hypothesis that you will be testing. Finally, you should provide some explanation for why this hypothesis is important and/or interesting. 2. Data Description (10): This section should contain the information about your data necessary to understand the rest of the report. This section should contain (at minimum), the precise statement of the random variable, a description of the source of your data and the data collection procedures, the descriptive statisti and some assertions that are consistent with the data. If you collect an original data by using questionnaire, attach a copy of the questionnaire with your report. cs. Hypothesis Testing Procedure (20): In this section, you should present the details concerning how you will test your hypothesis. You should describe the logic behind your null and altermate hypotheses where did they come from. why are they interesting. You should describe the test statistic you will use (i.e.. z,t) and why? [Specify if you are testing a hypothesis about a mean, if you have what appears to be normal data]. When explaining your choice of test statistic, you need to discuss whether you have satisfied the assumptions necessary for using the specific statistic (e.g. does the statistic require your population to be normal and is it?). You should also determine the alpha level you will use (i.e. 0.01. 0.05) and explain why you chose this particular alpha level. 3. Hypothesis Testing Results (20): This section should start with the results of your test. Clearly you should state the value of the test statistics and the result of the accept/reject decision. You should probably identify the p-value of the test. If appropriate, you should state what the point estimate is for the parameter and 4. construct a confidence interval around the parameter. S Discussion, Summary, and Conclusion 2Oy If you condactod a test on a the event that your null hy pothesis is rejected. Also yoa should summarine the process of the project and then prov ide the conchading staticmont concerning the hy pothesis and the resuls 6. "What I learned Statements (10y This section should contain brief reflections (1-2 paragraphs) on what was learned from the hypothesis- tosting project. For example, you might comment on the effort and difficulty associated with dentify ing a bo pothesis, the amount of time involved, and or the complexity of the overall proces. You might particularly focus on things that you did expect o learn - what surperised you, frustrated you, made you curious,etc. This component of the neport is to he done individually. if you are completing the project with another student, this section should contain individual statements from each student Acknon ledgement, You neod to acknow ledge all sources you have consulted inclading theoretical background of the problem and or data sources.(10 pts)

Answer 1

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

• Null Hypothesis: Population proportion of left-handed students in the College of Art and Architecture = 0.10 (p = 0.10).
• Alternative Hypothesis: Population proportion of left-handed students in the College of Art and Architecture > 0.10 (p > 0.10).

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......