Research Question for Parts 1 and 2: A health psychologist wants to study overall student health on a university campus. One measure he decides to take is that of minutes exercised per week. Assume that we know from previous studies that the population mean for minutes of exercise per week for college students is μ = 100 with a standard deviation of σ = 25.
The health psychologist in question is particularly interested in the myth of the “Freshmen 15.” This myth claims that most freshmen gain weight during the first year of college, mostly due to bad eating habits and lack of exercise and sleep. He wonders if the Freshmen on his campus actually exercise less than the general population of college students. He randomly selects a sample of 50 Freshmen students and asks them how many minutes they exercise per week. The raw data collected by the health psychologist are in this module/week’s Data Set, entitled “Data Set 5”.
Part 1: Confidence Interval
1. Open the Excel file entitled “Data Set 5”. The file contains the following: a) raw data for the sample of 50 Freshmen; b) a results table for Part 1; c) Questions for Part 1; d) a results table for Part 2; and e) Questions for Part 2.
2. Construct a 95% Confidence Interval of the population mean of minutes exercised per week.
a. First, fill in cells with information given in the research question above (N and sigma). (4 pts)
b. In the appropriate cell in the table, compute the sample mean using the raw data given in column A. (Use the AVERAGE function.) (4 pts)
c. Determine the alpha level for this problem and type it in the appropriate cell. (4 pts)
d. As seen in this module/week’s presentation, use the CONFIDENCE function to compute the 95% confidence interval in the appropriate cell in the table. (4 pts)
e. Again as seen in the presentation, compute the lower and upper limits of the confidence interval in the appropriate cells.(4 pts)
3. Answer all five questions beneath the first table. Type answers directly into the Excel file as indicated. (Questions = 3 points each for total of 15 pts.)
Part 2: Hypothesis Test
1. State the null and alternative (research) hypothesis in symbolic form. The hypothesis should be written based on the following information from the research situation: “The health psychologist in question is particularly interested in the myth of the ‘Freshmen 15.’ This myth claims that most freshmen gain weight during the first year of college, mostly due to bad eating habits and lack of exercise and sleep. He wonders if the Freshmen on his campus actually exercise less than the general population of college students (which has a μ = 100 and σ = 25).” (Remember that your hypothesis should include evaluators such as =, <, > or a combination of these.) (2 pts)
2. Is your hypothesis directional or non-directional? Read the wording again in question 1 if you are unsure. The evaluators (=, <, >, etc.) you used in stating the hypotheses in question 1. above should also give you a clue. Fill in the cell with either “one-tailed” or “two-tailed” based on whether the alternative hypothesis is directional or not. Also, if you fill in “one-tailed”, answer the question to the right of the table concerning the direction of the tail. This decision will help you determine the critical values of your test statistics later, so think carefully! (2 pts)
3. Fill in the cells for N, μ, and σ which are already known. These will be used in formulas as shown in this week’s presentation. (2 pts)
4. In the appropriate cell in the table, compute the Standard Error of the Mean (σM) using the steps shown in this week’s presentation. (2 pts)
5. Fill in the sample mean (M), again using the AVERAGE function. (2 pts)
6. We are going to test our hypothesis at the .05 level of significance. Enter the alpha value in the appropriate cell. (2 pts)
7. Find the critical Z value for our test, based on the alpha level, using the NORMSINV function as shown in this module/week’s presentation. Remember to consider the direction(s) of your hypothesis when computing this Z value! (2 pts)
8. Compute the sample Z score using the steps gone over in this module/week’s presentation. (2 pts)
9. Fill in the critical p-value based on your alpha level. (2 pts)
10. Compute your sample’s p-value (based on your sample’s Z score) by using the NORMSDIST function as shown in this week’s presentation. (2 pts)
11. Answer all five questions underneath the second table directly in Data Set 5, after each question as indicated. (Questions = 3 points each for total of 15 pts.)
We do not have access to "Data Set 5."
Besides, we do not do your homework for you. Although it might take more effort to do the work on your own, you will profit more from your effort. We will be happy to evaluate your work though.
. State the null and alternative (research) hypothesis in symbolic form. The hypothesis should be written based on the following information from the research situation: “The health psychologist in question is particularly interested in the myth of the ‘Freshmen 15.’ This myth claims that most freshmen gain weight during the first year of college, mostly due to bad eating habits and lack of exercise and sleep. He wonders if the Freshmen on his campus actually exercise less than the general population of college students (which has a μ = 100 and σ = 25).” (Remember that your hypothesis should include evaluators such as =, <, > or a combination of these.) (2 pts)
Part 1: Confidence Interval
To construct a 95% Confidence Interval of the population mean of minutes exercised per week, follow these steps:
1. Open the Excel file entitled "Data Set 5" and locate the raw data for the sample of 50 Freshmen in column A.
2. In the table, fill in the given information: N (sample size) and sigma (population standard deviation). In this case, N = 50 and sigma = 25.
3. Compute the sample mean using the raw data given in column A. To do this, use the AVERAGE function in Excel. Enter the formula "=AVERAGE(A1:A50)" in the appropriate cell in the table.
4. Determine the alpha level for this problem. In this case, the alpha level is 0.05 since we are constructing a 95% confidence interval.
5. Use the CONFIDENCE function in Excel to compute the 95% confidence interval in the appropriate cell in the table. The syntax for this function is "=CONFIDENCE(alpha, standard_dev, n)". Enter the formula "=CONFIDENCE(0.05, sigma, N)" in the appropriate cell.
6. Compute the lower and upper limits of the confidence interval. The lower limit is calculated by subtracting the confidence interval value from the sample mean, and the upper limit is calculated by adding the confidence interval value to the sample mean. Enter the formulas "=sample_mean - confidence_interval" and "=sample_mean + confidence_interval" in the appropriate cells.
3. Answer the five questions beneath the first table in the Excel file. These questions are regarding the interpretation of the confidence interval. Type your answers directly into the Excel file as indicated.
Part 2: Hypothesis Test
To conduct a hypothesis test, follow these steps:
1. State the null and alternative (research) hypothesis in symbolic form. The null hypothesis (H0) states that there is no difference between the mean minutes of exercise per week for Freshmen and the general population mean (μ = 100), while the alternative hypothesis (Ha) states that Freshmen exercise less than the general population mean (μ < 100).
2. Based on the wording of the research situation and the evaluators used in the hypotheses, it is clear that the alternative hypothesis is directional. Fill in the cell with "one-tailed" to indicate this. Also, answer the question concerning the direction of the tail, which is "less than" in this case.
3. Fill in the cells for N (sample size), μ (population mean), and σ (population standard deviation) with the given information: N = 50, μ = 100, σ = 25.
4. Compute the Standard Error of the Mean (σM) in the appropriate cell using the formula "=sigma / sqrt(N)".
5. Calculate the sample mean (M) using the AVERAGE function in Excel. Enter the formula "=AVERAGE(A1:A50)" in the appropriate cell.
6. Enter the alpha value (0.05) in the appropriate cell. This is the level of significance for the test.
7. Find the critical Z value for the test based on the alpha level using the NORMSINV function in Excel. The formula is "=NORMSINV(alpha)". Enter the formula "=NORMSINV(0.05)" in the appropriate cell. Consider the direction of your hypothesis when computing this Z value.
8. Compute the sample Z score using the formula "= (sample_mean - population_mean) / (sigma / sqrt(N))".
9. Fill in the critical p-value based on your alpha level. This value can be obtained from a Z-table or by using the NORMSDIST function in Excel. The formula to calculate the critical p-value is "=2 * NORMSDIST(-abs(critical_Z))" for a one-tailed test. Enter the formula in the appropriate cell.
10. Compute your sample's p-value based on your sample's Z score using the NORMSDIST function in Excel. The formula is "=2 * NORMSDIST(-abs(sample_Z))" for a one-tailed test. Enter the formula in the appropriate cell.
11. Answer the five questions underneath the second table in the Excel file. These questions are regarding the interpretation of the hypothesis test results. Type your answers directly into the Excel file as indicated.