Statistics Exam
Chelsea29440
UIW_SPS_MSC_3370_SUI20_FINAL_EXAMMcCrayChelsea.xlsxCHAPTER 8 - 20 POINTS
| 1. Of 1,496 randomly selected UIW SPS military affiliated students, 539 are Air Force, 571 are Army, 5 are Coast Guard, 35 are Marine Corp, 183 are Navy, 162 have no branch listed, and 1 has more than one military coding. The students were then listed as preferred major according to branch of service. We have determined that around 384 Army students prefer a Bachelor of Science in Business Administration degree. UIW wants to know the population proportion of Army students who prefer a Bachelor of Science in Business Administration. |
| a. What is x = |
| b. What is n = |
| c. What is p' = |
| d. Define the random variable X in words. |
| e. Define the random variable P' in words. |
| f. Which distribution will you use for this problem? |
| g. State the distribution |
| h. Construct a 90% confidence interval for the population proportion. |
| i. Calculate the error bound. |
| j. Sketch the graph (manually or electronically) |
CHAPTER 9 - 20 POINTS
| 2. Health experts claim that it takes around 14 days for a person to show symptoms of COVID-19 after exposure and a standard deviation of 2 days. A survey was presented to 30 people who have been sick of COVID-19, and the mean number of days after exposure was 15 days with a standard deviation of 3 days. Using alpha = 0.05, is the data highly consistent with the claim? |
| a. What is Ho? |
| b. What is Ha? |
| c. State the distribution to use for the test |
| d. Is this a right-tailed, left-tailed or two-tailed test? |
| e. What is the test statistic? |
| f. What is the p-value? |
| g. What is your decision? |
| h. Reason for decision: |
| i. Conclusion: |
| j. Calculate the confidence interval: |
CHAPTER 10 - 20 POINTS
| 3. You are given the table below. A nutritionist believes that patients with thyroid problem gain more weight by eating carbs than calories. 30 patients have been tested. The distribution is known to be normal. Test at the 2% level of significance. | ||
| Sample Mean | Pop Stand Deviation | |
| Carbs | 20 | 9 |
| Calories | 25 | 11 |
| a. What is Ho? | ||
| b. What is Ha? | ||
| c. Is this a right-tailed, a left-tailed or a two-tailed test? | ||
| d. What is the test statistic? | ||
| e. What is the p-value? | ||
| f. What is alpha? | ||
| g. What is your decision? | ||
| h. Reason for decision: | ||
| i. Conclusion: | ||
| j. Calculate the confidence interval | ||
CHAPTER 11 - 20 POINTS
| 4. I have reviewed the midterm grades for this term, and I am trying to predict how well the Summer I class will do in the final exam. The frequency values are your actual grades: | ||
| Grade | Frequency (Observed) | Expected |
| Greater than A | 5 | 3 |
| A | 10 | 8 |
| B | 5 | 8 |
| C | 1 | 2 |
| F | 1 | 1 |
| a. What is the degrees of freedom? | ||
| b. State Ho and Ha | ||
| c. What is the chi square (χ2) test statistic? | ||
| d. What is the p-value? | ||
| e. At the 5% significance level, what is your decision and the reason for the decision? | ||
| f. What is the conclusion? | ||
CHAPTER 12 - 20 POINTS
| 5. You are given the following table. | ||||
| X | Y | |||
| 1,000 | 500 | |||
| 3,000 | 400 | |||
| 7,000 | 750 | |||
| 12,000 | 1,000 | |||
| 15,500 | 1,200 | |||
| 17,000 | 1,000 | |||
| 17,500 | 1,800 | |||
| 21,000 | 2000 | |||
| 22,800 | 2,200 | |||
| 23,000 | 3,000 | |||
| a. Decide which variable should be the independent variable and which should be the dependent variable. | ||||
| b. Draw a scatter plot of the data. | ||||
| c. Does it appear from inspection that there is a relationship between the variables? Why or why not? | ||||
| d. Calculate the least-squares line. Put the equation in the form of: ŷ = a + bx. | ||||
| e. Find the correlation coefficient. Is it significant? | ||||
| f. Find estimated total values for column Y for 16,000, 24,000, and 36,000 | ||||
| 16,000= | 24,000= | 36,000= | ||
| g. Does it appear that a line is the best way to fit the data? Why or why not? | ||||
| h. Are there any outliers in the data? | ||||
| i. Based on these results, what would be the probate fees and taxes for an estate that does not have any assets? | ||||
| j. What is the slope of the least-squares (best-fit) line? Interpret the slope. | ||||
Extra Credit - 10 points
| You are given the following ANOVA Single factor output. | Anova: Single Factor | ||||||||||||||||
| a. What is the Sum of Squares Factor? | Groups | Count | Sum | Average | Variance | ||||||||||||
| b. What is the Sum of Squares Error? | 1 | 3.00 | 166.00 | 55.33 | 156.33 | ||||||||||||
| c. What is the df for the numerator? | 2 | 3.00 | 213.00 | 71.00 | 444.00 | ||||||||||||
| d. What is the df for the denominator? | 3 | 3.00 | 197.00 | 65.67 | 114.33 | ||||||||||||
| e. What is the Mean Square Factor? | 4 | 3.00 | 219.00 | 73.00 | 508.00 | ||||||||||||
| f. What is the Mean Square Error? | 5 | 3.00 | 235.00 | 78.33 | 786.33 | ||||||||||||
| g. What is the F statistic? | 6 | 3.00 | 160.00 | 53.33 | 92.33 | ||||||||||||
| h. What is the p-value? | 7 | 3.00 | 256.00 | 85.33 | 10.33 | ||||||||||||
| i. What is the F critical? | |||||||||||||||||
| j. At 1% significance level, would you reject or accept an hypothesis based on the alpha and p-value and why? | 8 | 3.00 | 206.00 | 68.67 | 574.33 | ||||||||||||
| 9 | 3.00 | 210.00 | 70.00 | 333.00 | |||||||||||||
| 10 | 3.00 | 290.00 | 96.67 | 2.33 | |||||||||||||
| ANOVA | |||||||||||||||||
| Source of Variation | SS | df | MS | F | P-value | F crit | |||||||||||
| Between Groups | 4527.20 | 9.00 | 503.02 | 1.66 | 0.16 | 1.96 | |||||||||||
| Within Groups | 6042.67 | 20.00 | 302.13 | ||||||||||||||
| Total | 10569.87 | 29.00 | |||||||||||||||
