Q 1 - A nation job placement company is interested in developing a model that might be used to explain the variation in starting salaries for college graduates based on the college GPA. through a random sample of the clients with which this company has been associated. The following data were collected |GPA Starting Salary 3.20 $35,000 3.40 $29,500 2.90 $30,000 3.60 $36,400 2.80 $31,500 2.50 $29,000 3.00 $33,200 3.60 $37,600 2.90 $32,000 3.50 $36,000 Based on this sample information: (a). Calculate the correlation coefficient between these two variables. (b). Conduct a test of hypothesis to determine if there exists a correlation between the two variables in the population. Use a significance level of 0.05. determine the least squares regression model. Also, develop a scatter plot of the data and locate the regression line on the scatter plot. (c).
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- Tourism is extremely important to the economy of Florida. Hotel occupancy is an often-reported measure of visitor volume and visitor activity (Orlando Sentinel, May 19, 2018). Hotel occupancy data for February in two consecutive years are as follows. Current Year Previous Year Occupied Rooms 1,435 1,501 Total Rooms 1,750 1,900 a. Formulate the hypothesis test that can be used to determine whether there has been an increase in the proportion of rooms occupied over the one-year period. Let pi = population proportion of rooms occupied for current year P2 = population proportion of rooms occupied for previous year Ho : P1 – P2 less than or equal to 0 Ha : Pi – P2 greater than 0 b. What is the estimated proportion of hotel rooms occupied each year (to 2 decimals)? Current year Previous Year c. Conduct a hypothesis test. What is the p-value (to 4 decimals)? Use Table 1 from Appendix B. p-valueHow productive are U.S. workers? One way to answer this question is to study annual profits per employee. A random sample of companies in computers (I), aerospace (II), heavy equipment (III), and broadcasting (IV) gave the following data regarding annual profits per employee (units in thousands of dollars). I II III IV 27.9 13.5 22.2 17.9 23.2 9.6 20.5 16.4 14.7 11.1 7.7 14.5 8.3 8.9 12.7 15.9 11.8 6.5 7.7 10.6 19.1 9.5 What are the degrees of freedom? (numerator) (denominator)(c) Find the P-value of the sample test statistic. P-value > 0.100 0.050 < P-value < 0.100 0.025 < P-value < 0.050 0.010 < P-value < 0.025 0.001 < P-value < 0.010 P-value < 0.001 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Since the P-value is greater than the level of significance at α = 0.05, we do not reject H0. Since the P-value is less than or equal to the level of significance at α = 0.05, we…C. Predicting Student Success STA believes there is a relationship between high school GPA (on a four-point scale) and college performance (as measured by GPA on a four-point scale). The following data were randomly selected from among students enrolling Fall 2020. HS GPA STA GPA Student 1 HS GPA STAGPA Student 21 2.9 2.5 3.6 3.4 2 3.4 3.1 3.0 22 3.4 4.0 1.7 3 3.1 23 2.9 2.9 1.7 3.0 3.2 3.3 4 24 3.5 5 3.4 25 4.0 3.6 3.6 3.0 26 3.6 3.8 3.2 3.9 3.1 27 8. 4.0 3.9 28 3.4 3.6 3.2 9. 3.0 3.0 29 3.7 10 2.9 2.0 3.0 30 4.0 3.3 4.0 3.2 11 3.3 31 12 3.6 3.8 32 3.7 3.2 3.4 3.0 13 3.7 3.9 33 14 3.8 3.6 34 2.5 2.0 15 2.5 2.5 35 2.9 2.9 3.7 2.2 16 2.9 2.5 36 3.8 17 2.8 2.1 37 2.9 18 3.8 1.7 3.5 38 3.6 3.5 3.6 19 3.7 39 3.6 20 3.9 3.0 40 3.1 3.6 How confident should St. Mary's be regarding the accuracy of their predictions? Why?
- C. Predicting Student Success STA believes there is a relationship between high school GPA (on a four-point scale) and college performance (as measured by GPA on a four-point scale). The following data were randomly selected from among students enrolling Fall 2020. HS GPA STA GPA Student 1 HS GPA STAGPA Student 21 2.9 2.5 3.6 3.4 2 3.4 3.1 3.0 22 3.4 4.0 1.7 3 3.1 23 2.9 2.9 1.7 3.0 3.2 3.3 4 24 3.5 5 3.4 25 4.0 3.6 3.6 3.0 26 3.6 3.8 3.2 3.9 3.1 27 8. 4.0 3.9 28 3.4 3.6 3.2 9. 3.0 3.0 29 3.7 10 2.9 2.0 3.0 30 4.0 3.3 4.0 3.2 11 3.3 31 12 3.6 3.8 32 3.7 3.2 3.4 3.0 13 3.7 3.9 33 14 3.8 3.6 34 2.5 2.0 15 2.5 2.5 35 2.9 2.9 3.7 2.2 16 2.9 2.5 36 3.8 17 2.8 2.1 37 2.9 18 3.8 1.7 3.5 38 3.6 3.5 3.6 19 3.7 39 3.6 20 3.9 3.0 40 3.1 3.6 Is high school GPA a good predictor of STA GPA? Why? What STA GPA would you predict for a student with a high school GPA of 3.75? How you would make the prediction.The owner of Maumee Ford-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year. Car Age (years) Selling Price ($000) 1 11 12.1 2 8 10.5 3 14 5.7 4 17 4.9 5 9 5.0 6 8 13.4 7 10 10.5 8 14 9.0 9 13 9.0 10 17 4.5 11 6 12.5 12 6 11.5 Click here for the Excel Data Filea. Determine the regression equation. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) a= b= Estimate the selling price of an 7-year-old car (in $000). (Round your answer to 3 decimal places.) Interpret the regression equation (in dollars). (Round your answer to the nearest dollar amount.)4. Straight As now, healthy later A study by Pamela Herd of the University of Wisconsin-Madison found a link between high-school grades and health. Analyzing data from the Wisconsin Longitudinal Study, which has tracked the lives of thousands of Wisconsin high-school graduates from the class of 1957, Herd found that students with higher grade-point averages were more likely to say they were in excellent or very good health in their early 60s. Does this mean people will live healthier lives if they increase their GPA? Explain.47
- When an audit must be conducted that involves a tedious examination of a large inventory, the audit may be very costly and time consuming if each item in the inventory must be examined. In such situations, the auditor frequently obtains a random sample of items from the complete inventory and uses the results of an audit of the sampled items to check the validity of the company's financial statement. A large company’s financial statement claims an inventory that averages $600 per item. The following data are the auditor’s assessment of a random sample of 75 items from the company’s inventory. The values resulting from the audit are rounded to the nearest dollar. Estimate the mean value of an item in the inventory using a 95% confidence interval. Is there substantial evidence (a 5 .01) that the mean value of an item in the inventory is less than $600? What is the target population for the above inferences? Would normal distribution–based procedures be appropriate for answering the…QSR Magazine published the latest results of its annual quick serve resturant drive-thru study. One aspect of the study examined the customer drive-thru wait times for various brands. The drive-thru wait times for random samples of customers at Chick-fil-A, McDonald's, and KFC are given in the table below. Brand Customers drive-thru wait times (in seconds) Chick-fil-A 485 496 489 460 487 477 495 McDonald's 356 362 343 327 369 351 350 KFC 291 269 251 283 286 294 278 (a) Conduct a hypothesis test using a=0.05 to determine whether the mean drive-thru wait times of customers at Chick-fila-A, and KFC are the same. Assume that drive thru wait times for each of these brands reasonably follow a normal distribution. (b) Use the sample data collected in Problem 4 to construct…How do the average weekly incomes of electricians and carpenters compare? A random sample of 17 regions in the United States gave the following information about average weekly income (in dollars). (Reference: U.S. Department of Labor, Bureau of Labor Statistics.) Region 1 2 3 4 5 6 7 8 9 Electricians 464 715 597 464 736 694 744 571 806 Carpenters 542 813 513 476 688 503 789 653 474 Region 10 11 12 13 14 15 16 17 Electricians 592 594 702 579 868 598 597 654 Carpenters 489 647 676 384 817 605 556 505 Does this information indicate a difference (either way) in the average weekly incomes of electricians compared to those of carpenters? Use a 5% level of significance. (a) What is the level of significance? (b) Compute the sample test statistic. (c) Find the P-value of the sample test statistic.
- A statistical program is recommended. Jensen Tire & Auto is in the process of deciding whether to purchase a maintenance contract for its new computer wheel alignment and balancing machine. Managers feel that maintenance expense should be related to usage, and they collected the following information on weekly usage (hours) and annual maintenance expense (in hundreds of dollars). Weekly Usage (hours) Annual Maintenance Expense 13 17.0 10 22.0 20 30.0 28 37.0 32 47.0 17 30.5 24 32.5 31 39.0 40 51.5 38 40.0 (a) Develop the estimated regression equation that could be used to predict the annual maintenance expense (in hundreds of dollars) given the weekly usage (in hours). (Round your numerical values to two decimal places.)team 1 9.11 9.22 9.5 9.62 9.68 9.59 team 2 9.7 9.8 9.8 9.81 9.85 team 3 9.88 9.89 9.9 9.9 9.9 10.01 9.85 team 4 9.91 9.91 9.94 9.95 team 5 9.96 9.96 9.96 9.97 9.98 Select the most diverse data. Is it statistically different at the 90% confidence level? Use the appropriate t-testA hospital has a main campus and three satellite locations. Management wants to reduce waiting time for ER cases. A random sample of 11 ER cases at each location was selected, and the waiting time was measured. (The table of data at the very end may be copied and pasted directly into Excel.) Complete parts (a) through (d) to determine if there is statistical evidence of a difference in the mean waiting times betweeen the four locations. Part 1 a. State the two hypotheses. Choose the correct answer below. A.H0:μ1=μ2=•••=μ4H1:Not allμjare equal (where j=1,2,...,4) B.H0:μ1=μ2=•••=μ4H1:μ1≠μ2≠•••≠μ4 C.H0:μ1=μ2=•••=μ11H1:μ1≠μ2≠•••≠μ11 D.H0:μ1=μ2=•••=μ11H1:Not allμjare equal (wherej=1,2,...,11) b. At the 0.05 level of significance, state the test statistic. (Round to two decimal places to the right of the decimal point as needed.) A.FSTAT = 0.005, from the first row of the ANOVA table B.FSTAT = 4.91, from the first row of the ANOVA table…