Automobile racing, high-performance driving schools, and driver education programs run by automobile clubs continue to grow in popularity. All these activities require the participant to wear a helmet that is certified by the Snell Memorial Foundation, a not-for-profit organization dedicated to research, education, testing, and development of helmet safety standards. Snell “SA” (Sports Application)-rated professional helmets are designed for auto racing and provide extreme impact resistance and high fire protection. One of the key factors in selecting a helmet is weight, since lower weight helmets tend to place less stress on the neck. Consider the following data showing the weight and price for 18 SA helmets.
Weight (oz) | Price ($) |
64 | 248 |
64 | 278 |
64 | 200 |
64 | 200 |
58 | 300 |
47 | 700 |
49 | 900 |
59 | 340 |
66 | 199 |
58 | 299 |
58 | 299 |
52 | 479 |
52 | 479 |
63 | 369 |
62 | 369 |
54 | 559 |
63 | 250 |
63 | 280 |
- a. Develop a
scatter diagram with weight as the independent variable. - b. Does there appear to be any relationship between these two variables?
- c. Develop the estimated regression equation that could be used to predict the price given the weight.
- d. Test for the significance of the relationship at the .05 level of significance.
- e. Did the estimated regression equation provide a good fit? Explain.
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Chapter 14 Solutions
STATISTICS F/BUSINESS+ECONOMICS-TEXT
- Cholesterol Cholesterol in human blood is necessary, but too much can lead to health problems. There are three main types of cholesterol: HDL (high-density lipoproteins), LDL (low-density lipoproteins), and VLDL (very low-density lipoproteins). HDL is considered “good” cholesterol; LDL and VLDL are considered “bad” cholesterol. A standard fasting cholesterol blood test measures total cholesterol, HDL cholesterol, and triglycerides. These numbers are used to estimate LDL and VLDL, which are difficult to measure directly. Your doctor recommends that your combined LDL/VLDL cholesterol level be less than 130 milligrams per deciliter, your HDL cholesterol level be at least 60 milligrams per deciliter, and your total cholesterol level be no more than 200 milligrams per deciliter. (a) Write a system of linear inequalities for the recommended cholesterol levels. Let x represent the HDL cholesterol level, and let y represent the combined LDL VLDL cholesterol level. (b) Graph the system of inequalities from part (a). Label any vertices of the solution region. (c) Is the following set of cholesterol levels within the recommendations? Explain. LDL/VLDL: 120 milligrams per deciliter HDL: 90 milligrams per deciliter Total: 210 milligrams per deciliter (d) Give an example of cholesterol levels in which the LDL/VLDL cholesterol level is too high but the HDL cholesterol level is acceptable. (e) Another recommendation is that the ratio of total cholesterol to HDL cholesterol be less than 4 (that is, less than 4 to 1). Identify a point in the solution region from part (b) that meets this recommendation, and explain why it meets the recommendation.arrow_forwardA psychologist develops an intervention designed to reduce test anxiety associated with taking the SAT. The psychologist claims that reduced test anxiety will lead to higher scores on the quantitative section of the SAT. Because she believes all students experience some degree of anxiety related to the SAT, she further claims her intervention should work for all students, not just those who report abnormal levels of test anxiety. She randomly selects 30 high school juniors, and with the consent of their parents, delivers her intervention. Subsequently, these students take the SAT, and she collects their scores. The quantitative section of the SAT has a mean of 500 and a standard deviation of 100 in the general population, and scores are normally distributed. a. What type of test should be used to analyze her data? i. Z-test ii. Single-sample t-test iii. Independent-measures t-test iv. Repeated-measures t-test b. What would the hypotheses be?arrow_forwardIn laparoscopic surgery, a video camera and several thin instruments are inserted into the patient's abdominal cavity. The surgeon uses the image from the video camera positioned inside the patient's body to perform the procedure by manipulating the instruments that have been inserted. The Top Gun Laparoscopic Skills and Suturing Program was developed to help surgeons develop the skill set necessary for laparoscopic surgery. Because of the similarity in many of the skills involved in video games and laparoscopic surgery, it was hypothesized that surgeons with greater prior video game experience might acquire the skills required in laparoscopic surgery more easily. Thirty‑three surgeons participated in the study and were classified into three categories, never used, under three hours, and three or more hours—depending on the daily number of hours they played video games at the height of their video game use. They also performed Top Gun drills and received a score based on the time to…arrow_forward
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