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. Suppose the following data show the weight and price for 18 SA helmets. Weight (oz) Price ($) 64 248 64 278 64 200 64 200 58 300 47 700 49 900 59 340 66 199 58 299 58 299 52 479 52 479 63 359 62 369 54 549 63 250 63 280(a) Develop a scatter diagram with weight as the independent variable. 1000 1000 - 1000 1000 800 800 800 800 . . 600- 600- 600 - 600 Price ($) Price ($) Price ($) Price ($) 400 400+ 400 400 . . . . 200 200 - 200- 200+ 50 55 60 65 70 50 55 60 65 70 50 55 60 65 70 50 55 60 65 70 Weight (oZ) Weight (oZ) Weight (oZ) Weight (oZ) (b) Does there appear to be any relationship between these two variables? O There appears to be a positive linear relationship between weight (oz) and price ($). There appears to be no noticeable relationship between weight (oz) and price ($). There appears to be a negative linear relationship between weight (oz) and price ($). (c) Develop the estimated regression equation that could be used to predict the price ($) given the weight (oz). (Round your value for the y-intercept to the nearest integer and your value for the slope to two decimal places.) = 2042.47 - 28.34x(d) Test for the significance of the relationship at the 0.05 level of significance. (Use the F test.) State the null and alternative hypotheses. OH: Bo = 0 OH : B 1 =0 Ha : B 1 = 0 OH: BO = 0 Ha: Bo = 0 OH : B, 20 OH: B, =0 Ha: B , = 0 Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. O Do not reject Ho. We conclude that the relationship between weight (oz) and price ($) is significant. O Reject Ho. We cannot conclude that the relationship between weight (oz) and price ($) is significant. O Do not reject Ho. We cannot conclude that the relationship between weight (oz) and price ($) is significant. O Reject Ho. We conclude that the relationship between weight (oz) and price ($) is significant. (e) Did the estimated regression equation provide a good fit? Explain. (Round your answer to three decimal places.) Since re = is ---Select--- v, the estimated regression equation |---Select--- a good fit