Attached is the assessment
Math 15 Math 15 Assessment # 4 1. A travel association says that the daily lodging cost for a family traveling in California is the same as in Florida. The daily lodging cost for 35 families traveling in California is $136 and the standard deviation is $25. The daily lodging cost for 35 families traveling in Florida is $140 and the standard deviation is $30. At is there enough evidence to reject the travel association’s claim? a) b) c) d) e) 2. A study was conducted to see if an herbal supplement helped to reduce weight. After 12 weeks, 42 subjects using the herbal supplement and a high- fiber, low-calorie diet had a mean weight loss of 3.2 kg. And a standard deviation of 3.3 kg. During the same period, 42 subjects using a placebo and a high-fiber, low-calorie diet had a mean weight loss of 4.1 kg. And a standard deviation of 3.9 kg. Part 1. At , test the claim that the mean weight loss for the group using the herbal supplement is greater than the mean weight loss for the group using the placebo. a) b) c) d) e) Part 2. Construct a 95% C. I. for mean differences. Part 3. Compare a) and b). Explain why you fail to reject the null hypothesis if the confidence interval contains 0. 3. The table below shows the gas mileage (in miles per gallon) of 8 cars with and without using a fuel additive. At , is there enough evidence to conclude that the fuel additive improved gas mileage? Car 1 2 3 4 5 6 7 8 without 35.8 37.7 39.4 36.8 36.6 33.7 38.4 37.3 with 36.2 39.8 40.1 39.3 36.9 34.5 38.8 39.1 3a) b) c) d) e) 4. In a random survey of 1500 adults in California and 1000 adults in Oregon, is found that the percent who are smokers are 18.4% and 20.7% respectively. At , is there enough evidence to conclude that the proportion of adults who are smokers is lower in California than in Oregon? a) b) c) d) e) 5. In crash tests at 5 mph, the mean bumper repair cost for 14 randomly selected small cars is $574 with a standard deviation 0f $185. In similar tests of 23 randomly selected midsize cars, the mean bumper repair cost is $734 with a standard deviation of $268. At , test the claim that the mean bumper repair cost is less for small cars than it is for midsize cars. a) b) c) d) e) 6. A market manager conducted a study to determine whether there is a linear relationship between money spent and advertising and company sales. Determine if there is a linear correlation or not. Use Advertising Expenses 2.4 1.6 2.0 2.6 1.4 1.6 2.0 2.2 Company Sales 225 184 220 240 180 184 186 215 (Each one times $1000). Find: a) The correlation coefficient r. b) In your opinion, is there a strong linear correlation? Weak linear correlation? Explain. b) What is the centroid? d) Find the regression line equation for the advertising expenditures and company sales data. e) Use this equation to predict the expected company sales when 1.5 thousand dollars have been used in advertising. Math 15 Math 15 Assessment # 4 1. A travel association says that the daily lodging cost for a family traveling in California is the same as in Florida. The daily lodging cost for 35 families traveling in California is $136 and the standard deviation is $25. The daily lodging cost for 35 families traveling in Florida is $140 and the standard deviation is $30. At is there enough evidence to reject the travel association’s claim? a) b) c) d) e) 2. A study was conducted to see if an herbal supplement helped to reduce weight. After 12 weeks, 42 subjects using the herbal supplement and a high- fiber, low-calorie diet had a mean weight loss of 3.2 kg. And a standard deviation of 3.3 kg. During the same period, 42 subjects using a placebo and a high-fiber, low-calorie diet had a mean weight loss of 4.1 kg. And a standard deviation of 3.9 kg. Part 1. At , test the claim that the mean weight loss for the group using the herbal supplement is greater than the mean weight loss for the group using the placebo. a) b) c) d) e) Part 2. Construct a 95% C. I. for mean differences. Part 3. Compare a) and b). Explain why you fail to reject the null hypothesis if the confidence interval contains 0. 3. The table below shows the gas mileage (in miles per gallon) of 8 cars with and without using a fuel additive. At , is there enough evidence to conclude that the fuel additive improved gas mileage? Car 1 2 3 4 5 6 7 8 without 35.8 37.7 39.4 36.8 36.6 33.7 38.4 37.3 with 36.2 39.8 40.1 39.3 36.9 34.5 38.8 39.1 3a) b) c) d) e) 4. In a random survey of 1500 adults in California and 1000 adults in Oregon, is found that the percent who are smokers are 18.4% and 20.7% respectively. At , is there enough evidence to conclude that the proportion of adults who are smokers is lower in California than in Oregon? a) b) c) d) e) 5. In crash tests at 5 mph, the mean bumper repair cost for 14 randomly selected small cars is $574 with a standard deviation 0f $185. In similar tests of 23 randomly selected midsize cars, the mean bumper repair cost is $734 with a standard deviation of $268. At , test the claim that the mean bumper repair cost is less for small cars than it is for midsize cars. a) b) c) d) e) 6. A market manager conducted a study to determine whether there is a linear relationship between money spent and advertising and company sales. Determine if there is a linear correlation or not. Use Advertising Expenses 2.4 1.6 2.0 2.6 1.4 1.6 2.0 2.2 Company Sales 225 184 220 240 180 184 186 215 (Each one times $1000). Find: a) The correlation coefficient r. b) In your opinion, is there a strong linear correlation? Weak linear correlation? Explain. b) What is the centroid? d) Find the regression