Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information. x 67 64 75 86 73 73 y 44 41 48 51 44 51 (a) Verify that Σx = 438, Σy = 279, Σx2 = 32264, Σy2 = 13059, Σxy = 20493, and r ≈ 0.800. Σx Correct: Your answer is correct. Σy Correct: Your answer is correct. Σx2 Correct: Your answer is correct. Σy2 Correct: Your answer is correct. Σxy Correct: Your answer is correct. r Correct: Your answer is correct. (b) Use a 5% level of significance to test the claim that ρ > 0. (Round your answers to two decimal places.) t Correct: Your answer is correct. critical t Incorrect: Your answer is incorrect. Conclusion Reject the null hypothesis, there is sufficient evidence that ρ > 0. Reject the null hypothesis, there is insufficient evidence that ρ > 0. Fail to reject the null hypothesis, there is insufficient evidence that ρ > 0. Fail to reject the null hypothesis, there is sufficient evidence that ρ > 0. (c) Verify that Se ≈ 2.7729, a ≈ 14.783, b ≈ 0.4345, and x ≈ 73.000. Se Correct: Your answer is correct. a Correct: Your answer is correct. b Correct: Your answer is correct. x Correct: Your answer is correct. (d) Find the predicted percentage y hat of successful field goals for a player with x = 71% successful free throws. (Round your answer to two decimal places.) % (e) Find a 90% confidence interval for y when x = 71. (Round your answers to one decimal place.) lower limit % upper limit % (f) Use a 5% level of significance to test the claim that β > 0. (Round your answers to two decimal places.) t critical t Conclusion Reject the null hypothesis, there is sufficient evidence that β > 0. Reject the null hypothesis, there is insufficient evidence that β > 0. Fail to reject the null hypothesis, there is insufficient evidence that β > 0. Fail to reject the null hypothesis, there is sufficient evidence that β > 0. (g) Find a 90% confidence interval for β. (Round your answers to three decimal places.) lower limit upper limit Interpret its meaning. For every percentage increase in successful free throws, the percentage of successful field goals increases by an amount that falls outside the confidence interval. For every percentage increase in successful free throws, the percentage of successful field goals increases by an amount that falls within the confidence interval. For every percentage increase in successful free throws, the percentage of successful field goals decreases by an amount that falls outside the confidence interval. For every percentage increase in successful free throws, the percentage of successful field goals decreases by an amount that falls within the confidence interval.

The percentage of people not covered by health care insurance was 15.8%. A congressional committee has been charged with conducting a sample survey to obtain more current information.

1. What sample size would you recommend if the committee's goal is to estimate the current proportion of individuals without health care insurance with a margin of error of 0.03? Use a 95% confidence level.
2. Repeat part (a) using a 99% confidence level

An insurance company is interested in estimating the percentage of auto accidents that involve teenage drivers. Suppose the percentage of auto accidents that involved teenage drivers last year was 15%. The company wants to know if the percentage has changed this year. They check the records of 600 accidents selected at random from this year and note that teenagers were at the wheel in 60 of them.

(a) Create a 90% confidence interval for the percentage of all auto accidents that involve teenager drivers this year. Make sure to state any necessary conditions. [3 marks]

(b) Explain what 90% confidence means in this context. [1 mark]

(c) Suppose the insurance company wants to re-estimate the proportion of teenagers who were at the wheel. This time they want the estimate to be correct within 0.02 with 95% confidence. What is the maximum tolerable margin of error proposed by the company? How large a sample would be required? [2 marks]

The home run percentage is the number of home runs per 100 times at bat. A random sample of 43 professional baseball players gave the following data for home run percentages. 1.6 2.4 1.2 6.6 2.3 0.0 1.8 2.5 6.5 1.8 2.7 2.0 1.9 1.3 2.7 1.7 1.3 2.1 2.8 1.4 3.8 2.1 3.4 1.3 1.5 2.9 2.6 0.0 4.1 2.9 1.9 2.4 0.0 1.8 3.1 3.8 3.2 1.6 4.2 0.0 1.2 1.8 2.4 (a) Use a calculator with mean and standard deviation keys to find x bar and s (in percentages). (For each answer, enter a number. Round your answers to two decimal places.) x bar = x bar = % s = % (b) Compute a 90% confidence interval (in percentages) for the population mean μ of home run percentages for all professional baseball players. Hint: If you use the Student's t distribution table, be sure to use the closest d.f. that is smaller. (For each answer, enter a number. Round your answers to two decimal places.) lower limit % upper limit % (c) Compute a 99% confidence interval (in percentages) for the population mean μ of home run percentages for all professional baseball players. (For each answer, enter a number. Round your answers to two decimal places.) lower limit % upper limit % (d) The home run percentages for three professional players are below. Player A, 2.5 Player B, 2.3 Player C, 3.8 Examine your confidence intervals and describe how the home run percentages for these players compare to the population average. We can say Player A falls close to the average, Player B is above average, and Player C is below average. We can say Player A falls close to the average, Player B is below average, and Player C is above average. We can say Player A and Player B fall close to the average, while Player C is above average. We can say Player A and Player B fall close to the average, while Player C is below average. (e) In previous problems, we assumed the x distribution was normal or approximately normal. Do we need to make such an assumption in this problem? Why or why not? Hint: Use the central limit theorem. Yes. According to the central limit theorem, when n ≥ 30, the x bar distribution is approximately normal. Yes. According to the central limit theorem, when n ≤ 30, the x bar distribution is approximately normal. No. According to the central limit theorem, when n ≥ 30, the x bar distribution is approximately normal. No. According to the central limit theorem, when n ≤ 30, the x bar distribution is approximately normal.

What is the MAPE (mean absolute percentage error) and when would I use it for a model?

The home run percentage is the number of home runs per 100 times at bat. A random sample of 43 professional baseball players gave the following data for home run percentages.

(a) Use a calculator with mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)

(b) Compute a 90% confidence interval for the population mean μ of home run percentages for all professional baseball players. Hint: If you use the Student's t distribution table, be sure to use the closest d.f. that is smaller. (Round your answers to two decimal places.)

(c) Compute a 99% confidence interval for the population mean μ of home run percentages for all professional baseball players. (Round your answers to two decimal places.)

Assume the following sales data for a company:

If 2017 is the base year, what is the percentage increase in sales from 2017 to 2018?

Determine quantities of reagents used, theoretical yield of products and percentage yield of products.

The Centers for Disease Control reported the percentage of people 18 years of age and older who smoke (CDC website, December 14, 2014). Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke of .32. a. How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of .02 (to the nearest whole number)? Use 95% confidence. b. Assume that the study uses your sample size recommendation in part (a) and finds 520 smokers. What is the point estimate of the proportion of smokers in the population (to 4 decimals)? c. What is the 95% confidence interval for the proportion of smokers in the population (to 4 decimals)? ( , )