GEORGIA PIEDMONT TECHNICAL COLLEGE MATH1127: Introduction to Statistics (Asynchronous (100% Online)) 20337 Chapter 7: Linear Regressi Score: U/ 18 U/ 4 answered Question 1 Listed below are paired data consisting of amounts spent on advertising (in millions of dollars) and the profits (in millions of dollars). Determine if there is a significant positive linear correlation between advertising cost and profit . Use a significance level of 0.05 and round all values to 4 decimal places. Advertising Cost | Profit 3 22 4 20 27 6 31 7 30 8 22 9 34 10 25 Ho: p = 0 Ha: p > 0 Find the Linear Correlation Coefficient Find the p-value p-value = The p-value is O Less than (or equal to) a O Greater than ox IMG_20221129 21....jpg IMG_20221129 21...jpg IMG_20221129_21....jpg 9 Type here to search OF - C gptc.blackboard.com/webapps/blackboard/content/contentWrapper.jsp?content_id# GEORGIA PIEDMONT TECHNICAL COLLEGE MATH1127: Introduction to Statistics (Asynchronous (100% Online)) 20337 ... Chapter 7: Linear Regression The p-value is O Less than (or equal to) a O Greater than a The p-value leads to a decision to O Reject Ho O Do Not Reject Ho O Accept Ho The conclusion is There is insufficient evidence to make a conclusion about the linear correlation between advertising expense and profit. There is a significant linear correlation between advertising expense and profit. There is a significant positive linear correlation between advertising expense and profit. There is a significant negative linear correlation between advertising expense and profit. Hint: Helpful Video on the Linear Regression Line # [+] Helpful Video on Correlation [+] Helpful Video on Hypothesis Tests for Correlation [+] Hints Submit Question IMG_20221129_21....jpg IMG_20221129 21....jpg IMG_20221129_21....jpg Type here to search OBb Cha Bb Chapter 10 X Calendar - x Bb My Grades X Course Her x https://gpt x C a gptc.blackboard.com/webapps/blackboard/content/contentWrapper.jsp?content_id=_184 GEORGIA PIEDMONT TECHNICAL COLLEGE MATH1127: Introduction to Statistics (Asynchronous (100% Online)) 20337 Chapter 7: Linear Regression and Score: U/ 18 / 4 answered Question 2 What is the relationship between the number of minutes per day a woman spends talking on the phone and the woman's weight? The time on the phone and weight for 7 women are shown in the table below. Time 72 77 17 60 10 76 52 Pounds 134 139 105 134 93 159 129 a. Find the correlation coefficient: r = Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho: ? = 0 H1: 2 0 The p-value is: (Round to four decimal places) c. Use a level of significance of a = 0.05 to state the conclusion of the hypothesis test in the context of the study. There is statistically significant evidence to conclude that there is a correlation between the time women spend on the phone and their weight. Thus, the regression line is useful. There is statistically insignificant evidence to conclude that a woman who spends more time on the phone will weigh more than a woman who spends less time on the phone. There is statistically significant evidence to conclude that a woman who spends more time on the phone will weigh more than a woman who spends less time on the phone. There is statistically insignificant evidence to conclude that there is a correlation between the time women spend on the phone and their weight. Thus, the use of the regression line is not appropriate. d. 72 (Round to two decimal places) IMG_20221129_21....jpg - IMG_20221129_21..jpg IMG_20221129_21....jpg Type here to search O at OC * gptc.blackboard.com/webapps/blackboard/content/contentWrapper.jsp?content_id=_ GEORGIA PIEDMONT TECHNICAL COLLEGE MATH1127: Introduction to Statistics (Asynchronous (100% Online)) 20337 ... Chapter 7: Linear Regression a d. 72 (Round to two decimal places) e. Interpret ? : O Given any group of women who all weight the same amount, 89% of all of these women will weigh the predicted amount. O 89% of all women will have the average weight. There is a 89% chance that the regression line will be a good predictor for women's weight based on their time spent on the phone. O There is a large variation in women's weight, but if you only look at women with a fixed weight, this variation on average is reduced by 89%. f. The equation of the linear regression line is: y = x (Please show your answers to two decimal places) g. Use the model to predict the weight of a woman who spends 60 minutes on the phone. Weight = (Please round your answer to the nearest whole number.) h. Interpret the slope of the regression line in the context of the question: For every additional minute women spend on the phone, they tend to weigh on averge 0.74 additional pounds. As x goes up, y goes up. The slope has no practical meaning since you cannot predict a women's weight. i. Interpret the y-intercept in the context of the question: The best prediction for the weight of a woman who does not spend any time talking on the phone is 89 pounds. The y-intercept has no practical meaning for this study. The average woman's weight is predicted to be 89. pounds. O If a woman does not spend any time talking on the phone, then that woman will weigh 89 Type here to search O OBb My Grades X *Course Her X https://gpt x _ Calendar - x Bb Chapter 10 X -> C a gptc.blackboard.com/webapps/blackboard/content/contentWrapper.jsp?content_id GEORGIA PIEDMONT TECHNICAL COLLEGE 8 MATH1127: Introduction to Statistics (Asynchronous (100% Online)) 20337 Chapter 7: Linear Regression Chapter 7: Linear Regression Score: 0/18 0/4 answered Question 3 A biologist looked at the relationship between number of seeds a plant produces and the percent of those seeds that sprout. The results of the survey are shown below. Seeds Produced 47 53 59 51 57 60 62 58 56 Sprout Percent 74.2 56.8 59.4 61.6 58.2 54 59.2 60.8 60.6 a. Find the correlation coefficient: r = Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho: ? = 0 H1: ?v * 0 The p-value is: Round to four decimal places) of the study. c. Use a level of significance of o = 0.05 to state the conclusion of the hypothesis test in the context There is statistically significant evidence to conclude that there is a correlation between the number of seeds that a plant produces and the percent of the seeds that sprout. Thus, the regression line is useful. There is statistically insignificant evidence to conclude that a plant that produces more seeds will have seeds with a lower sprout rate than a plant that produces fewer seeds. There is statistically significant evidence to conclude that a plant that produces more seeds will have seeds with a lower sprout rate than a plant that produces fewer seeds. There is statistically insignificant evidence to conclude that there is a correlation between the number of seeds that a plant produces and the percent of the seeds that sprout. Thus, the use d. 72 = of the regression line is not appropriate. (Round to two decimal places) Type here to search OBb Chapter 10 X 5 https://gpt x Calendar - x Bb My Grades X |Course Her X Bb Chapt C gptc.blackboard.com/webapps/blackboard/content/contentWrapper.jsp?content_id=_18465 GEORGIA PIEDMONT TECHNICAL COLLEGE MATH1127: Introduction to Statistics (Asynchronous (100% Online)) 20337 Chapter 7: Linear Regression and Co of the regression line is not appropriate. d. 72 . (Round to two decimal places) e. Interpret ? : Given any group of plants that all produce the same number of seeds, 53% of all of these plants will produce seeds with the same chance of sprouting. 53% of all plants produce seeds whose chance of sprouting is the average chance of sprouting. There is a large variation in the percent of seeds that sprout, but if you only look at plants that produce a fixed number of seeds, this variation on average is reduced by 53%. O There is a 53% chance that the regression line will be a good predictor for the percent of seeds that sprout based on the number of seeds produced. f. The equation of the linear regression line is: y = T (Please show your answers to two decimal places) g. Use the model to predict the percent of seeds that sprout if the plant produces 60 seeds. Percent sprouting = (Please round your answer to the nearest whole number.) h. Interpret the slope of the regression line in the context of the question: For every additional seed that a plant produces, the chance for each of the seeds to sprout tends to decrease by 0.86 percent. The slope has no practical meaning since it makes no sense to look at the percent of the seeds that sprout since you cannot have a negative number. As x goes up, y goes down. i. Interpret the y-intercept in the context of the question: The y-intercept has no practical meaning for this study. The average sprouting percent is predicted to be 108.88. if plant produces no seeds, then that plant's sprout rate will be 108.88. The best prediction for a plant that has 0 seeds is 108.88 percent. Type here to search O 9GEORGIA PIEDMONT TECHNICAL COLLEGE MATH1127: Introduction to Statistics (Asynchronous (100% Online)) 20337 ... Chapter 7: Linear Regres Chapter 7: Linear Regression Score: 0/18 0/4 answered Question 4 A study was done to look at the relationship between number of vacation days employees take each year and the number of sick days they take each year. The results of the survey are shown below. Vacation Days 6 0 15 4 8 7 14 5 Sick Days 5 12 0 5 -0 0 0 a. Find the correlation coefficient: r = Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho: ? = 0 H1: ?~ * 0 The p-value is: (Round to four decimal places) c. Use a level of significance of o = 0.05 to state the conclusion of the hypothesis test in the context of the study. There is statistically insignificant evidence to conclude that there is a correlation between the number of vacation days taken and the number of sick days taken. Thus, the use of the regression line is not appropriate. There is statistically significant evidence to conclude that there is a correlation between the number of vacation days taken and the number of sick days taken. Thus, the regression line is useful. There is statistically significant evidence to conclude that an employee who takes more vacation days will take fewer sick days than an employee who takes fewer vacation days . There is statistically significant evidence to conclude that an employee who takes more d. p2 vacation days will take more sick days than an employee who takes fewer vacation days. (Round to two decimal places) 9 Type here to search O 9GEORGIA PIEDMONT TECHNICAL COLLEGE MATH1127: Introduction to Statistics (Asynchronous (100% Online)) 20337 Chapter 7: Linear Regression e. Interpret ?: There is a 68% chance that the regression line will be a good predictor for the number of sick days taken based on the number of vacation days taken. There is a large variation in the number of sick days employees take, but if you only look at employees who take a fixed number of vacation days, this variation on average is reduced by 68%. O 68% of all employees will take the average number of sick days. Given any group with a fixed number of vacation days taken, 68% of all of those employees will take the predicted number of sick days. f. The equation of the linear regression line is: y = x (Please show your answers to two decimal places) g. Use the model to predict the number of sick days taken for an employee who took 8 vacation days this year. Sick Days = (Please round your answer to the nearest whole number.) h. Interpret the slope of the regression line in the context of the question: As x goes up, y goes down. The slope has no practical meaning since a negative number cannot occur with vacation days and sick days. O For every additional vacation day taken, employees tend to take on average 0.73 fewer sick days. i. Interpret the y-intercept in the context of the question: The best prediction for an employee who doesn't take any vacation days is that the employee will take 9 sick days. The average number of sick days is predicted to be 9. O The y-intercept has no practical meaning for this study. O If an employee takes no vacation days, then that employee will take 2 sick days. Type here to search O OC gptc.blackboard.com/webapps/blackboard/content/contentWrapper.jsp?content_i GEORGIA PIEDMONT TECHNICAL COLLEGE MATH1127: Introduction to Statistics (Asynchronous (100% Online)) 20337 Chapter 8: Confidence Inte Chapter 8 Confidence Intervals (Mean) Score: 0/4 0/4 answered Question 1 A researcher is interested in finding a 95% confidence interval for the mean number minutes students are concentrating on their professor during a one hour statistics lecture. The study included 150 students who averaged 32.3 minutes concentrating on their professor during the hour lecture. The standard deviation was 11.8 minutes. Round answers to 3 decimal places where possible. a. To compute the confidence interval use a |? ~| distribution. b. With 95% confidence the population mean minutes of concentration is between and minutes. c. If many groups of 150 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean minutes of concentration and about percent will not contain the true population mean minutes of concentration. Hint: Hints Video ) [+ 1 Submit Question Type here to search OBb My Grades X * Course Her X Bb Chapter 10 X https://gpt x Calendar - x C * gptc.blackboard.com/webapps/blackboard/content/contentWrapper.jsp? content_id GEORGIA PIEDMONT TECHNICAL COLLEGE 8 MATH1127: Introduction to Statistics (Asynchronous (100% Online)) 20337 Chapter 8: Confidence Inter Chapter 8 Confidence Intervals (Mean) Score: 0/4 0/4 answered Question 2 You are interested in finding a 95% confidence interval for the average number of days of class that college students miss each year. The data below show the number of missed days for 14 randomly selected college students. Round answers to 3 decimal places where possible. 10 10 5 9 5 5 9 9 10 0 8 1 4 3 a. To compute the confidence interval use a ? ~ |distribution. b. With 95%% confidence the population mean number of days of class that college students miss is between and days. c. If many groups of 14 randomly selected non-residential college students are surveyed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean number of missed class days and about percent will not contain the true population mean number of missed class days. Hint: Hints Video ' [+ ] Submit Question Type here to searchBb Chapter 10 x https://gpt x Calendar - x Bb My Grades X Course Her X C o gptc.blackboard.com/webapps/blackboard/content/contentWrapper.jsp?conten GEORGIA PIEDMONT TECHNICAL COLLEGE MATH1127: Introduction to Statistics (Asynchronous (100% Online)) 20337 Chapter 8: Confidence Chapter 8 Confidence Intervals (Mean) Score: 0/4 0/4 answered Question 3 If n = 16, x = 49, and s = 2, construct a confidence interval at a 90% confidence level. Assume the data came from a normally distributed population. Give your answers to three decimal places.