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A manufacturer of exercise bicycles is studying the relationship between the number of months an exercise bicycle has been owned and the length of time it was used last week. Data for a random sample of 7 owners are provided in the table below assignment4a.docx assignment5a.docx assignment6a.docx Unformatted Attachment Preview Assignment 4A Total Marks = 75 Please show all your work. Some questions require you to use graphs, tree diagrams, formulas, and so on that are difficult or impossible to reproduce in word-processing programs, so you will have to print the entire assignment and fill it out and mail it to your tutor. As an alternative to mailing, you might be able to photograph or scan your assignment and submit it through the appropriate drop box. If you do, make sure the material you are submitting is legible. Question 1 Grade point averages of math majors at a large distance education university are normally distributed with a mean of  = 2.85 and a standard deviation of  = 0.30 . If a random sample of 25 math majors is selected from that university, what is the probability that the sample mean grade point average will be 6 marks a. 3 marks b. at least 2.757? Introduction to Statistics either less than 2.709 or more than 2.955? 1 Question 2 Psychologists estimate that 80\% of male drivers, when lost in trying to find a location, continue to drive rather than asking for directions. If this estimate is correct, what is the probability that, in a random sample of 100 lost male drivers, the proportion who continue to drive is 2 4 marks a. at least 0.70? 3 marks b. less than 0.85? Mathematics 215 / Assignment 4A Question 3 A researcher wishes to estimate the mean age of all runners who participate in the annual Vancouver marathon. A random sample of 36 participants indicated a mean age of 31.4 years. It is known that the population standard deviation of ages is  = 7.2 years. 5 marks Construct a 97\% confidence interval for the population mean age. Note: Express the confidence interval to 2 decimal places of accuracy. Introduction to Statistics 3 Question 4 A random sample of representatives from seven companies was interviewed in order to find the number of computers they planned to order next year. The results are shown below. 8 8 marks 15 33 10 9 25 12 Assuming that the population of number of computers planned to be ordered next year is normally distributed, construct a 95\% confidence interval for the population mean. Note: Express the confidence interval to 2 decimal places of accuracy. 4 Mathematics 215 / Assignment 4A Question 5 4 marks Introduction to Statistics A survey is being planned to estimate, with a 98\% confidence interval, the mean amount of time per week that seniors spend watching television. The population standard deviation is known to be 5.2 hours. What sample size will be required to obtain an estimate that is within 0.5 hours of the population mean? 5 Question 6 A survey was conducted to determine the percentage of students at a postsecondary institution who prefer the new alpha-grading system. The responses from a random sample of 30 students are shown below. 7 marks Yes No Yes Yes No Yes No Yes Yes No Yes No Yes No Yes No Yes Yes Yes Yes No Yes No No No Yes Yes No Yes Yes Construct a 98.5\% confidence interval for the population proportion who prefer the new alpha-grading system. Note: Express the confidence interval to 4 decimal places of accuracy. 6 Mathematics 215 / Assignment 4A Question 7 A researcher wishes to estimate the proportion of eligible voters who will vote for a particular candidate in an upcoming election. 4 marks a. How large should the sample size be so that a 85\% confidence interval for the population proportion has a margin of error of 0.05? Assume that a preliminary sample suggests the proportion is 0.65. 4 marks b. Assuming that the results of a preliminary survey are not available, what is the most conservative estimate of the sample size that would limit the margin of error to within 0.05 of the population proportion for an 95\% confidence interval? Introduction to Statistics 7 Question 8 A study conducted last year indicated that adults spent an average of 14 hours on household chores during the weekend. A research group wishes to determine if the average hours spent on household chores during the weekend this year is different from the 14 hours of last year. Consequently, the research group selects a random sample of 64 adults and finds the mean hours spent on household chores during the weekend to be 15.05 hours. The population standard deviation is known to be 3.0 hours. 8 8 marks a. Formulate and test the appropriate hypotheses using the p -value approach. What is the p -value of the test? Would you reject the null hypothesis at  = 0.01 ? What would be your conclusion? 2 marks b. Would you reject the null hypothesis at  = 0.001 ? What would be your conclusion? 1 mark c. How strong is the evidence against H 0 ? [Refer to Unit 4, Section 7, in the Study Guide.] Mathematics 215 / Assignment 4A Question 9 8 marks Introduction to Statistics A psychologist believes that if classical music is played during a test, test scores will increase. In the past, the mean test score was 60. A random sample of 49 individuals wrote the test while classical music was in the background. The sample results showed a mean test score of 62 and a standard deviation of 6.3. Using a 5\% level of significance, can the psychologist conclude that the mean test score has increased with classical music? Formulate and test the appropriate hypotheses. Use the critical value approach. 9 Question 10 8 marks 10 A telephone company estimates that 30\% of its customers are interested in high-speed Internet service. To test this estimate, a random sample of 100 customers was selected and the results showed that 25 were interested in high-speed Internet service. Can it be concluded that the percentage of customers interested in high-speed Internet service is different from 30\%? Formulate and test the appropriate hypotheses at a 5\% significance level. Use the critical value approach. Mathematics 215 / Assignment 4A Assignment 5A Total Marks = 88 Please show all your work. Some questions require you to use graphs, tree diagrams, formulas, and so on that are difficult or impossible to reproduce in word-processing programs, so you will have to print the entire assignment and fill it out and mail it to your tutor. As an alternative to mailing, you might be able to photograph or scan your assignment and submit it through the appropriate drop box. If you do, make sure the material you are submitting is legible. Question 1 A researcher is comparing the reaction times of 10-year-olds who play video games and 10-year-olds who do not. Random samples from each group provided the results shown below. Reaction times of 10-year-olds Sample size Players of Video Games Non-players of Video Games 15 10 Mean reaction time (seconds) 0.50 0.52 Standard deviation of reaction times (seconds) 0.01 0.02 Assume that the reaction times for both populations are normally distributed with the same population standard deviation. 7 marks a. Construct a 98\% confidence interval for the difference between the population means of reaction times. Note: Express your answer to 5 decimal places of accuracy. Introduction to Statistics 1 8 marks 2 b. Using a 2.5\% significance level, can the researcher conclude that the mean reaction time of players of video games is less than the mean reaction time of non-players of video games? Formulate and test the appropriate hypotheses. Use the critical value approach. Mathematics 215 / Assignment 5A Question 2 Is there any difference between the proportion of Americans who wish they were rich and the proportion of Canadians who wish they were rich? A random sample of 1,000 Americans showed that 550 wish they were rich, while a random sample of 500 Canadians showed that 225 wished they were rich. 6 marks a. Find a 97.5\% confidence interval for the difference between the population proportions who wish they were rich. Note: Express your answer to 4 decimal places of accuracy. Introduction to Statistics 3 9 marks 4 b. Test, at the 1\% level of significance, whether the two population proportions are significantly different. Formulate and test the appropriate hypotheses. Use the critical value approach. Mathematics 215 / Assignment 5A Question 3 A motivational program was designed to increase the number of hours each student who took it studied per week. Eight randomly selected students were involved in the program. The table below shows the number of hours each student studied per week before the taking motivational program and after taking the program. Before program After program 11 marks 8 12 10 12 5 10 10 12 12 11 14 15 8 15 9 6 At the 10\% level of significance, can it be concluded the motivational program increased the average number of hours students studied per week? Formulate and test the appropriate hypotheses. Use the critical value approach. Assume that the population of paired differences has a normal distribution. Introduction to Statistics 5 Question 4 It has been hypothesized that the distribution of seasonal colds in Canada is as follows: Season Percentage Fall 35\% Winter 25\% Spring 30\% Summer 10\% A random sample of 200 Canadian citizens provided the following results: Season 10 marks 6 Observed Frequency Fall 80 Winter 40 Spring 70 Summer 10 Do the observed data contradict the hypothesis? Formulate and test the appropriate hypotheses at the 5\% level of significance. Use the critical value approach. Mathematics 215 / Assignment 5A Question 5 A large company is interested in knowing whether there is any relationship between a person’s age and that person’s opinion about a new wage incentive plan. A random sample of 100 employees was selected and crossclassified as shown below. Opinion Neutral 5 5 10 35 to 55 10 30 10 Over 55 15 10 5 Under 35 10 marks Introduction to Statistics In Favour Opposed At the 1\% level of significance, can it be concluded that there is a relationship between an employee’s age and an employee’s opinion about the new wage incentive plan? Formulate and test the appropriate hypotheses. Use the critical value approach. 7 Question 6 A random sample of 16 students showed that the variance in the number of hours they spend studying for a final exam was 25 hours2. 7 marks 8 a. Construct a 95\% confidence interval for the population variance and standard deviation of hours spent studying. Assume the population of hours spent studying is normally distributed. Mathematics 215 / Assignment 5A 8 marks Introduction to Statistics b. Test, at the 5\% level of significance, whether the population standard deviation of hours spent studying is less than 10. Use the critical value approach. 9 Question 7 Three different brands of pain relief medication are available for minor aches and pains. It is of interest to know whether the mean time to relieve the pain differs from brand to brand. To find out, twelve individuals with minor aches and pains were randomly assigned to one of the three brands. The time to relieve the pain (in minutes) for each individual is provided in the table below. 12 marks 10 Brand A Brand B Brand C 10 15 20 12 22 25 15 25 20 14 19 11 Given that the necessary assumptions are satisfied, can it be concluded, at the 2.5\% level of significance, that not all mean times to relieve pain are equal? Formulate and test the appropriate hypotheses. Use the critical value approach. Mathematics 215 / Assignment 5A Assignment 6A Total Marks = 63 Please show all your work. Some questions require you to use graphs, tree diagrams, formulas, and so on that are difficult or impossible to reproduce in word-processing programs, so you will have to print the entire assignment and fill it out and mail it to your tutor. As an alternative to mailing, you might be able to photograph or scan your assignment and submit it through the appropriate drop box. If you do, make sure the material you are submitting is legible. Question 1 A manufacturer of exercise bicycles is studying the relationship between the number of months an exercise bicycle has been owned and the length of time it was used last week. Data for a random sample of 7 owners are provided in the table below Introduction to Statistics Months Owned (x) Hours Used Last Week ( y) 14 6 8 8 5 7 3 9 10 6 4 8 12 7 1 4 marks a. Construct a scatter diagram for these data with “Months Owned” on the horizontal ( x ) axis, and “Hours Used Last Week” on the vertical ( y ) axis. Note: Try to make relatively full use of the graph area. 2 marks b. Describe the general pattern of the relationship between the two variables. 11 marks c. Calculate the least squares regression line with hours used as the dependent variable and months owned as the independent variable. Note: Express a and b to 4 decimal places of accuracy. 3 marks d. Plot the regression line on the scatter diagram you constructed in part (a). Note: Show your calculations for x = 4 and x = 12 . 2 Mathematics 215 / Assignment 6A 10 marks Introduction to Statistics e. Can it be concluded that the slope of the regression line is negative? Formulate and test the appropriate hypotheses at the 5\% significance level. Use the critical value approach. 3 4 marks f. Construct a 95\% confidence interval for B. 2 marks g. Interpret the numerical value of b in the sample regression line. What does it mean in the context of this question? 2 marks h. Use the equation of the regression line to predict hours used last week if an exercise bicycle has been owned for 11 months. Note: Express your answer to 2 decimal places of accuracy. 4 Mathematics 215 / Assignment 6A Question 2 An ice cream vendor would like to predict daily sales of ice cream cones based on the temperature outdoors. Data for a random sample of 8 days are provided in the table below. Temperature (C) (x) Daily Sales (Litres) ( y) 6 135 8 50 12 125 16 100 18 200 22 150 28 250 28 175 The regression line with “daily sales” as the dependent variable and “temperature” as the independent variable has been calculated as: ˆ = 55.217 + 5.38597 x y You may use the following sums of squares and cross products for the questions below.  x = 138  y = 1185 SSxx = 495.5 SSyy = 26446.875 SSxy = 2668.75 2 marks a. Interpret the value of b in the sample regression line. What does it mean in the context of this question? 2 marks b. Compute the linear correlation between “daily sales” and “temperature.” Note: Express your answer to 4 decimal places of accuracy. Introduction to Statistics 5 6 8 marks c. At the 5\% significance level, can it be concluded that the correlation between daily sales and temperature is positive? Formulate and test the appropriate hypotheses. Use the critical value approach. 2 marks d. What percentage of the variation in daily sales is explained by its linear relationship with temperature? Mathematics 215 / Assignment 6A 11 marks Introduction to Statistics e. Using the regression line and sums of squares and cross products provided above, construct a 90\% prediction interval for daily sales when the outside temperature is 24C. 7 ... Purchase answer to see full attachment