] Makayla and Rahquez began arguing about who did better on their tests, but they couldn't decide who 91 did better given that they took different tests. Makayla took a test in Art History and earned a 71.6, and Rahquez took a test in Math and earned a 67.1. Use the fact that all the students' test grades in the Art History class had a mean of 76.4 and a standard deviation of 11.8, and all the students' test grades in Math had a mean of 64.9 and a standard deviation of 8,5 to answer the following questions. a) Calculate the z-score for Makayla's test grade. 'z=' [Round your answer to two decimal places.] bi Calculate the z-score for Rahquez's test grade. z= [Round your answer to two decimal places.] c) Which person did relatively better? Makayla Rahquez They did equally well. 0 Question 13 I2. 011 pt '0 2 According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 64 inches and a standard deviation of 2.5 inches. Suppose one Martian adult male is randomly chosen. Let X = height of the individual. Round all answers to 4 decimal places where possible, a. What is the distribution of X? X - N( , ) b, Find the probability that the person is between 59.1 and 60.9 inches. c. The middle 30% of Martian heights lie between what two numbers? Low: inches High: inches . Question 14 B 0/1 pt '0 Z A special deck of cards has 5 green cards , and 3 yellow cards. The green cards are numbered 1, Z, 3, 4, and 5. The yellow cards are numbered 1, Z, and 3. The cards are well shuffled and you randomly draw one card, 6 = card drawn is green E = card drawn is even-numbered a. How many elements are there in the sample space? C] b, PlE) = (Round to 4 decimal places) 0 Question 15 B 0/1 pt '0 Z A doctor knows that the medical test for a certain health condition gives accurate results 77% of the time. Find the probability that if 4 of these tests are randomly selected, at least one of them is accurate. 0.92 0.35153041 0.00179841 0.64846959 0.23 0.99720159 0 Question 16 B 0/1 pt E) 2 An experiment consists of first rolling a die and then tossing a coin: a. How many elements are there in the sample space? b, Let A be the event that either a 3 or 4 is rolled firsty followed by landing a head on the coin toss. P(A) = Present your answer as a decimal rounded to four decimal places. c. Let B be the event that a number less than 3 is rolled, followed by landing a head on the coin toss. Are the events A and B mutually exclusive? Yes, they are Mutually Exclusive No, they are not Mutually Exclusive \\ The amount of coffee that people drink per day is normally distributed with a mean of 17 ounces and a standard deviation of 5 ounces. 35 randomly selected people are surveyed. Round all answers to 4 decimal places where possible. a. What is the distribution of 'X'? 'X' - N( , ) b. What is the distribution of 'bar x'? 'bar x' - N( , ) c. What is the probability that one randomly selected person drinks between 16.8 and 17.2 ounces of coffee per day? d. For the 35 people, find the probability that the average coffee consumption is between 16.8 and 17.2 ounces of coffee per day. e. For part d), is the assumption that the distribution is normal necessary? Yes No f. Find the IQR for the average of 35 coffee drinkers. Q1 = ounces Q3 = ounces IQR: ounces 0 Question 18 80/1 pt '0 2 If the confidence level is decreased and the standard deviation and sample size stay the same, then the Error will be increased. True False 0 Question 19 BIO/1 pt '0 Z A 95% confidence interval for the mean was computed with a sample of size 100 to be (10,14). Then the Error is :2. True False . Question 20 E: 0/1 pt '0 2 With a large sample size such as n = 100, we do not need to assume the distribution is normal Q in order to compute a 95% confidence interval for the mean. True False 0 Question 21 I3 0/1 pt 0 2 A fitness center is interested in finding a 98% confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center. Records of 217 members were looked at and their mean number of visits per week was 3.5 and the standard deviation was 1.8. Round answers to 3 decimal places where possible. a. To compute the confidence interval use a ? v distribution. b. With 98% confidence the population mean number of visits per week is between and visits. c. if many groups of 217 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 number of visits per week and about percent will not contain the true population mean number of visits per week. . Question 22 B 0/1 pt '0 Z You are interested in constructing a 95% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 379 randomly selected caterpillars observed, 48 lived to become butterflies. Round answers to 4 decimal places where possible. a. With 95% confidence the proportion of all caterpillars that lived to become a butterfly is between and b. If many groups of 379 randomly selected caterpillars were observed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of caterpillars that become butterflies and about percent will not contain the true population proportion. Q 3 A political candidate has asked you to conduct a poll to determine what percentage of people support her. If the candidate only wants a 3% margin of error at a 99% confidence level, what size of sample is needed? When finding the z-value, round it to four decimal places. . uestion 24 /0/1 t 2 p A manufacturer of rechargeable laptop batteries markets its batteries as having, on average, 500 charges. A consumer group decides to test this claim by assessing the number of times 30 of their laptop batteries can be recharged and finds the average is 497, with a standard deviation of 10. The resulting p-value is .1111; thus, the null hypothesis is not rejected. The consumer group concludes that the manufacturer's claim that its laptop batteries can be recharged, on average, 500 times is accurate. What type of error is possible in this situation? type [ type II neither both 0 Question 25 30/1 pt '0 2 The average salary in this city is 546,600. Is the average more for single people? 41 randomly selected single people who were surveyed had an average salary of $49,557 and a standard deviation of 59,750. What can be concluded at the 'alpha' = 0.10 level of significance? a. For this study, we should use Select an answer V b. The null and alternative hypotheses would be: 'H,0:' ? V Selectananswer V 'HJF ? V Selectananswer v c. The test statistic ? v = (please show your answer to 3 decimal places.) d. The p-value = (Please show your answer to 4 decimal places.) e. The p-value is ? V 'alpha' f. Based on this, we should Select an answer V the null hypothesis, g. Thus, the final conclusion is that The data suggest that the populaton mean is significantly greater than 46,600 at 'alpha' = 0. 10, so there is statistically significant evidence to conclude that the population mean salary for singles is greater than 46,600 The data suggest that the sample mean is not significantly greater than 46,600 at 'alpha' = 0.10, so there is statistically insignificant evidence to conclude that the sample mean salary for singles is greater than 49,557. The data suggest that the population mean is not significantly greater than 46,600 at 'alpha' = 0.10, so there is statistically insignificant evidence to conclude that the population mean salary for singles is greater than 46,600. ht Interpret the p-value in the context of the study. There is a 23612401896 chance that the population mean salary for singles is greater than $46,600 , If the population mean salary for singles is 546,600 and if another 41 singles are surveyed then there would be a 2.961 2401 8% chance that the population mean salary for singles would be greater than 546,600, If the population mean salary for singles is $46,600 and if another 41 singles are surveyed then there would be a 29612401896 chance that the sample mean for these 41 singles surveyed would be greater than $49, 557. There is a 2.9612401896 chance of a Type I error: it Interpret the level of significance in the context of the study. If the population population mean salary for singles is greater than $46,600 and if another 41 singles are surveyed then there would be a 10% chance that we would end up falsely concluding that the population mean salary for singles is equal to $46,600. If the population mean salary for singles is $46,600 and if another 41 singles are surveyed then there would be a 10% chance that we would end up falsely concluding that the population mean salary for singles is greater than $46,600, There is a 10% chance that you won the lottery, so you may not have to even have to worry about passing this class. There is a 10% chance that the population mean salary for singles is greater than $46,600