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Maths Multiple Choice Questions with A+ Solution

Question 1A customer wants to estimate the average delivery time of a pizza from the local pizza parlor. The customer wants to obtain a sample mean that falls within 3.204 minutes of the true average delivery time with 99% confidence. If the customer knows the standard deviation of the delivery times of all pizzas is 9.646, how many pizzas will need to be ordered?Question 1 options:1) We do not have enough information to answer this question since we were not given the sample mean.2) 713) 664) 605) 61Margin of error = z.?/?nOr, 3.204 = 2.58×9.646/?nTherefore n = 60.33 ? 61Question 2 You read an article in Golf Digest that someone with your average drive distance will have an average score of 72.76. You keep track of your scores for the next 14 rounds and see that your average score is 77.74 with a standard deviation of 2.413 strokes. You create a 95% confidence interval for your average score and it is (76.347, 79.133). Given this information, what is the best conclusion?Question 2 options:1) The percentage of rounds in which you score more than 72.76 is 95%.2) We are 95% confident that your average score is less than 72.76.3) We cannot determine the proper interpretation based on the information given.4) We are 95% confident that your average score is greater than 72.76.5) We are 95% confident that your average score is no different from 72.76.Question 3 Suppose that you are the director of table game operations at a large casino, known especially for its poker room. You are interested in determining the average number of hands the casino should expect per hour during peak hours in the poker room. You monitor the number of hands over the next week and given a random sample of 30 hours, you see that on average 172.99 hands are played per hour, with a standard deviation of 7.695 hands and you calculated a 90% confidence interval to be (170.603, 175.377). Your manager believes the true mean is 242.4. Which of the following is the best conclusion?Question 3 options:1) We are 90% confident that the average number of hands played per hour is less than 242.4.2) We cannot determine the proper interpretation based on the information given.3) We are 90% confident that the average number of hands played per hour is no different from 242.4.4) We are 90% confident that the average number of hands played per hour is greater than 242.4.5) The percentage of hours in which more than 242.4 hands of poker are played is 90%.Question 4 You are curious about the average number of yards Matthew Stafford throws for each game for the Detroit Lions. You randomly select 26 games and see that the average yards per game is 271.6 with a standard deviation of 32.08 yards. You want to create a 90% confidence interval for the true average number of yards per game he throws. What is the margin of error for this estimate?Question 4 options:1) 10.73072) 1.45183) 10.74664) 8.28175) 6.2914Question 5A customer wants to estimate the average delivery time of a pizza from the local pizza parlor. Over the course of a few months, the customer orders 29 pizzas and records the delivery times. The average delivery time is 26.7 with a standard deviation of 8.527. If the customer estimates the time using a 99% confidence interval, what is the margin of error?Question 5 options:1) 0.90142) 4.37543) 4.36454) 1.58345) 3.9065Question 6It is believed that using a solid state drive (SSD) in a computer results in faster boot times when compared to a computer with a traditional hard disk (HDD). You sample 13 computers with an HDD and note a sample average of 30.74 seconds with a standard deviation of 6.37 seconds. A sample of 19 computers with an SSD show an average of 12.28 seconds with a standard deviation of 2.664 seconds. Construct a 99% confidence interval for the difference between the true average boot times of the two types of hard drives. Assume the difference will represent (HDD-SSD) and that the population standard deviations are statistically the same.Question 6 options:1) We only have the sample means, we need to know the population means in order to calculate a confidence interval.2) (14.26, 22.66)3) (16.83, 20.09)4) (12.95, 23.97)5) (13.98, 22.94)Question 7 The owner of a local supermarket wants to estimate the difference between the average number of gallons of milk sold per day on weekdays and weekends. The owner samples 20 weekdays and finds an average of 265.551 gallons of milk sold on those days with a standard deviation of 36.4693. 24 (total) Saturdays and Sundays are sampled and the average number of gallons sold is 370.357 with a standard deviation of 48.9046. Construct a 90% confidence interval to estimate the difference of (average number of gallons sold on weekdays – average number of gallons sold on weekends). Assume the population standard deviations are the same for both weekdays and weekends.Question 7 options:1) (-126.578, -83.034)2) (-127.07, -82.542)3) (-126.487, -83.125)4) We only have the sample means, we need to know the population means in order to calculate a confidence interval.5) (-118.043, -91.569)Question 8It is believed that using a solid state drive (SSD) in a computer results in faster boot times when compared to a computer with a traditional hard disk (HDD). You sample a group of computers and use the sample statistics to calculate a 95% confidence interval of (-10.95, -1.5). This interval estimates the difference of (average boot time (HDD) – average boot time (SSD)). What can we conclude from this interval?Question 8 options:1) We are 95% confident that the difference between the two sample means falls within the interval.2) We do not have enough information to make a conclusion.3) There is no significant difference between the average boot time for a computer with an SSD drive and one with an HDD drive at 95% confidence.4) We are 95% confident that the average boot time of all computers with an SSD is greater than the average of all computers with an HDD.5) We are 95% confident that the average boot time of all computers with an HDD is greater than the average of all computers with an SSD.Question 9 A pharmaceutical company is testing a new drug to increase memorization ability. It takes a sample of individuals and splits them randomly into two groups. After the drug regimen is completed, all members of the study are given a test for memorization ability with higher scores representing a better ability to memorize. You are presented a 90% confidence interval for the difference in population mean scores (with drug – without drug) of (-17.81, -7.24). What can you conclude from this interval?Question 9 options:1) We are 90% confident that the difference between the two sample means falls within the interval.2) There is no significant difference between the average memorization abilities for those on the drug compared to those not on the drug.3) We do not have enough information to make a conclusion.4) We are 90% confident that the average memorization ability of those not on the drug is higher than those who are on the drug.5) We are 90% confident that the average memorization ability of those on the drug is higher than those who are not on the drug.Question 10 The owner of a golf course wants to determine if his golf course is more difficult than the one his friend owns. He has 23 golfers play a round of 18 holes on his golf course and records their scores. Later that week, he has the same 23 golfers play a round of golf on his friend’s course and records their scores again. The average difference in the scores (treated as the scores on his course – the scores on his friend’s course) is 2.48 strokes and the standard deviation of the differences is 8.038 strokes. The owner uses this information to calculate the 99% confidence paired t-interval of (-2.244, 7.204). Which statement is the correct interpretation of this interval?Question 10 options:1) We are certain the the average difference in scores between the two courses for all golfers is between -2.244 and 7.204.2) The proportion of all golfers that had a difference in scores between the two courses is 99%.3) We are 99% confident that the average difference in scores between the two courses for all golfers is between -2.244 and 7.204.4) We are 99% confident that the difference between the average score on the owner’s golf course and the average score on the friend’s golf course is between -2.244 and 7.204.5) We are 99% confident that the average difference in the scores of the golfers sampled is between -2.244 and 7.204.Question 11 Automobile manufacturers are interested in the difference in reaction times for drivers reacting to traditional incadescent lights and to LED lights. A sample of 19 drivers are told to press a button as soon as they see a light flash in front of them and the reaction time was measured in milliseconds. Each driver was shown each type of light. The average difference in reaction times (traditional – LED) is 3.7 ms with a standard deviation of 5.19 ms. A 99% confidence interval for The average difference between the two reaction times was (0.27, 7.13). Which of the following is the best interpretation?Question 11 options:1) We are certain the the average difference in reaction times between the two light types for all golfers is between 0.27 and 7.13.2) The proportion of all drivers that had a difference in reaction times between the two lights is 99%.3) We are 99% confident that the difference between the average reaction time for LED lights and the average reaction time for traditional lights is between 0.27 and 7.13.4) We are 99% confident that the average difference in the reaction times of the drivers sampled is between 0.27 and 7.13.5) We are 99% confident that the average difference in reaction time between the two light types for all drivers is between 0.27 and 7.13.Question 12 Automobile manufacturers are interested in the difference in reaction times for drivers reacting to traditional incadescent lights and to LED lights. A sample of 30 drivers are told to press a button as soon as they see a light flash in front of them and the reaction time was measured in milliseconds. Each driver was shown each type of light. The average difference between the two reaction times (traditional – LED) was 87.396 ms with a standard deviation of 41.231 ms. If they wanted to calculate a 95% confidence interval for the difference in the average reaction time to the two types of light for all drivers, what is the margin of error?Question 12 options:1) 7.52772) 1.52733) 15.39594) 15.37365) 12.7765Question 13 A new drug to treat high cholesterol is being tested by pharmaceutical company. The cholesterol levels for 27 patients were recorded before administering the drug and after. The mean difference in total cholesterol levels (after – before) was 14.509 mg/dL with a standard deviation of 9.561 mg/dL. When creating a 99% confidence interval for the true average difference in cholesterol levels by the drug, what is the margin of error?Question 13 options:1) 4.54972) 5.11293) 0.93574) 1.845) 5.0981Question 14You hear on the local news that for the city of Kalamazoo, the proportion of people who support President Obama is 0.4. However, you think it is less than 0.4. The hypotheses you want to test are Null Hypothesis: p ? 0.4, Alternative Hypothesis: p < 0.4. You take a random sample around town and calculate a p-value for your hypothesis test of 0.0913. What is the appropriate conclusion? Conclude at the 5% level of significance.Question 14 options:1) We did not find enough evidence to say the proportion of people who support President Obama is less than 0.4.2) The proportion of people who support President Obama is significantly less than 0.4.3) We did not find enough evidence to say the proportion of people who support President Obama is larger than 0.4.4) The proportion of people who support President Obama is greater than or equal to 0.4.5) We did not find enough evidence to say a significant difference exists between the proportion of people who support President Obama and 0.4Question 15 A USA Today article claims that the proportion of people who believe global warming is a serious issue is 0.63, but given the number of people you've talked to about this same issue, you believe it is greater than 0.63. The hypotheses for this test are Null Hypothesis: p ? 0.63, Alternative Hypothesis: p > 0.63. You take a random sample and perform a hypothesis test, getting a p-value of 0.2578. What is the appropriate conclusion? Conclude at the 5% level of significance.Question 15 options:1) We did not find enough evidence to say the proportion of people who believe global warming is a serious issue is less than 0.63.2) We did not find enough evidence to say the proportion of people who believe global warming is a serious issue is larger than 0.63.3) The proportion of people who believe global warming is a serious issue is significantly larger than 0.63.4) The proportion of people who believe global warming is a serious issue is less than or equal to 0.63.5) We did not find enough evidence to say a significant difference exists between the proportion of people who believe global warming is a serious issue and 0.63Question 16 As of 2014: 2024 – Essay Writing Service. Custom Essay Services Cheap, the proportion of students who use a MacBook as their primary computer is 0.36. You believe that at your university the proportion is actually greater than 0.36. If you conduct a hypothesis test, what will the null and alternative hypotheses be?Question 16 options:1) HO: p = 0.36HA: p ? 0.362) HO: p ? 0.36HA: p < 0.363) HO: p > 0.36HA: p ? 0.364) HO: p < 0.36HA: p ? 0.365) HO: p ? 0.36HA: p > 0.36Question 17 You hear on the local news that for the city of Kalamazoo, the proportion of people who support President Obama is 0.59. However, you think it is less than 0.59. If you conduct a hypothesis test, what will the null and alternative hypotheses be?Question 17 options:1) HO: p > 0.59HA: p ? 0.592) HO: p = 0.59HA: p ? 0.593) HO: p < 0.59HA: p ? 0.594) HO: p ? 0.59HA: p > 0.595) HO: p ? 0.59HA: p < 0.59Question 18 Your friend tells you that the proportion of active Major League Baseball players who have a batting average greater than .300 is greater than 0.56, a claim you would like to test. The hypotheses for this test are Null Hypothesis: p ? 0.56, Alternative Hypothesis: p > 0.56. If you randomly sample 24 players and determine that 14 of them have a batting average higher than .300, what is the test statistic and p-value?Question 18 options:1) Test Statistic: 0.23, P-Value: 0.8182) Test Statistic: -0.23, P-Value: 0.5913) Test Statistic: 0.23, P-Value: 0.5914) Test Statistic: 0.23, P-Value: 0.4095) Test Statistic: -0.23, P-Value: 0.409Question 19 A USA Today article claims that the proportion of people who believe global warming is a serious issue is 0.5, but given the number of people you’ve talked to about this same issue, you believe it is greater than 0.5. The hypotheses for this test are Null Hypothesis: p ? 0.5, Alternative Hypothesis: p > 0.5. If you randomly sample 26 people and 16 of them believe that global warming is a serious issue, what is your test statistic and p-value?Question 19 options:1) Test Statistic: 1.177, P-Value: 0.122) Test Statistic: 1.177, P-Value: 0.883) Test Statistic: 1.177, P-Value: 0.244) Test Statistic: -1.177, P-Value: 0.885) Test Statistic: -1.177, P-Value: 0.12Question 20 In the year 2000, the average car had a fuel economy of 21.06 MPG. You are curious as to whether this average is greater than today. The hypotheses for this scenario are as follows: Null Hypothesis: ? ? 21.06, Alternative Hypothesis: ? > 21.06. You perform a one sample mean hypothesis test on a random sample of data and observe a p-value of 0.2157. What is the appropriate conclusion? Conclude at the 5% level of significance.Question 20 options:1) The true average fuel economy today is less than or equal to 21.06 MPG.2) The true average fuel economy today is significantly greater than 21.06 MPG.3) We did not find enough evidence to say the true average fuel economy today is greater than 21.06 MPG.4) We did not find enough evidence to say a significant difference exists between the true average fuel economy today and 21.06 MPG.5) We did not find enough evidence to say the true average fuel economy today is less than 21.06 MPG.Question 21 In the year 2000, the average car had a fuel economy of 21.61 MPG. You are curious as to whether this average is greater than today. The hypotheses for this scenario are as follows: Null Hypothesis: ? ? 21.61, Alternative Hypothesis: ? > 21.61. You perform a one sample mean hypothesis test on a random sample of data and observe a p-value of 0.0095. What is the appropriate conclusion? Conclude at the 5% level of significance.Question 21 options:1) The true average fuel economy today is significantly less than 21.61 MPG.2) We did not find enough evidence to say the true average fuel economy today is greater than 21.61 MPG.3) The true average fuel economy today is less than or equal to 21.61 MPG.4) The true average fuel economy today is significantly different from 21.61 MPG.5) The true average fuel economy today is significantly greater than 21.61 MPG.Question 22 In the year 2000, the average car had a fuel economy of 23.6 MPG. You are curious as to whether the average in the present day is greater than than the historical value. What are the appropriate hypotheses for this test?Question 22 options:1) HO: ? = 23.6HA: ? ? 23.62) HO: ? ? 23.6HA: ? > 23.63) HO: ? ? 23.6HA: ? < 23.64) HO: ? > 23.6HA: ? ? 23.65) HO: ? < 23.6HA: ? ? 23.6Question 23It is reported in USA Today that the average flight cost nationwide is $342.59. You have never paid close to that amount and you want to perform a hypothesis test that the true average is actually less than $342.59. What are the appropriate hypotheses for this test?Question 23 options:1) HO: ? ? 342.59HA: ? < 342.592) HO: ? > 342.59HA: ? ? 342.593) HO: ? < 342.59HA: ? ? 342.594) HO: ? = 342.59HA: ? ? 342.595)HO: ? ? 342.59HA: ? > 342.59

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