M263 C4U (All FE Review Qs)

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Central Arizona College *

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263

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Mechanical Engineering

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Feb 20, 2024

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M263 Class #21 Intro (FE Review Q's) 1. The histogram shown in the image attached represents the high temperatures in Tucson for the month of March 2019. Which of the following is the best estimate for the median of this data set? 2. The histogram shown in the image attached represents the high temperatures in Tucson for the month of March 2019. Which of the following is a t±ue statement? 3. Which of the following is a resistant measure? Between 60 and 65 degrees A Between 65 and 70 degrees B Between 70 and 75 degrees C Between 75 and 80 degrees D What? It was that hot in March of 2019? That was so long ago .... E The dist±ibution of data is roughly symmet±ic. A There appears to be at least one outlier. B The mean temperature is probably less than the median temperature C The mean temperature is probably equal to the median temperature D The range of this data is more than 50 degrees E The mean of a sample A The standard deviation of a population B The range of a sample C The slope of a linear regression D The interqua±tile range of a population E

4. The measure of the circumference of a white pine tree at 25 years of growth is approximately no±mally dist±ibuted with a mean of 123.5 inches and a standard deviation of 4.5 inches. Approximately 95% of all white pine trees are between what two values? 5. The measure of the circumference of a white pine tree at 25 years of growth is approximately no±mally dist±ibuted with a mean of 123.5 inches and a standard deviation of 4.5 inches. Which of the following is the closest to the circumference which marks the 90th percentile? Between 119 and 128 inches. A Between 121.64 and 125.36 inches B Between 114.5 and 132.5 inches C Between 114.5 and 128 inches D Between 110 and 137 inches E 114.5 inches A 118 inches B 128 inches C 129 inches D 132.5 inches E

M263 Class #22 Intro (FE Review Q's) 1. The events A and Z are independent with P²A³ = 0.4 and P²A and Z³ = 0.28 Which of the following is t±ue? 2. Summa±y statistics for a set of data is given in the diagram attached. Which of the following is a t±ue statement? P²Z³ = 0.24 A P²Z³´ 0.12 B P²A or Z³ = 0.82 C P²A or Z³ = 0.112 D P²A or Z³´ 0.68 E Approximately 21 of the obse±vations are less than 32. A Approximately 21 of the obse±vations are less than 30. B Since the mean is greater than the median, this data set is most likely skewed to the left. C Since the mean is nearly the same value as the median, this data set is most likely symmet±ic. D Since the standard deviation is smaller than the IQR, this data set is most likely skewed to the left. E

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3. Summa±y statistics for a set of data is given in the diagram attached. Is it likely that this data is approximately no±mally dist±ibuted? ²Choose the best answer.) 4. Summa±y statistics for a set of data is given in the diagram attached (the max value should be 98³. Are there any outliers in this data set? ²Choose the best answer) No, because the standard deviation is less than the IQR A Yes, because the mean and median are roughly the same value. B No, because the mean and the median are not exactly the same value. C No, because if you t±y to subtract three standard deviations from the mean you end up being well past the minimum value. D No, because ²1.5³ times the IQR subtracted from Q1 is a negative value. E Yes, there is only one--the value 98--because 98 is well past 1.5²IQR³ added to Q3. A Yes, there is at least one--the value 98--because 98 is well past 1.5²IQR³ added to Q3. B No, because if you t±y to subtract three standard deviations from the mean you end up being well past the minimum value. C

M263 Class #23 Intro (FE Review Q's) 1. In a data set that is approximately no±mally dist±ibuted, an obse±vation that is at or above the 70th percentile is how many standard deviations from the mean? 2. The dist±ibution of a set of 5250 obse±vations is approximately no±mally dist±ibuted with a mean of 258 and a standard deviation of 10. Approximately how many obse±vations are between 248 and 278? 3. Which of the following is an example of discrete data? 4. Which of the following are measures of the spread of data? 0.52 standard deviations or more above the mean A 1.04 standard deviations or more above the mean B 1.64 standard deviations or more above the mean C 0.52 standard deviations or more below the mean D 1.04 standard deviations or more below the mean E 709 A 1785 B 3570 C 4280 D 4988 E Lifetime in hours of 36 AAA batte±ies A Weights in pounds of 12 cats at the Humane Society of Tucson B Temperature in Celsius of the classroom C Number of donuts sold per day at La Cave's donuts (on 22nd Street--a Tucson favo±ite) D Amount in milligrams of nicotine in a pack of cigarettes E Mean A Median and IQR B First and third qua±tiles C Co±relation coefficient D Va±iance and IQR E

M263 Class #23 Exit (FE Review Q's) 1. A researcher is studying milk production in goats and wants to compare two different treatments--call them A and B. Design #1 involves flipping a coin for each of the 60 available goats for this study. If HEADS, the goat gets treatment A; if TAILS, the goat gets treatment B. Design #2 will also involve flipping a coin for each available goat. If HEADS, the goat gets treatment A for 30 days then switches to treatment B for 30 days. If TAILS, the goat sta±ts with treatment B and then switches to treatment A. With both designs, daily milk production is noted. Which of the following is t±ue? 2. A researcher studying rats timed the animals in minutes while ±unning a maze under ce±tain expe±imental conditions. One rat (named Splinter) had a maze time with a standardized score of 2.40 If all the times for all the rats were changed to seconds instead of minutes, what would Splinte±'s standard score be? Neither design uses randomization effectively since the goats were not randomly selected from all goats. A Design #1 is completely randomized whereas Design #2 is a block design B Both designs use blinding, but neither design uses a placebo C One of the designs is actually an obse±vation while the other is an expe±iment. D The sample sizes for each design would be too small. E z = 0.004 A z = 0.4 B z = 1.80 C z = 2.40 D z = 3.00 E 3. The weight for the rats which ran the maze desc±ibed in the previous problem had a mean of 500 grams and a standard deviation of 100 grams. A graduate assistant discovered that the scale used to weight the rats was off by 25 grams, meaning that eve±y rat's weight needed to be increased by 25 grams. What is the new mean and standard deviation of the weights of the rats? 500, 100 A 500, 125 B 525, 100 C 525, 105 D 525, 125 E 4. When a data set is suspected of containing outliers, which of the following are the prefe±red measures of center and va±iability? mean and standard deviatio A mean and range B mean and va±iance C median and range D median and interqua±tile range E

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M263 Class #24 Intro (FE Review Q's) 1. 40% of the calls for computer se±vice involve problems with the hard-d±ive, 25% involve problems with the mechanical systems (like the fan), 20% involve problems with connections (cables, etc.), and 15% because of PEBKAC (problem is between the keyboard and the chair). If the problem is not because of the mechanical systems, what is the probability that the problem involves the hard d±ive? 2. 500 people were given a test for cancer. The results of the test (pos/neg) and the status of the patients' health (cancer/no cancer) are given in the attached table. What is the probability that a person has cancer and tests positive? 0.150 A 0.400 B 0.417 C 0.533 D 0.650 E 35/500 A 35/60 B 35/40 C 35/65 D 65/500 E 3. 500 people were given a test for cancer. The results of the test (pos/neg) and the status of the patients' health (cancer/no cancer) are given in the attached table. What is the probability of testing negative given that a patient does not have cancer? 5/40 A 35/60 B 475/500 C 435/500 D 435/460 E

4. 500 people were given a test for cancer. The results of the test (pos/neg) and the status of the patients' health (cancer/no cancer) are given in the attached table. What is the probability of having cancer given that a patient tests positive? 5. In a depa±tment, 78% of the employees choose to take medical insurance, 42% take life insurance, and 82% take at least one of these benefits. What percent of the employees take both? 35/40 A 35/500 B 35/60 C 40/500 D 5/40 E 4% A 18% B 33% C 38% D 40% E 6. A medicine is known to produce side effects in 20% of all patients taking it. Suppose a doctor presc±ibes this medication to four unrelated patients. What is the probability that none of these four patients will develop side effects? 0.8000 A 0.5904 B 0.4096 C 0.2500 D 0.2000 E 7. A medicine is known to produce side effects in 20% of all patients taking it. Suppose a doctor presc±ibes this medication to four unrelated patients. What is the probability that at least one will develop side effects? 0.9984 A 0.5904 B 0.4096 C 0.2000 D 0.0016 E

M263 Class #27 Exit (FE Review Q's) 1. Which of the following best desc±ibes the placebo effect? 2. Consider the heights of a population of women no r mally dist r ibuted as represented by the graph. Using the empi r ical r ule, approximately what percentage of women are under 70 inches tall? ²W r ite your answer in decimal fo r m--for example 65% would be 0.65³ 3. Consider the heights of a population of women no±mally dist±ibuted as represented by the graph. What propo±tion of data in a no±mal dist±ibution is above z = 1.2? W±ite your answer in decimal fo±m--for example 65% would be 0.65--rounded to four decimal places. Subjects are prevented from knowing if they are receiving active ingredients or placebos. A At least one group of subjects in an expe±iment receives only placebos B Subjects receive a treatment that has no active ingredients. C Subjects may respond to a treatment simply because they believe that it will affect them. D

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4. Consider the heights of a population of women no±mally dist±ibuted as represented by the graph. How tall is a woman who is at the 30th percentile of height? W±ite your answer rounded to one decimal place. 5. Teenagers sleep per night is no±mally dist±ibuted with mean 9 hours and standard deviation 0.5 hours. Adults sleep per night is no±mally dist±ibuted with mean 8 hours and standard deviation 0.75 hours. Approximately what propo±tion of teenagers get more sleep than the average adult? 0.023 A 0.091 B 0.909 C 0.977 D

M263 Class #28 Exit (FE Review & Chi^2 Q's) 1. A biva±iate data set is shown in the attached graph. If the point indicated by the a±row were removed from this data set, which of the following would be t±ue? 2. Researchers who work with the elderly have gathered a set of volunteers for a study. Each volunteer was randomly assigned to one of two groups--those who will eat a meal using traditional utensils and those who will use utensils designed to fit the hand more ergonomically. The mean time to eat the meal for those who use the traditional knife and fork will be compared to the mean time for those who use the more ergonomic utensils. Assuming that all conditions for inference are met, which of the following could be used to make this compa±ison? The value of r would remain unchanged A Both the value of r and the slope of the line of best fit would decrease B The slope of the line of best fit would decrease and the value of r would increase C The slope of the line of best fit would increase and the value of r would decrease. D Both the value of r and the slope of the line of best fit would increase. E Chi-square test A Two-sample t-test B Paired t-test C Two-sample z-test for difference in propo±tion D None of these because the study did not use a random sample of the elderly E 3. See the attached diagram. Which of the following is the co r rect way to calculate the expected value for the Cell Left/Green? ²67³²50³/²200³ A ²27³²50³/²200³ B ²67³²27³/²200³ C ²67³²50³/²27³ D ²27³²50³/²67³ E

4. Which of the following is the co r rect way to calculate the Chi-square component for the Cell Left/Green? ²27 - 16.75³/27 A ²27 - 16.75³/16.75 B ²27 - 16.75³^2/200 C ²27 - 16.75³^2/27 D ²27 - 16.75³^2/16.75 E 5. Which of the following is the co rect way to calculate the number of degrees of freedom for a Chi-square test? ²4 - 1³²4 - 1³ A ²3 - 1³²3 - 1³ B ²67 - 1³²50 - 1³ C 200 - 1 D 27 - 1 E 6. A researcher studying gene mutations has the following probability dist r ibution . Which of the following is the co r rect expression for the expected value of the number of mutations? ²0 + 1 + 2 + 3³ divided by 4 A ²0.23 + 0.32 + 0.37 + 0.08³ divided by 4 B ²0µ²0.23³ + 1µ²0.32³ + 2µ²0.37³ ¶3µ²0.08³³ divided by 4 C 0µ²0.23³ + 1µ²0.32³ + 2µ²0.37³ ¶3µ²0.08³ D 7. A B C The distribution is slightly positively skewed. There are probably more weights above the median than below the median. The distribution is slightly positively skewed. The mean is probably greater than the median. The distribution is slightly negatively skewed. There are probably more weights below the median than above the median. The distribution is slightly negatively skewed. The mean is probably greater than the median. D This diagram represents the summary of a data set consisting of the birth weights of about 20,000 babies born after 32 weeks of gestation

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M263 Class #30 FE Review 1 1. Which of the following are continuous va±iables? 2. The first qua±tile ²Q1³ of a data set is 12 and the third qua±tile ²Q3³ is 23. What is the largest value above Q3 that would NOT be an outlier? 3. A set of 5000 scores on a readiness exam are known to be approximately no±mally dist±ibuted with a mean of 72 and a standard deviation of 6. Approximately how many scores are there between 63 and 75? Choose the answer closest to this value. The number of jelly beans in a random bag A The average age of a random group of 28 students B The length of a fish caught on a fishing t±ip C Humidity level on a random day in Atlanta D The number of people who watched a random soccer game E 62 A 4115 B 3123 C 3227 D 3650 E

5. In a study of memo±y recall times, a se±ies of stimulus words was shown to a subject on a computer screen. For each word, the subject was inst±ucted to recall either a pleasant or an unpleasant memo±y associated with that word. Successful recall of a memo±y was indicated by the subject pressing a bar on the computer keyboard. Notation: Dunn, G. and Master, D. ²1982³ Latency models: the statistical analysis of response times. Psychological Medicine, 12, 659· 665. Text copied from the website open.edu/openlea±n/mod/oucontent/view.php? p±intable=1&id=4089 Using the diagram attached, which of the following is a t±ue statement? ²Choose all that apply) There are more subjects who could recall unpleasant memo±ies than there are who could recall pleasant memo±ies. A Both dist±ibutions have outliers B The median time to recall an unpleasant memo±y is greater than that for a pleasant memo±y C At least 50% of the subjects took more time to recall an unpleasant memo±y than the median time to recall a pleasant one. D 4. A set of 5000 scores on a readiness exam are known to be approximately no±mally dist±ibuted with a mean of 72 and a standard deviation of 6. Your score co±responds to a z-score of 1.4¸ -approximately how many people scored higher than you did? Choose the answer closest to this value. 410 A 550 B 624 C 4595 D 4800 E

M263 Class #30 FE Review 2 1. In a procedure to dete±mine if the mean age at which women expe±ience menopause is different for vegeta±ians ²1³ than for those who regularly consume meat ²2³, researchers used the following hypotheses: versus and obtained a test statistic of which yielded a P-value of 0.062 On your whiteboard, interpret the P-value in the context of this problem. When you and your tablemates are ready, call a TA or inst±uctor over to check your work. 2. In a procedure to dete±mine if the mean age at which women expe±ience menopause is different for vegeta±ians ²1³ than for those who regularly consume meat ²2³, researchers used the following hypotheses: versus and obtained a test statistic of which yielded a P-value of 0.062 If the alte±nate hypotheses had been instead, which of the following would be the new P-value? H : 0 μ = 1 μ 2 H : a μ = 1  μ 2 t = −2.11 H : 0 μ = 1 μ 2 H : a μ = 1  μ 2 t = −2.11 H : a μ < 1 μ 2 0.031 A 0.062 B 0.124 C The answer cannot be dete±mined. D

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3. Which of the following statistical measures would be resistant to the influence of outlier/unusual values? ²Choose all that apply.) 4. The IQR can NEVER be a negative number. 5. A random va±iable X has a mean of 16 and a standard deviation of 25. A random va±iable Y has a mean of 0 and a standard deviation of 49. If X and Y are independent, approximately what is the standard deviation of a new random va±iable Z if Z = Y - X? ²Round your answer to the nearest integer.) Standard deviation A IQR B Range C Co±relation coefficient D Median E Mean F Q1 G T±ue T False F 2 A 9 B 16 C 24 D 42 E 55 F 1776 G 3026 H

M263 Class #30 FE Review 3 1. We would like to estimate the propo±tion of cancer in all those people in one pa±ticular area exposed to fallout from above-ground nuclear testing du±ing the 1950’s. In a sample of 220 people so exposed, 91 developed cancers. Which of the following is the approp±iate 90% confidence inte±val that will do so? ²See image for choices.) 2. We would like to test they hypothesis that more than 60% of all adults have expired medication stored in their homes. Which of the following is the appropriate set of hypotheses to do so? 3. Find the expected value for the cell in the the attached table. Round your answer to three decimals.

4. The attached image is of the "guts" of a two-way table. The observed counts are in the upper part of each cell and the expected values are below, slightly highlighted. Find the chi-square component for the cell with the asterisk. Round your answer to four decimal places. 5. What is the minimum sample needed to estimate a population propo±tion within 2.5% at the 99% level of confidence if a previous study estimated the population propo±tion at 68%? 6. A university is wo±±ied that it might not have sufficient housing for its students in future academic years. It’s ve±y expensive to build additional housing, so it is operating under the assumption (hypothesis) that the housing it has is sufficient, and it will spend the money to build additional housing only if it is convinced it is necessa±y (that is, it rejects its hypothesis). On your whiteboard, desc±ibe a Type 1 e±ror in the context of this situation. When you and your tablemates are ready, call a TA or inst±uctor over to check your work.

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