1. A lawyer researched the average number of years served by 45 different justices on the Supreme Court. The average number of years served was 13.8 years with a standard deviation of 7.3 years. What is the 95% confidence interval estimate for the average number of years served by all Supreme Court justices? Place your limits, rounded to 1 decimal place, in the blanks. When entering your answer into the Final Exam Shell do not use any labels or symbols. Simply provide the numerical values. For example, 12.3 would be a legitimate entry.
Lower limit (first blank) = __________, Upper limit (second blank) = ___________.
2. Some defendants in criminal proceedings plead guilty and are sentenced without a trial, whereas others who plead innocent are subsequently found guilty and then are sentenced. In recent years, legal scholars have speculated as to whether sentences of those who plead guilty differ in severity from sentences for those who plead innocent and are subsequently judged guilty. Consider the data given below on defendants accused of robbery, all of whom, by the way, had previous prison records. At the .01 level of significance, do these data suggest that the proportion of all defendants in these circumstances who plead guilty and are sent to prison differs from the proportion who are sent to prison after pleading innocent and being found guilty?
A. No, because the test value -1.96 is inside the interval (-2.58, 2.58)
B. No, because the test value -4.94 is outside the interval (-1.96, 1.96)
C. Yes, because the test value -4.94 is outside the interval (-2.58, 2.58)
D. Yes, because the test value 2.58 is inside the interval (-4.94, 4.94)
3. Serum ferritin is used in diagnosing iron deficiency. In a study conducted recently researchers discovered that in a sample of 28 elderly men the sample standard deviation of serum ferritin was 52.6 mg/L. For 26 younger men the sample standard deviation was 84.2 mg/L. At the .01 level of significance, do these data support the conclusion that the ferritin distribution in elderly men has a smaller variance than in younger men?
A. No, because the test value 1.60 is less than the critical value of 2.54
B. Yes, because the test value 2.56 is greater than the critical value of 2.54
C. Yes, because the test value 0.390 is less than the critical value 2.54
D. Yes, because the test value 2.56 is greater than the critical value 0.394
4. The data presented in the table below resulted from an experiment in which seeds of 5 different types were planted and the number of seeds that germinated within 5 weeks after planting was recorded for each seed type. At the .01 level of significance, is the proportion of seeds that germinate dependent on the seed type?
A. Yes, because the test value 16.86 is greater than the critical value of 13.28
B. Yes, because the test value 16.86 is less than the critical value of 14.86
C. No, because the test value 16.86 is greater than the critical value of 13.28
D. No, because the test value 13.28 is less than the critical value of 16.86
5. A manufacturer of flashlight batteries took a sample of 13 batteries from a day's production and used them continuously until they failed to work. The life lengths of the batteries, in hours, until they failed were: 342, 426, 317, 545, 264, 451, 1049, 631, 512, 266, 492, 562, and 298. These data are also available in the worksheet Batteries in the Excel workbook MATH302_Final.xls.
At the .05 level of significance, is there evidence to suggest that the mean life length of the batteries produced by this manufacturer is more than 400 hours?
A. No, because the p-value for this test is equal to .1164
B. Yes, because the test value 1.257 is less than the critical value 1.782
C. No, because the test value 1.257 is greater than the critical value 1.115
D. Yes, because the test value 1.257 is less than the critical value 2.179
6. A survey of 85 families showed that 36 owned at least one DVD player. Find the 99% confidence interval estimate of the true proportion of families who own at least on DVD player. Place your limits, rounded to 3 decimal places, in the blanks. When entering your answer into the Final Exam Shell do not use any labels or symbols other than the decimal point. Simply provide the numerical values. For example, 0.123 would be a legitimate entry.
Lower limit (first blank) = __________, Upper limit (second blank) = ___________.
7. An agent for a residential real estate company in a large city would like to be able to predict the monthly rental cost of apartments based on the size of the apartment. Data for a sample of 25 apartments in a particular neighborhood are provided in the worksheet Apartments in the Excel workbook MATH302_Final.xls. At the .05 level of significance determine if the correlation between rental cost and apartment size is significant.
A. No, there is not a statistically significant linear relationship between monthly rental cost and apartment size, because the sample correlation coefficient is less than .95.
B. Yes, there is a statistically significant linear relationship between monthly rental cost and apartment size, because the p-value for this test is less than .0001.
C. Yes, there is a statistically significant linear relationship between monthly rental cost and apartment size, because the t-test value, 7.74, is greater than the critical value 1.96.
D. Yes, there is a statistically significant linear relationship between monthly rental cost and apartment size, because the sample correlation coefficient 0.85 exceeds 0.50.
8. Given the same data referenced in problem 7 above, find the estimated regression equation which can be used to estimate the monthly rent for apartments in this neighborhood using size as the predictor variable.
A.
B.
C.
D.
9. Given the same data referenced in problem 7 above, find a point estimate for the average monthly rent for apartments having 1,000 square feet of space. Place your answer, rounded to the nearest whole dollar, in the blank. When entering your answer into the Final Exam Shell do not use any labels or symbols. Simply provide the numerical value. For example, 123 would be a legitimate entry. ________________
10. A company operates four machines during three shifts each day. From production records, the data in the table below were collected. At the .05 level of significance test to determine if the number of breakdowns is independent of the shift.
A. The number of breakdowns is dependent on the shift, because the test value 11.649 is less than the critical value of 12.592.
B. The claim that the number of breakdowns is independent of the shift cannot be rejected, because the test value 11.649 is less than the critical value of 12.592.
C. The number of breakdowns is dependent on the shift, because the p-value is .07.
D. The number of breakdowns is independent of the shift, because the test value 12.592 is greater than the critical value of 11.649.
11. Find the probability, P(Z < 0.17), using the standard normal distribution.
A. .8300
B. .4325
C. .5675
D. .0675
12. The average height of flowering cherry trees in a nursery is 11 feet. If the heights are normally distributed with a standard deviation of 1.6, find the probability that a randomly selected cherry tree in this nursery is less than 13 feet tall.
A. 0.67
B. 0.89
C. 0.95
D. 0.11
13. Mrs. Smith's reading class can read a mean of 175 words per minute with a standard deviation of 20 words per minute. The top 3% of the class is to receive a special award. What is the minimum number of words per minute a student would have to read in order to get the award? Place your answer, rounded to the nearest whole number, in the blank. When entering your answer into the Final Exam Shell do not use any labels or symbols. Simply provide the numerical value. For example, 123 would be a legitimate entry.
14. The mean weight of loads of coal placed in train cars by a loading machine is 43.0 tons with a standard deviation of 8.0 tons. Assuming that the weight of loads placed in the train cars by this loader are normally distributed, if a random sample of 9 loads is chosen for a weight check, find the probability that the mean weight of those loads is more than 40.60 tons.
Place your answer, rounded to four decimal places, in the blank. When entering your answer into the Final Exam Shell do not use any labels or symbols other than a decimal point. Simply provide the numerical value. For example, 0.1234 would be a legitimate entry.
15. In a particular region of Cape Cod, it is known that lobstermen trap on average of 32 pounds of lobster per day with a standard deviation of four pounds. If a random sample of 30 lobster fishermen is selected, what is the probability that their average catch is less than 31.5 pounds?
Place your answer, rounded to four decimal places, in the blank. When entering your answer into the Final Exam Shell do not use any labels or symbols other than a decimal point. Simply provide the numerical value. For example, 0.1234 would be a legitimate entry.
16. Find the mean of the following probability distribution?
Place your answer, rounded to two decimal places, in the blank. When entering your answer into the Final Exam Shell do not use any labels or symbols other than a decimal point. Simply provide the numerical value. For example, 1.23 would be a legitimate entry.
17. If a gambler rolls two dice and gets a sum of four, he wins $10; and if he gets a sum of three, he wins $25. The cost to play the game is $5. What is the expectation of this game?
Place your answer, rounded to two decimal places, in the blank. When entering your answer into the Final Exam Shell do not use a dollar sign. However, if the expected payoff is negative be sure to use a minus sign. For example, -1.23 would be a legitimate entry.
18. At a certain college, there were 600 science majors, 200 engineering majors, and 500 business majors. If a student is selected at random, what is the probability that the student is an engineering major?
Place your answer, rounded to four decimal places, in the blank. When entering your answer into the Final Exam Shell do not use any labels or symbols other than a decimal point. Simply provide the numerical value. For example, 0.1234 would be a legitimate entry.
19. According to an Internet posting, 80% of adults enjoy drinking beer. If a group of 3 adults is selected at random, find the probability that none of them enjoy drinking beer.
Place your answer, rounded to three decimal places, in the blank. When entering your answer into the Final Exam Shell do not use any labels or symbols other than a decimal point. Simply provide the numerical value. For example, 0.123 would be a legitimate entry.
20. The median can be a more appropriate measure of central tendency than the mean if the distribution of the data is extremely skewed.
A. False
B. True
C. It doesn't matter, when data are skewed the mean and the median are the same
D. It doesn't matter, when data are skewed the mean, median, and mode are the same
21. According to Chebyshev's theorem, the proportion of values from a data set that is further than 2 standard deviations from the mean is at most:
A. 0.50
B. 0.13
C. 1.00
D. 0.25
22. In a study of elephants a researcher wishes to determine the average weight of a certain subspecies of elephants. From previous studies, the standard deviation of the weights of elephants in this subspecies is known to be 1500 pounds. How many elephants does the researcher need to weigh so that he can be 80% confident that the average weight of elephants in his sample is within 350 pounds of the true average weight for this subspecies?
A. 31
B. 39
C. 50
D. 166
23. A snack food manufacturer selected a sample of 15 bags of pretzels off the assembly line and weighed their contents. If the sample mean is 10.0 and the sample standard deviation is 0.15, find the 95% confidence interval estimate for the true mean weight of bags of this type of pretzel.
A. (9.92, 12.34)
B. (8.54, 11.46)
C. (10.42, 10.58)
D. (9.92, 10.08)
24. The city of Oakdale wishes to see if there is a linear relationship between the temperature and the amount of electricity used (in kilowatts). Based on the data in the table below, is there a significant linear relationship between temperature and the amount of electricity used? These data are also available in the worksheet temperature in the Excel workbook MATH302_Final.xls.
A. Yes, the sample correlation coefficient is equal to 0.981, which provides evidence of a significant linear relationship.
B. Yes, the sample correlation coefficient is equal to 0.878, which provides evidence of a significant linear relationship.
C. No, the sample correlation coefficient is equal to 0.098, which does not provide evidence of a significant linear relationship.
D. No, the sample correlation coefficient is equal to 0.981, which does not provide evidence of a significant linear relationship.
25. In a chi-square goodness-of-fit test when there is close agreement between the observed frequency and the expected frequency, the chi-square test value will be small.
A. True
B. False