Math 1330 Practice Final Exam The following scatterplot shows the percentage of t he vote Kerry received in the 2004 presidential election according to the voter’s income level based on an exit poll of voters conducted by CNN. The income levels 1 8 correspond to the following income classes: classes: 1 Under $15,000; 2 $15 30,000; 3 $30 50,00 50,000; 0; 4 $50 75,000 75,000;; 5 $75 100 100,000 ,000;; 6 $100 150,000; 7 $150 200,000; 8 $200,000 or more. -
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1) Which of the following describes the linear association between income level and percentage of the vote won by Kerry? A) weak, negative B) weak, positive C) no linear association D) strong, positive E) strong, negative Provide an appropriate response. 2) The correlation between the total box office receipts of the Oscar winner for best picture and the total number of Oscar nominations nominations won is 0.69 for the best picture winners from 1990 to 2006 (www.boxofficemojo.com/oscar). (www.boxofficemojo.com/oscar ). Assuming that the association association is linear, describe the association. A) Weak linear association in a positive direction evidence of association B) No evidence linear association in a negative negative direction C) Strong linear D) Weak linear association in a negative direction linear association in a positive direction E) Strong linear 3) A random sample of records of electricity usage of homes gives the amount of electricity used in July and size (in square feet) of 135 homes. A regression to predict predict the amount of electricity used used (in kilowatt- hours) based on size was performed. Assume that a linear model is appropriate. What are the variables and units in this regression? A) Size (in square feet) is y and number of homes is x. B) Amount of electricity used (in kilowatt - hours) is y and size (in square feet) is x. C) Amount of electricity used (in kilowatt - hours) is y and number of homes is x. D) Number of homes is y and amount of electricity used (in kilowatt - hours) is x. E) Size (in square feet) is y and amount of electricity used (in kilowatt - hours) is x. 1
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4) A psychologist does an experiment to determine whether an outgoing person can be identified by his or her handwriting. She claims that the correlation of 0.89 shows that there is a strong causal relationship between personality type and handwriting. Explain what is wrong with her interpretation. A) This value for the correlation does not show any association between personality type and handwriting B) Finding an association between personality type and handwriting does not imply a causal connection. The high correlation could also be due to an outlier. C) Her interpretation is correct. D) This value for the correlation proves only that there is a weak causal relationship between personality type and handwriting E) This value for the correlation proves that there is not a causal relationship between personality type and handwriting
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5) A study of consumer behavior finds a positive correlation between sales of ice cream and sales of soda. What might explain the strong correlation? A) People generally have ice cream for dessert if they have drunk soda with a meal. B) Ice cream creates a thirst for soda C) No lurking variable D) Outdoor temperature E) Arithmetic mistake
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Select the most appropriate answer. 6) Which of the following statements is true? A) Correlation does not imply causation. B) None of these. C) Association does not imply causation. D) The direction of the association between two variables can change with the inclusion of a third variable. E) All of these. Provide an appropriate response. 7) Of the 5000 outpatients released from a local hospital in the past year, one hundred were contacted and asked their opinion on the care they received. Select the first five patients who belong to the simple random sample. 16348
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A) 16, 34, 69, 38, 13 B) 1, 6, 3, 4, 8 C) 163, 487, 693, 169, 513 D) 1634, 3890, 1695, 1392, 1509 E) 163, 169, 15, 92, 97 List all possible samples from the specified population. 8) A swim team must select two of its four assistant coaches to accompany the team to an upcoming swim meet. What is the chance that assistant coach C attends the meet? A) 0.5 B) 0.17 C) 0.33 D) 0.25
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Identify which type of sampling is used. 9) A market researcher selects 500 drivers under 30 years of age and 500 drivers who are 30 years of age and older. A) Matched pair sample B) Stratified random sample C) Convenience sample D) Cluster random sample E) Simple random sample 10) The student dean of a university uses a computer to randomly select 500 student indentification numbers then interviews the students corresponding to those indentification numbers. A) Matched pair sample B) Convenience sample C) Simple random sample D) Cluster random sample E) Stratified random sample Provide an appropriate response. 11) You flip a coin x number of times and calculate the probability of heads as (number of heads)/x. What happens to this probability as x gets larger? A) It gets smaller B) It gets closer and closer to 0.50 C) It gets larger D) It stays the same, 0.50
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12) You play a game where you are to guess under which of 4 cups a coin has been placed. How many times would you expect to guess correctly in 20 plays of the game? Note that the coin is moved after each play. A) 1 B) 5 C) 10 D) 4
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13) Suppose the following tree diagram summarizes the responses of 500 people to two questions, where the first response is either yes or no and the second is multiple choice with three possible answers (A, B or C). Use the tree diagram to calculate the probability that a person answered B to the multiple choice question.
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A) 0.07
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D) 0.04
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E) 0.31
Find the indicated probability. 14) If two balanced die are rolled, the possible outcomes can be represented as follows. (1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (1, 2) (2, 2) (3, 2) (4, 2) (5, 2) (1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (1, 6) (2, 6) (3, 6) (4, 6) (5, 6)
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(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)
Determine the probability that the sum of the dice is 4 or 12. 1 1 5 A) B) C) 9 6 36
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Provide an appropriate response. 15) A group of volunteers for a clinical trial consists of 88 women and 87 men. 20 of the women and 17 of the men have high blood pressure. Are high blood pressure and gender independent? Explain. A) Yes; P(High blood pressure Female) =0.227 P(High blood pressure Male) =0.227 These are equal. B) Yes; P(High blood pressure Female) =0.211 P(High blood pressure Male) =0.211 These are equal. C) No; P(High blood pressure and Male) =0.097 P(High blood pressure and Female) =0.114 These are not equal D) Yes; a patient with high blood pressure cannot be both male and female E) No; P(High blood pressure) =0.211 P(High blood pressure Female) =0.227 These are not equal Find the indicated probability. 16) A group of volunteers for a clinical trial consists of 81 women and 77 men. 18 of the women and 19 of the men have high blood pressure. If one of the volunteers is selected at random find the probability that the person has high blood pressure given that it is a woman. A) 0.486 B) 0.234 C) 0.356 D) 0.114 E) 0.222 Provide an appropriate response. 17) The expression P(A and B) =P(A)P(B|A) is valid if A) A and B are dependent. B) A and B are independent. C) only if A equals B . D) for any events A and B. E) A and B are mutually exclusive.
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1 2 18) If A and B are independent events, with P(A) = , P(B) = , then P(A or B) 5 5
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A) cannot be determined from the given information. 3 B) equals . 25 C) equals
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D) equals
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3 E) equals . 5 Determine the possible values of the random variable. 19) For a randomly selected student in a particular high school, let Y denote the number of living, blood- related grandparents of the student. What are the possible values of the random variable Y? A) 0, 1, 2, 3, 4 B) 0, 1, 2 C) 4 D) 1, 2, 3, 4 Find the mean of the given probability distribution. 20) The random variable X is the number of houses sold by a realtor in a single month at a particular real estate office. Its probability distribution is given in the table below. x P(X =x) 0 0.24 1 0.01 2 0.12 3 0.16 4 0.01 5 0.14 6 0.11 7 0.21 A) 3.60 B) 3.50 C) 3.35 D) 3.40 Use the empirical rule to solve the problem. 21) The systolic blood pressure of 18- year- old women is normally distributed with a mean of 120 mmHg and a standard deviation of 12 mmHg. What percentage of 18 - year- old women have a systolic blood pressure between 96 mmHg and 14 4 mmHg? A) 68% B) 67% C) 95% D) 99.99% E) 99.7% Use a table of areas to find the specified area under the standard normal curve. 22) The area that lies between - 1.10 and - 0.36 A) 0.4951 B) 0.2237 C) - 0.2237 D) 0.7763
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E) 0.2239
Find the mean of the binomial random variable. 23) According to a college survey, 22% of all students work full time. Find the mean for the random variable X, the number of students who work full time in samples of size 16. A) 2.75 B) 0.22 C) 4.00 D) 4.26 E) 3.52 Find the standard deviation of the binomial random variable. 24) According to a college survey, 22% of all students work full time. Find the standard deviation for the random variable X, the number of students who work full time in samples of size 16. A) 1.88 B) 3.52 C) 1.98 D) 2.75 E) 1.66 5
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Find the mean/standard error of the sampling distribution of the proportion. 25) Based on past experience, a bank believes that 8% of the people who receive loans will not make payments on time. The bank has recently approved 600 loans. Describe the sampling distribution model of the proportion of clients in this group who may not make timely payments. A) mean =92%; standard error =1.1% B) mean =8%; standard error =0.3% C) mean =92%; standard error =0.3% D) mean =8%; standard error =1.1% E) There is not enough information to describe the distribution.
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For samples of the specified size from th e population described, find the mean and standard error of the sampling distribution of the sample mean x. 26) The mean and the standard deviation of the sampled population are, respectively, 113.9 and 32.1.
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n =64 A) mean=113.9; standard error =4.0 B) mean=113.9; standard error =0.5 C) mean=4.0; standard error =113.9 D) mean=113.9; standard error =32.1 E) mean=113.9; standard error =2.3 Provide an appropriate response. 27) Assume that the heights of adult Caucasian women have a mean of 63.6 inches and a standard deviation of 2.5 inches. If 100 women are randomly selected, find the probability that they have a mean height greater than 63.0 inches. A) not enough information to determine B) 0.9918 C) 0.2881 D) 0.8989 E) 0.0082
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28) According to a Harris poll conducted in October, 2007, 71% of 1052 American adults believe that increased carbon dioxide and other gases released into the atmosphere will, if unchecked, lead to global warming and an increase in average temperatures. Assuming the population proportion i s .75, how many standard deviations above or below the mean does the Harris poll sample fall? A) 3 below B) 3 above C) 0.003 below D) 2.86 above E) 2.86 below
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29) In a survey of 500 residents, 300 were opposed to the use of the photo - cop for issuing traffic tickets. Find a 95% confidence interval for the population proportion who are opposed to the use of the photo- cop for issuing traffic tickets if the standard error of the estimate is 0.022. A) (0.564, 0.636) B) (0.578, 0.622) C) (300, 500) D) none of these E) (0.557, 0.643)
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30) Why is a point estimate alone not sufficiently informative?
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Find the standard error 31) In a sample of 200 observations, there were 80 positive outcomes. Find the standard error for the sample proportion. A) 0.0420 B) 0.0692 C) 0.0616 D) 0.120 E) 0.0346
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Use the given degree of confidence and sample data to construct a confidence interval for the population proportion. 32) A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature. 32) Construct a 95% confidence interval for the proportion of all voters in the state who favor ap proval. A) (0.469, 0.475) B) (0.423, 0.520) C) (0.431, 0.512) D) (0.444, 0.500) E) (0.438, 0.505) Determine the margin of error in estimating the population parameter. 33) Based on a sample of 39 randomly selected years, a 90% confidence interval for the mean annual precipitation in one city is from 42.8 inches to 45.2 inches. A) 2.4 inches B) 0.60 imches C) 1.2 inches D) 0.32 inches E) 0.10 inches Construct the requested confidence interval from the supplied information. 34) Thirty randomly selected students took the statistics final. If the sample mean was 82 and the standard deviation was 12.2, construct a 99% confidence interval for the mean score of all students. A) (75.86, 85.78) B) (75.86, 88.14) C) (76.52, 87.48) D) (78.22, 85.78) E) (75.88, 88.19) Provide an appropriate response. 35) A survey of shoppers is planned to determine what percentage use credit cards. Prior surveys suggest 63% of shoppers use credit cards. How ma ny randomly selected shoppers must we survey in order to estimate the proportion of shoppers who use credit cards to within 4% with 95% confidence? A) 1513 B) 504 C) 560 D) 432 E) 967 Select the most appropriate answer. 36) What factor or factors affect the choice of the sample size when estimating µ or p? A) variability in the data B) all of these C) financial cost D) desired precision E) confidence level
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Express the null hypothesis. 37) Which could be the null hypothesis for the true proportion of fireflies unable to produce light? A) H0 : p 0.0012 B) H0 : p <0.0012 C) H0 : p =0.0012 D) H0 : p >0.0012 E) H0 : p 0.0012
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Examine the given statement, then identify whether the statement is a null hypothesis, an alternative hypothesis or neither. 38) The mean income of workers who have majored in history is less than $25,000. 38) A) Neither B) Null hypothesis C) Alternative hypothesis
Find the P value for the indicated hypothesis test. 39) A medical school claims that more than 28% of its students plan to go into general practice. It is found that among a random sample of 130 of the school's students, 39% of them plan to go into general practice. Find the P- Value for testing the school's claim. A) 0.1635 B) 0.3461 C) 0.0026 D) 0.3078 E) 0.0280 -
State conclusion to significance test in terms of the null hypothesis 40) In a random sample of 88 adults from a particular town, it is found that 6 of them have been exposed to a certain flu strain. At the 0.01 significance level, test the claim that the proportion of all adults in the town that have been exposed to this flu strain differs from the nationwide percentage of 8%. H0 : p =0.08 Ha : p 0.08. = 0.01 Test statistic: z =- 0.41. P- Value =0.6828 State your conclusion in terms of H 0 . A) Reject H 0 since the P - value is larger than . B) Since the P- value is larger than , we conclude that the proportion of adults in this particular town that have been exposed to this flu strain differs from the nationwide percentage of 8%. C) Do not reject H0 since the P- value is larger than . D) Do not reject Ha since the P- value is larger than . E) Reject H a since the P - value is larger than .
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Assume that a simple random sample has been selected from a normally distributed population. State the final conclusion. 41) Test the claim that for the adult population of one town, the mean annual salary is given by 41)
µ =$30,000. Sample data are summarized as n =17, x =$22,298, and s =$14,200. Use a significance level of =0.05. H0 : µ =30,000 Ha : µ 30,000 State your conclusion about H0 . A) t =- 9.22, reject H0 B) t =- 2.24, do not reject H0 C) t =- 2.24, reject H0 D) z =- 2.24, reject H0 E) t =2.24, reject H0
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