Statistics
#61: In a hypothesis test, the value of αα represents: BONUS QUESTION: When testing a claim, if the test statistic is in the critical region (rejection region), then our decision is to:
the probability of accepting H1 when it is false. *the probability of rejecting H0 when it is true. the probability of making a correct decision the probability of failing to reject H0 when it is false. the probability that the significance level is true. *reject H0 fail to reject H0 accept H1 accept H0
#77: The coefficient of determination, r2, is a measure of:
the slope of the regression line skew *the amount of variation in the y-variable that is explained by the regression line the location of the regression line the spread of the predicted values
#59: In a Gallup poll of 300 randomly selected adults, 163 of them said that they were underpaid. Construct a 99% confidence interval estimate of the percentage of all adults who say that they are underpaid. Can we safely conclude that the majority of adults say that they are underpaid?
* 46.9% < p < 61.7%, no
#50: All possible random samples of size n = 4,096 are selected from a population with mean μμ = 256 and standard deviation σσ = 16. The standard error of the mean σ¯xσx¯ is:
*.25
#30: The probability that a person will get a cold this year is 0.7. If 3 people are selected at random, find the probability that all 3 will get a cold this year.
*0.343 2.1 0.21 0.0343 None of these
#51: IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. If 4 people are randomly selected, find the probability that their mean IQ is less than 107.
*0.8247 0.3204 0.6796 0.1753 0.9690
#31: In a recent survey of TV watching at 6:00 on Sunday night, 4 people watched ABC, 12 people watched NBC, and 7 people watched CBS. If a person is picked at random, what is the probability that the person watched NBC or CBS?
*19/23
#20: The approximate percentage of values in a data set that will fall between the 15thpercentile and the 43rd percentile is:
*28% 15% 58% 43% None of these
#54: Given that the 98% confidence limits for μμ are 37 and 61, which of the following could possibly be the 90% confidence limits?
*38 and 60 35 and 63 37 and 61 38 and 59 None of these could be the 90% confidence limits.
#41: Consider the following probability distribution. Find the variance.
*4.89 5 6.1 0.31 None of these
#28: Rosa is dealing you a four-card hand from a standard deck of 52 cards, 4 of which are tens. The probability that Rosa will deal you exactly four tens is:
*4/52⋅3/51⋅2/50⋅1/49
#78:A veterinarian collected a random sample of 19 pairs of data consisting of heights (x) and weights (y) of Chihuahuas. She computed the test statistic for this data to be r = -0.476, the mean height (¯xx¯) to be 6.65 inches, the mean weight (¯yy¯) to be 5.21 pounds, and the regression equation to be ˆy=0.71x−0.01y^=0.71x-0.01. Use a significance level of αα = 0.01, and find the best predicted weight (in pounds) for a Chihuahua that is 8.1 inches tall.
*5.21 6.65 4.71 5.74 None of these
#15: A distribution has a range of 65. The lowest score is 14. The highest score is:
*79 144 100 51 None of these
#49: Find the percentage of z scores that lie between z = -1.66 and z = 2.49 in a standard normal distribution.
*94.51% 4.21% 45.15% 49.36% 5.49%
#74: If the corelation between x and y is r = -0.79, which one of the following statements is true?
*Low values of x are associated with high values of y. The slope of the least-square regression line is m = b1 = -0.79. Low values of x are associated with low values of y. The y-intercept of the least-square regression line is the point (0, -0.79).
#64: A hypothesis test yields a test statistic of z = 2.18. Compute the P-value if this is a one-tailed test and if it is a two-tailed test.
*one-tailed P-value is 0.0146; and two-tailed P-value is 0.0292 one-tailed P-value is 0.9854; and two-tailed P-value is 0.4927 one-tailed P-value is 0.0146; and two-tailed P-value is 0.0073 one-tailed P-value is 0.9854; and two-tailed P-value is 1.9708
#48: (a) Use the normal distribution to approximate the desired binomial probability. IPS reports that 82% of its trains are on time. A check of 60 randomly selected trains shows that 55 of them arrived on time. Find the probability that among the 60 trains, 55 or more arrive on time. (b) Based on the result from part (a), would it be unusual for 55 or more trains to arrive on time?
0.0107 0.0256 *0.0375 0.0171 None of these *yes
#44: Assume a binomial probability distribution. Suppose seven percent of the population has hazel eyes. If 104 people are randomly selected, find the probability that more than 5 of them have hazel eyes.
0.1395 0.5978 0.9221 *0.7433 0.1172
#26: The batting average of the Macomb College baseball team is normally distributedwith a mean of 0.266 and a standard deviation of 0.034. If Ricardo is at the 40thpercentile, find his batting average.
0.275 0.257 0.300 *0.252 0.280
#45: In a standard normal distribution, find the area that is less than z = -1.34.
0.4099 None of these 0.1802 *0.0901 0.9099
#46: In a standard normal distribution, find the area that is greater than z = 0.66.
0.7454 0.2454 0.7546 *0.2546 None of these
#56: The 98% confidence interval estimate of the proportion of female medical school students is (0.309,0.389)(0.309,0.389). Find the point estimate of the proportion of females for all medical school students.
0.980 0.309 *0.349 0.389 0.010
#40: Consider the following probability distribution. Find the mean (or expected value).
1.3 *1.2 0.2 2 None of these
#53: Computed using the same data, a 93% confidence interval for a population mean is ________ a 97% confidence interval for the same mean.
less than or equal to equal to *narrower than wider than
#73: Which of the following value of r indicates the weakest linear correlation between two variables?
*r = -0.11 r = 0.48 r = -0.34 r = 0.43
#35: If P(A) = 0.44, P(B) = 0.35, and the events A and B are disjoint, then P(A or B) is:
0.154 0.636 0.21 *0.79 None of these
#39: True or false: The data given in the following table satisfies all of the required conditions for a probability distribution.
False, because ∑(P(x))≠1∑(P(x))≠1 False, because there is a missing value of x = -1 False, because there is a negative value for x *True
#1: Which of the following data sets measure attributes that are categorical (qualitative)?
heights test scores weights *colors
#60: If you are using a t-test when testing a claim about a population mean and the sample size is 25, the number of degrees of freedom is:
*24 25 26 None of these
#82: A study is done to determine, at the 20% level of significance, if traffic accidents occur with equal frequency throughout the week. Of the 280 accidents pulled from the files, the distribution of observed traffic accidents is shown below. What is the value of the test statistic for a χ2 Goodness-of-Fit/Multinomial test? BONUS QUESTION: State the decision of this test.
*75.150 *reject H0
#70: Captopril is a drug designed to lower systolic blood pressure. When subjects were tested with this drug, their systolic blood pressure readings were measured before and after drug treatment, with the results given below. Assume an approximately normal distribution, if necessary. Use the sample data to construct a 95% confidence interval for the mean difference between the before and after readings.
*9.4 < μ1−μ2μ1-μ2 < 35.9 8.4 < μdμd < 37 9.3 < μ1−μ2μ1-μ2 < 36 11 < μdμd < 34.3 9.9 < μdμd < 35.4
#80:A study investigates income level in the U.S. to determine if it is independent of region. If there are eleven regions and ten income levels, how many degrees of freedom are there to find the critical value for a χ2χ2 test of independence?
*90 109 110 108 10
#38: Provide a written description of the complement of the given event: "At most five of the six connections are bad."
*All of the connections are bad. At most five of the connections are good. None of the connections are bad. All of the connections are good. At most four of the connections are bad.
#76: When testing the claim H1:ρ≠0 for 14 pairs of (x, y) data, the Pearson correlation coefficient test statistic is r = -0.428. Find the critical values for this test, and state the decision and conclusion of this test at a significance level of 0.05.
*Fail to reject H0: ρρ = 0, and conclude that there is no linear correlation.
#71:When testing the claim that the mean of the differences is at least zero, suppose you get a test statistic of t = -0.44 and a P-value of 0.3312. What should we conclude about the claim?
*There is not sufficient evidence to warrant rejection of the claim.
#25: A sample of children has a mean weight of ¯xx¯ = 42 pounds and a standard deviation of s = 6 pounds. If one of the children weighs x = 51.6 pounds, find his z score.
*z = 1.6 z = 57.6 z = -1.6 There is not enough information to answer this question. None of these.
23: What is the mode for the data set summarized by the following stem and leaf plot?
0 and 9 9 9 and 10 *10 0
#10. The taxi-in time for 40 flights that landed in Los Angeles have a mean of 10.3 minutes and a standard deviation of 5.7 minutes. Approximately what percentage of taxi-in times is less than the 61st percentile?
0% 39% 50% *61% 100%
#47: Assume values are normally distributed with a mean of 16 and a standard deviation of 4. The probability that a randomly selected value lies between 21 and 23 is:
0.9599 0.8543 *0.0655 0.8944 None of these
#68: In a survey of 345 randomly selected workers, 24.06% got their jobs through ads placed in technical publications. Consider a hypothesis test that uses a 0.025 significance level to test the claim that more than 20% of workers get their jobs through ads placed in technical publications. What is the P-value?
1.884 between 0.95 and 1 between 0.05 and 0.95 *between 0 and 0.05 -1.884
#84: The contingency table below shows the results from a survey of 321 randomly selected Macomb County registered voters. This survey was conducted to test the claim that voters' opinions on a particular bill and their party affiliation are independent. (a) At αα = 0.1, what is the critical value? (b) Find the expected frequency (E) used in the calculation of the χ2χ2 test statistic for the cell in the third row (Green Party) and second column (Disapprove). BONUS QUESTIONS: Calculate the test statistic, and state the conclusion for this test of independence. Test statistic: χ2 = (Give your answer rounded to 3 places after the decimal point.) Conclusion of this test:
10.645 16.682 3.053 There is not sufficient evidence to warrant rejection of the claim that voters' opinions on a particular bill and their party affiliation are independent.
#83: The contingency table below shows the results from a survey of 343 randomly selected Macomb County registered voters. This survey was conducted to test the claim that voters' opinions on a particular bill and their party affiliation are independent. (a) At αα = 0.01, what is the critical value? (b) Find the expected frequency (E) used in the calculation of the χ2χ2 test statistic for the cell in the fourth row (Independent) and first column (Approve). BONUS QUESTIONS: Calculate the test statistic, and state the conclusion for this test of independence. Test statistic: χ2 = (Give your answer rounded to 3 places after the decimal point.) Conclusion of this test:
16.812 12.848 7.623 There is not sufficient evidence to warrant rejection of the claim that voters' opinions on a particular bill and their party affiliation are independent.
#21: There are 490 statistic students at Macomb Community College who have a mean grade point average of ¯xx¯ = 2.9 and a standard deviation of s = 0.4. Which of the following grade point averages would be an unusual grade for statistics students at MCC? Consider a value unusual if it is not within 2 standard deviations of the mean.
3.6 2.2 2.8 3.4 *None of the above
#43: If a procedure yields a binomial probability distribution with n = 500 trials and probability of success p = 0.65, then use μ±2σ to find the range of usual values.
315 to 335 229 to 271 212 to 438 98 to 552 *304 to 346
#12. Use the following frequency distribution table to find the value of the mean score. Follow-up Question: Find the value of the standard deviation. Give your answer accurate to 1 place after the decimal point.
33.5 13.3 34.0 30.5 13.3 *15.8
#37: A family has 6 children. Assuming that only two genders (male or female) are possible for each child, how many different gender sequences are possible?
36 12 *64 6 None of these
#24: Use the histogram to approximate the mode heart rate of adults in the gym.
38 95 *80 44 75 and 85
#55:What is the minimum sample size needed to estimate the mean age of books in a library to within 6 months with 99.8% confidence if the standard deviation of the ages is thought to be about 95 months?
46 2,116 49 *2,395 None of these
#79: A veterinarian collected a random sample of 16 pairs of data consisting of heights (x) and weights (y) of Chihuahuas. She computed the test statistic for this data to be r = 0.398, the mean height (¯xx¯) to be 7.92 inches, the mean weight (¯yy¯) to be 5.24 pounds, and the regression equation to be ˆy=0.92x−1.63y^=0.92x-1.63. Use a significance level of αα = 0.05, and find the
5.66 *5.24 4.44 7.92 None of these
#22: The Locator formula is L = (k/100)n. Find the value of the first quartile Q1 for the data set summarized by the following stem and leaf plot.
54 53.5 *53 50.5 None of these
#32: In horse racing, a trifecta is a bet that the first three finishers in a race are selected in the correct order. In a race with 11 horses, how many different trifecta bets are possible?
6 39,916,800 165 *990 None of these
#14: If the standard deviation for a set of data is 36, then the variance is:
72 *1296 1679616 18 6 None of these
#13. The percent of values in a data set that lie between Q1 and Q2 is:
75% 34% *25% 68% 50% 100% None of these
#57: Find the minimum sample size needed to estimate the percentage of librarians who have a child. Use a 0.07 margin of error, use a confidence level of 95%, and use results from a prior Harris poll suggesting that 32% of librarians have a child.
9 3 121 *171 None of these
#81: A researcher surveys 51 people--consisting of heavy smokers, moderate smokers, light smokers, and non-smokers--to see how many times per year they have an illness requiring them to see a doctor. The categories for the columns are 0-1 visits, 2-3 visits, and 4 or more visits. If the researcher wishes to test the null hypothesis that the number of illnesses per year requiring a visit to the doctor are independent of smoking, what is the critical value for the χ2 test of independence at αα = 0.2?
9.803 5.989 15.812 *8.558 58.164
#16: The mean of a distribution of test scores is 60 and the standard deviation is 8. We plan to curve the exam by adding 12 points to each score. How will this change the mean and standard deviation of the distribution?
Both the mean and standard deviation of the distribution will be increased by 12 points. *The mean of the distribution will be increased by 12 points, but the standard deviation will remain unchanged. Neither the mean nor the standard deviation will be changed. The mean will be unchanged, but the standard deviation will increase by 12 points. None of these.
#63: Suppose p represents the true proportion of college freshmen who can read at the 12th grade level. Some educators claim that 19% of all college freshmen can read at the 12th grade reading level. Select the appropriate alternate hypothesis.
H1: p < 0.19 *H1: p ≠≠ 0.19 H1: p > 0.19 H1: p = 0.19 None of these
#72: A researcher would like to test the claim that the mean lung capacity of middle-aged smokers is less than the mean lung capacity of senior citizen nonsmokers. Independent random samples of 41 middle-aged smokers and 41 senior citizen nonsmokers will be used in a hypothesis test of this claim, and it is believed that the standard deviations of the lung capacities in the populations of middle-aged smokers and senior citizen nonsmokers are the same. Which test statistic formula should be used for this test?
None of the above
#27: Which of the following probabilities for an event B suggest that event B can be considered an unusual event?
P(B) = 0.546 *P(B) = 0.048 P(B) = 0.525 P(B) = 0.9999 all of the above
#89: In the course of a game, WNBA player Cynthia Ciiper shoots 11 free throws. Denoting shots made by H (for hit) and denoting missed shots by M, her results are as follows: H, M, M, H, M, H, M, M, H, H, H Use a 0.05 significance level to test for randomness in the sequence of hits and misses.
Test Statistic: G = 7; Lower critical value: 3; Fail to reject H0
#86: A random sample of nine luxury cars were ranked according to their comfort levels and their prices. Find the rank correlation coefficient and test the claim there is no correlation between comfort and price. Use a significance level of 0.05.
Test Statistic: rs = 0.083, Critical Values: rs = ±±0.700, There does not appear to be a correlation between comfort and price.
#42: Which of the following is not a characteristic of a binomial experiment?
The probability of success is the same for each trial. *There must be more than 2 possible outcomes for each trial. There is a fixed number of trials. The outcome of each trial is independent of the outcome of any other trial. None of these
#5: A researcher wants to determine what percent of all first graders still believe in Santa Claus. He obtains a database of all current first graders in the country, selects the 100th name in this database, and every 100th name thereafter to be included in his sample. The sampling technique used by this researcher is:
convenience sampling *systematic sampling stratified sampling cluster sampling random sampling
#18: The sample data set 9, 24, 25, 27, 38, 1800 contains an extreme value. Which measures of center are influenced the most by the extreme value?
mean and mode median and mode mean and median *mean and midrange median and midrange
#75: If the Pearson linear correlation coefficient is r = 0.81, then describe the slope of the regression line.
negative *positive infinite zero
#3: What is a level of measurement that consists of classifying data into mutually exclusive categories in which the data can be ordered or ranked?
nominal *ordinal interval ratio
#88: In the runs test for randomness, the underlying concept is that if the number of runs is very low or very high, then the data is probably:
not random
#17: The mean and standard deviation of the sample data set 14, 19, 23, 24, 29 is:
only the mean can be computed ¯xx¯ = 21.8 and s = 5 ¯xx¯ = 21.5 and s = 5 *¯xx¯ = 21.8 and s = 5.6 ¯xx¯ = 23 and s = 5.6
#36: Events that cannot occur simultaneously are called:
random *disjoint (mutually exclusive) binomial independent
#2:A sample of students from your school is created by surveying the people in your next class. This best describes what kind of sampling method?
random systematic stratified cluster *convenience none of these
#4: A numerical measurement that describes a population is called a(n):
sample population statistic inference *parameter
#11. Which parameter is NOT a measure of dispersion (spread)?
standard deviation range variance *mode all of the above are measures of dispersion (spread)
Assume that matched pairs of data result in the given number of signs when the value of the second variable is subtracted from the corresponding value of the first variable. There are 9 positive signs, 5 negative signs, and 4 ties. Use the sign test with a 0.01 significance level to test the null hypothesis of no difference.
test Statistic: x = 5; Critical Value: 1; Fail to reject no difference
#67: The CEO of D-Lishus Juices, Inc. claims that their bottler (Hill River Bottling Company) is over-filling bottles with more than one gallon (128 ounces) of their juice. The CEO randomly selects 39 of these bottles, measures their content, and obtains a mean of 128.19 oz. and a standard deviation of 0.68 oz. (a) Find the value of the test statistic and critical value(s) for testing the CEO's claim at the αα = 0.10 level. (b) Peform the appropriate hypothesis test at αα = 0.10 and at αα = 0.02. The CEO will: (c) When αα = 0.10 is used, state the conclusion to this hypothesis test using nontechnical terms.
test statistic t = 1.745, critical value 1.304 Reject the null hypothesis at αα = 0.10 but fail to reject the null hypothesis at αα = 0.02. There is sufficient evidence to support the claim that this bottler is over-filling bottles with more than 128 oz.
#19: Molly's z score for her test was z = 1. The class mean was ¯xx¯ = 84.25. The class standard deviation was s = 1.4. What was her actual test score?
x = 82.85 x = 81.85 *x = 85.65 x = 86.65
#8: When one is constructing a table representing the frequency distribution of weights (grams), the first two classes of a frequency distribution are 1.01 - 1.50 and 1.51 - 2.00. What is the class width?
*0.500 0.490 0.990 1.000 0.495
#34: Winning a Power Ball lottery jackpot requires that you select the correct seven numbers (in any order) between 1 and 35 inclusive and, in a separate drawing, you must also select the correct single number between 1 and 30 inclusive. Find the probability of winning the jackpot.
*1/201735600
#33: A card is drawn from a standard deck of 52 cards. What is the probability of getting a red king? LOOK AT PHOTO OF CARDS ON PHONE
*1/26
#29: A drawer contains 4 black socks, 8 brown socks, and 6 white socks. If a sock is selected at random, find the probability that it is white.
*1/3
#9: When one is constructing a table representing the frequency distribution of weights (lbs.), the first two classes of a frequency distribution are 15.01 - 15.50 and 15.51 - 16.00. What is the upper class limit of the second class?
*16.000 15.500 0.990 0.490 1.000 0.495
#58: A sample of 37 statistics classes yields a mean class size of ¯xx¯ = 23.1 students with a standard deviation of s = 7.8 students. The 99% confidence interval estimate for the population mean is:
*19.61 students < μ < 26.59 students
#52: The z score that is used for a 96% confidence interval is:
*2.054 1.751 2.652 1.405 1.555
#85: Given that the rank correlation coefficient for 11 pairs of data is rs = 0.34, test the claim that there is a correlation between the two variables. Use a significance level of 0.2.
Critical Values rs = ±0.427; There does not appear to be a correlation between the variables.
#6: A town will collect employment data by polling 10,000 of its citizens every 3 years for the next 15 years. Identify the type of observational study being conducted.
Cross-Sectional *Prospective Retrospective
#90: A standard aptitude test is given to several randomly selected programmers, and the scores are given below for the mathematics and verbal portions of the test. (a) Suppose you were to use the sign test to test the claim that programmers do better on the mathematics portion of the test. Select the appropriate null and alternate hypotheses. (b) Use the sign test to test the claim that programmers do better on the mathematics portion of the test at a 0.01 level of significance.
H0: The math scores are equal to the verbal scoresH1: The math scores are greater than the verbal scores Test Statistic: x = 1; Critical Value: x = 0; Fail to reject H0
#91: A standard aptitude test is given to several randomly selected programmers, and the scores are given below for the mathematics and verbal portions of the test. (a) Suppose you were to use the sign test to test the claim that there is nodifference in programmers' scores on the mathematics and verbal portions of the test. Select the appropriate null and alternate hypotheses. (b) Use the sign test to test the claim that there is no difference in programmers' scores on the mathematics and verbal portions of the test at a 0.05 level of significance.
H0: The math scores are equal to the verbal scoresH1: The math scores are not equal to the verbal scores Test Statistic: x = 2; Critical Value: x = 2; Reject H0
#69: A simple random sample of 17 four-cylinder cars and a simple random sample of 21 six-cylinder cars is obtained. When using the samples below to test the claim that the mean braking distance of four-cylinder cars is greater than the mean braking distances of six-cylinder cars, find the alternative hypothesis. Four-cylinder Six-cylinder n1 = 17n2 = 21¯x1x¯1 = 136.4 ft¯x2x¯2 = 134.1 fts1 = fts2 = ft
H1:μ1−μ2>0
#7: What is the shape of the distribution formed by the following distribution frequency table? Age of Oscar Winning Actress Frequency
approximately normal or bell-shaped skewed right (positively skewed) skewed left (negatively skewed) *approximately uniform unknown
#65: The CEO of D-Lishus Juices, Inc. claims that their bottler (Hill River Bottling Company) is over-filling bottles with more than one quart (32 ounces) of their juice. The CEO randomly selects 32 of these bottles, measures their content, and obtains a mean of 32.25 oz. and a standard deviation of 0.61 oz. (a) Find the value of the test statistic and critical value(s) for testing the CEO's claim at the αα = 0.10 level. (b) Peform the appropriate hypothesis test at αα = 0.10 and at αα = 0.02. The CEO will: (c) When αα = 0.10 is used, state the conclusion to this hypothesis test using nontechnical terms.
test statistic t = 2.318, critical value 1.309 Reject the null hypothesis at αα = 0.10 and αα = 0.02. There is sufficient evidence to support the claim that this bottler is over-filling bottles with more than 32 oz.
#66: The manager of Riverside Bottling Corporation claims that her company is filling bottles with one pint (16 ounces) of juice. She randomly selects 39 of these bottles, measures their content, and obtains a mean of 16.2 oz. and a standard deviation of 0.52 oz. (a) Find the value of the test statistic and critical value(s) for testing the manager's claim at the αα = 0.02 level. (b) Peform the appropriate hypothesis test at αα = 0.02 and at αα = 0.05. The manager will: (c) When αα = 0.02 is used, state the conclusion to this hypothesis test using nontechnical terms.
test statistic t = 2.402, critical values ±2.429 Reject the null hypothesis at αα = 0.05 but fail to reject the null hypothesis at αα = 0.02. There is not sufficient evidence to warrant rejection of the claim that this bottler is filling bottles with 16 oz.
#62: Given the following information, which test statistic would be appropriate to test the null hypothesis? Assume a normal distribution if necessary. H0: μμ = 134 vs. H1: μμ > 134n = 18¯xx¯ = 114.4s = 7
z statistic Pearson r Chi-squared *t statistic None of these
