stats final exam
#84 A random sample of 502 adults are shown in the contingency table below. This data will be used to test the claim that the region in which an adult lives and his/her highest level of education are dependent. (a) At αα = 0.2, 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 second row (Southeast) and third column (Bachelor's degree).
(a) 12.242 (b) 41.898 There is not sufficient evidence to support the claim that the region in which an adult lives and his/her highest level of education are dependent.
#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 alternative hypotheses. b) Use the sign test to test the claim that programmers do better on the mathematics portion of the test at a 0.005 level of significance.
(a) H0: The math scores are equal to the verbal scores H1: The math scores are greater than the verbal scores (b) Test Statistic: x = 0; Critical Value: x = 1; 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 a difference in programmers' scores on the mathematics and verbal portions of the test. Select the appropriate null and alternative hypotheses. (b) Use the sign test to test the claim that there is a difference in programmers' scores on the mathematics and verbal portions of the test at a 0.05 level of significance.
(a) H0: The math scores are equal to the verbal scores H1: The math scores are not equal to the verbal scores (b) Test Statistic: x = 0; Critical Value: x = 3; Reject H0
#96 Which of the following control charts illustrates a process that is within statistical control?
(see practice exam)
#47 Assume values are normally distributed with a mean of 8 and a standard deviation of 4. The probability that a randomly selected value lies between 4 and 7 is:
0.2426
#26 The batting average of the Macomb College baseball team is normally distributed with a mean of 0.289 and a standard deviation of 0.029. If Marcus is at the 65th percentile, find his batting average.
0.300
#56 The 97% confidence interval estimate of the proportion of female medical school students is (0.384,0.504)(0.384,0.504). Find the point estimate of the proportion of females for all medical school students.
0.444
#51 IQ scores measured on a certain scale are normally distributed with a mean of 180 and a standard deviation of 15. If 4 people are randomly selected, find the probability that their mean IQ is more than 178.
0.6051
#35 If P(A) = 0.17, P(B) = 0.44, and the events A and B are disjoint, then P(A or B) is:
0.61
#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 at most 8 of them have hazel eyes.
0.6956
#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 - 17.50 and 17.51 - 20.00. What is the upper class limit of the first class?
17.500
#14 If the variance for a set of data is 16, then the standard deviation is:
4
#15 A distribution has a range of 22. The highest score is 74. The lowest score is:
52
#79 A college tested for linear correlation between its statistics students' attitude ratings (x) and grades (y) by using a random sample of 8 students. In this test, the significance level was αα = 0.01, the test statistic was r = 0.928, the regression equation was ˆy=1.42x−7.74, the mean attitude rating (¯x) was 59.88, and the mean grade (¯y) was 76.65. Find the best predicted grade for a student whose attitude rating is 57.3.
73.63
#37 A family has 3 children. Assuming that only two genders (male or female) are possible for each child, how many different gender sequences are possible?
8
#48 (a) Use the normal distribution to approximate the desired binomial probability. American Railways reports that 82% of its trains are on time. A check of 80 randomly selected trains shows that 65 of them arrived on time. Find the probability that among the 80 trains, 65 or fewer arrive on time. (b) Based on the result from part (a), would it be unusual for 65 or fewer trains to arrive on time?
(a) 0.4884 (b) no
#82 A study is done to determine, at the 5% level of significance, if traffic accidents occur with equal frequency throughout the week. Of the 70 accidents pulled from the files, the distribution of observed traffic accidents is shown below. (a) What is the value of the test statistic for a χ2χ2 Goodness-of-Fit/Multinomial test? (b) BONUS QUESTION: State the decision of this test.
(a) 12.000 (b) fail to reject H0
#83 The contingency table below shows the results from a survey of 424 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 dependent. (a) At αα = 0.005, 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 first row (Democrat) and second column (Approve).
(a) 23.589 (b) 42.807
#92 (a) Find the values of the UCL and LCL of the -x chart for this data. (b) Find the values of the UCL and LCL of the R chart for this data. (c) Find the values of the UCL and LCL of the p chart for this data.
(a) 3.493 and 2.672 (b) 2.050 and 0.150 (c) 0.888 and 0.000
#94 (a) Find the values of the UCL and LCL of the ¯xx¯ chart for this data. (b) Find the values of the UCL and LCL of the R chart for this data. (c) Find the values of the UCL and LCL of the p chart for this data.
(a) 68.521 and 51.214 (b) 27.087 and 0.000 (c) 0.800 and 0.000
#61 (a) In a hypothesis test, the value of αα represents: (b) BONUS QUESTION: When testing a claim, if the test statistic is not in the critical region (rejection region), then our decision is to:
(a) the probability of rejecting H0 when it is true. (b) fail to reject H0
#46 In a standard normal distribution, find the area that is greater than z = 1.45.
0.0735
#45 In a standard normal distribution, find the area that is less than z = -1.34.
0.0901
#30 The probability that a person will get a cold this year is 0.7. If 5 people are selected at random, find the probability that all 5 will get a cold this year.
0.1681
#57 Find the minimum sample size needed to estimate the percentage of Republicans who have a dog. Use a 0.03 margin of error, use a confidence level of 95%, and assume that no previous estimates of the percentage of Republicans who have a dog are available.
1,068
#40 Consider the following probability distribution. Find the mean (or expected value).
1.2
#21 There are 500 statistic students at Macomb Community College who have a mean grade point average of ¯xx¯ = 2.4 and a standard deviation of s = 0.3. 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.
1.6
#52 The z score that is used for a 92% confidence interval is:
1.751
#34 Winning a Power Ball lottery jackpot requires that you select the correct six numbers (in any order) between 1 and 50 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.
1/476721000
#50 All possible random samples of size n = 15,625 are selected from a population with mean μμ = 625 and standard deviation σσ = 25. The standard error of the mean σ¯xσx¯ is:
1/5
#23 What is the mode for the data set summarized by the following stem and leaf plot?
10 and 31
#43 If a procedure yields a binomial probability distribution with n = 2000 trials and probability of success p = 0.6, then use μ±2σμ±2σ to find the range of usual values.
1157 to 1243
#81 A researcher surveys 41 people--consisting of 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, 4-5 visits, 6-7 visits, and 8 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 χ2χ2 test of independence at αα = 0.005?
14.860
#55 What is the minimum sample size needed to estimate the mean age of books in a library to within 14 months with 99.5% confidence if the standard deviation of the ages is thought to be about 60 months?
145
#80 A study investigates income level in the U.S. to determine if it is independent of region. If there are six regions and four income levels, how many degrees of freedom are there to find the critical value for a χ2 test of independence?
15
#60 If you are using a t-test when testing a claim about a population mean and the sample size is 20, the number of degrees of freedom is:
19
#20 The approximate percentage of values in a data set that will fall between the 13th percentile and the 32nd percentile is:
19%
#8 When one is constructing a table representing the frequency distribution of weights (grams), the first two classes of a frequency distribution are 0.01 - 2.00 and 2.01 - 4.00. What is the class width?
2.000
#58 A sample of 56 statistics classes yields a mean class size of ¯xx¯ = 27.1 students with a standard deviation of s = 7.9 students. The 99% confidence interval estimate for the population mean is:
24.28 students < μ < 29.92 students
#31 In a recent survey of TV watching at 6:00 on Sunday night, 15 people watched ABC, 12 people watched NBC, and 8 people watched CBS. If a person is picked at random, what is the probability that the person watched ABC or NBC?
27/35
#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 99% confidence interval for the mean difference between the before and after readings.
3.6 < μd < 45.4
#33 A card is drawn from a standard deck of 52 cards. What is the probability of getting a black face card (J, Q, or K)?
3/26
#10 The taxi-in time for 46 flights that landed in Los Angeles have a mean of 10.9 minutes and a standard deviation of 2.9 minutes. Approximately what percentage of taxi-in times is less than the 33rd percentile?
33%
#28 Holly is dealing you a three-card hand from a standard deck of 52 cards, 4 of which are aces. The probability that Holly will deal you exactly three aces is:
4/52, 3/51, 2/50
#78 A veterinarian collected a random sample of 12 pairs of data consisting of heights (x) and weights (y) of Chihuahuas. She computed the test statistic for this data to be r = -0.4, the mean height (¯x) to be 6.67 inches, the mean weight (¯yy¯) to be 5.42 pounds, and the regression equation to be ˆy=0.91x−1.45. Use a significance level of αα = 0.10, and find the best predicted weight (in pounds) for a Chihuahua that is 8.5 inches tall.
5.42
#13 The percent of values in a data set that lie between Q1 and Q3 is:
50%
#59 In a Gallup poll of 400 randomly selected adults, 220 of them said that they were underpaid. Construct a 95% 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?
50.1% < p < 59.9%, yes
#22 The Locator formula is L = (k/100)n. Find the value of the third quartile Q3 for the data set summarized by the following stem and leaf plot.
61
#54 Given that the 93% confidence limits for μμ are 64 and 74, which of the following could possibly be the 92% confidence limits?
66 and 72
#41 Consider the following probability distribution. Find the variance.
7.41
#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 10 horses, how many different trifecta bets are possible?
720
#24 Use the histogram to approximate the mode heart rate of adults in the gym. (heart rates of adults in the gym)
75
#49 Find the percentage of z scores that lie between z = -1.06 and z = 1.41 in a standard normal distribution.
77.61%
#29 A drawer contains 8 black socks, 6 brown socks, and 16 white socks. If a sock is selected at random, find the probability that it is white.
8/15
#85 Given that the rank correlation coefficient for 27 pairs of data is rs = 0.145, test the claim that there is a correlation between the two variables. Use a significance level of 0.2.
Critical Values rs = ±0.255; There does not appear to be a correlation between the variables.
#95 Given below are the sample means for fifteen samples of five students each. Assume that the mean of the sample means is ten and the computed values for the UCL and LCL of the ¯xx¯ chart are fifteen and five, respectively. Construct an ¯xx¯ chart. Is this process in statistical control? Why or why not?
No, because there are eight consecutive points all above or all below the centerline.
#38 Provide a written description of the complement of the given event: "At least one of the microphones is good."
None of the microphones are good.
#16 The mean of a distribution of test scores is 71 and the standard deviation is 10. We plan to curve the exam by adding 15 points to each score. How will this change the mean and standard deviation of the distribution?
The mean of the distribution will be increased by 15 points, but the standard deviation will remain unchanged.
#71 When testing the claim that the population proportion is 45%, suppose you get a test statistic of z = 3.52 and a P-value of 0.0004. What should we conclude about the claim?
There is sufficient evidence to warrant rejection of the claim.
#42 Which of the following is not a characteristic of a binomial experiment?
There must be more than 2 possible outcomes for each trial
#1 Which of the following data sets measure attributes that are categorical (qualitative)?
colors
#5 A researcher wants to determine what percent of all first graders who believe in Santa Claus. He decides to use the first graders at Warren Holland Elementary School, which is the school his son attends, as his sample. The sampling technique used by this researcher is:
convenience sampling
#36 Events that cannot occur simultaneously are called:
disjoint (mutually exclusive)
#18 The sample data set 3, 13, 28, 32, 37, 2300 contains an extreme value. Which measures of center are influenced the most by the extreme value?
mean and midrange
#11 Which parameter is NOT a measure of dispersion (spread)?
mode
#75 If the Pearson linear correlation coefficient is r = -0.69, then describe the slope of the regression line.
negative
#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
#64 A hypothesis test yields a test statistic of z = -1.98. Compute the P-value if this is a one-tailed test and if it is a two-tailed test.
one-tailed P-value is 0.0239; and two-tailed P-value is 0.0478
#73 Which of the following value of "r" indicates the strongest linear correlation between two variables?
r=-0.95
#2 A sample of people is created by writing their names on scraps of paper, and blindly drawing them from a bowl. This best describes what kind of sampling method?
random
#3 What is a level of measurement that consists of classifying numeric data in which both their differences and ratios are meaningful?
ratio
#6 A town obtains employment data by examining the tax returns filed by a sample of its citizens in the past decade. Identify the type of observational study being conducted.
retrospective
#25 A sample of children has a mean of ¯xx¯ = 49 pounds. If one of the children weighs x = 50.5 pounds and has a z score of z = 0.3, find s, the standard deviation of the sample.
s= 5 pounds
#4 A numerical measurement that describes a sample is called a(n):
statistic
#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. Which test statistic formula should be used for this test?
t= (x1−x2)−(μ1−μ2)/√s21/n1+s22/n2
#77 The coefficient of determination, r2, is a measure of:
the amount of variation in the y-variable that is explained by the regression line
#53 Computed using the same data, a 97% confidence interval for a population mean is ________ a 90% confidence interval for the same mean.
wider than
#19 Kristina's z score for her test was z = 0.3. The class mean was ¯xx¯ = 80.04. The class standard deviation was s = 1.2. What was her actual test score?
x=80.4
#62 Given the following information, which test statistic would be appropriate to test the null hypothesis? Assume a normal distribution if necessary. H0: μ = 222 vs. H1: μ < 222 n = 18 x = 219.6 σ= 12
z statistic
#39 True or false: The data given in the following table satisfies all of the required conditions for a probability distribution.
False, because E(P(x))≠1
#63 Suppose μμ represents the true mean number of combined credit hours taken by college freshmen during the fall and winter semesters. Some college administrators claim that the mean number of credit hours taken by college freshmen is at most 22. Select the appropriate alternate hypothesis.
H1: μ > 22
#69 A simple random sample of 47 four-cylinder cars and a simple random sample of 33 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: n1=47, x=135.3ft, s1=ft Six-cylinder: n2=33, x2=131.9ft, s2=ft
H1:μ1−μ2>0
#74 If the correlation between x and y is r = -0.63, which one of the following statements is true?
High values of x are associated with low values of y.
#27 Which of the following probabilities for an event A suggest that event A can be considered an unusual event?
P(A)=0.017
#76 When testing the claim H1:ρ≠0H1:ρ≠0 for 15 pairs of (x, y) data, the Pearson correlation coefficient test statistic is r = -0.512. Find the critical values for this test, and state the decision and conclusion of this test at a significance level of 0.1.
Reject H0: ρρ = 0, and conclude that there is linear correlation.
#89 In the course of a game, WNBA player Cynthia Ciiper shoots 12 free throws. Denoting shots made by H (for hit) and denoting missed shots by M, her results are as follows: M, H, H, H, H, M, H, H, M, H, M, M 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 ten 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 0.2.
Test Statistic: rs = 0.273, Critical Values: rs =±0.455, There does not appear to be a correlation between comfort and price.
#87 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 7 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
#17 The mean and standard deviation of the sample data set 12, 14, 15, 29, 37 is:
_ x = 21.4 and s = 11
#7 What is the shape of the distribution formed by the following distribution frequency table?
approx. uniform
#68 In a survey of 263 randomly selected workers, 23.57% got their jobs through personal connections with someone in the company. Consider a hypothesis test that uses a 0.10 significance level to test the claim that more than 20% of workers get their jobs through personal connections with someone in the company. What is the P-value?
between 0.05 and 0.95