Business Stats 1 Final Review
(9) The mean x of a data set is 35.16, and the sample standard deviation s is 4.57. Find the interval representing measurements within one standard deviation of the mean.
(30.59, 39.73)
(28) A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 415 seconds and a standard deviation of 89 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 340 seconds.
.2005
(27) Find a value of the standard normal random variable z, called Zo, such that P(z≤z) = 0.7123
.56
(51) You are interested in purchasing a new car. One of the many points you wish to consider is the resale value of the car after 5 years. Since you are particularly interested in a certain foreign sedan, you decide to estimate the resale value of this car with a 95% confidence interval. You manage to obtain data on 17 recently resold 5-year-old foreign sedans of the same model. These 17 cars were resold at an average price of $12,550 with a standard deviation of $800. What is the 95% confidence interval for the true mean resale value of a 5-year-old car of this model?
12550±2.12(800/17)
(50) Find the value of t0 such that the following statement is true. P(−t0≤t≤t0)=0.99 where df=9
3.250
(48) A 90% confidence interval for the mean percentage of airline reservations being cancelled on the day of the flight is (1.8,5.7). What is the point estimator of the mean percentage of reservations that are cancelled on the day of the flight?
3.75%
(26) If x is a binomial random variable, calculate μ for n=51 and p=0.6.
30.6
(44) What is the confidence level of the following confidence interval for μ? x±1.645(s/n)
90
(4) Identify each of the following variables as qualitative or quantitative. A. Number of sick days taken in a year B. Favorite color C. College major d. Time worked in a week
A. number of sick days is quantitative; values are numerical B. favorite color is qualitative; values are not numerical C. college major is qualitative; values are not numerical D. time worked in a week is quantitative; values are numerical
(12) Calculate the variance and standard deviation for samples with the following statistics. A. n=8, ∑x^2=83, ∑x=16 B. n=39, ∑x^2=389, ∑x=90 C. n=20, ∑x^2=17, ∑x=16
A. variance = 7.286 standard deviation = 2.699 B. variance = 4.771 standard deviation = 2.184 C. variance = .221 standard deviation = .470
(31) Toss three fair coins and let x equal the number of heads observed. A. Identify the sample points associated with this experiment and assign a value of x to each sample point. Then list all the possible values of x. B. Calculate p(x) for the values x=1 and x=2. C. What is P(x=1 or x=3)?
A. x = 0, 1, 2, 3 B. p(1) = 3/8 p(2) = 3/8 C. P(x=1 or x=3) = .5
(40) A random sample of n=100 observations is selected from a population with μ=29 and σ=25. A. Find μx and σx. B. Describe the shape of the sampling distribution of x. C. Find P(x≥28) D. Find P(22.1≤x≤26.8) E. Find P(x≤28.2) F. Find P(x≥27.0)
A. μx = 29 σx = 2.5 B. approximately normal C. P(x≥28) = .6554 D. P(22.1≤x≤26.8) = .1865 E. P(x≤28.2) = .3745 F. P(x≥27.0) = .7881
(2) Explain the difference between descriptive and inferential statistics.
Descriptive statistics describes sets of data. Inferential statistics draws conclusions about the sets of data based on sampling
(6) T/F: A Pareto diagram is a pie-chart where the slices are arranged from largest to smallest in a counterclockwise direction.
False
(37) T/F: The term statistic refers to a population quantity, and the term parameter refers to a sample quantity.
False statistics refers to a sample and parameter refers to a population
(25) T/F: If A and B are independent events, then P(A)=P(B|A).
False: if A and B are independent, then P(A) = P(A|B)
(10) Calculate the mean, median, and mode of the following grade point averages. 3.7 3.6 2.1 3.3 3.7 2.7
Mean = 3.18 Median = 3.45 Mode = 3.7
(39) Will the sampling distribution of x always be approximately normally distributed?
No, because the Central Limit Theorem states that the sampling distribution of x is approximately normally distributed only if the sample size is large enough.
(7) The amount spent on textbooks for the fall term was recorded for a sample of five hundred university students. The mean expenditure was calculated to be $500 and the median expenditure was calculated to be $425. Which of the following interpretations of the mean is correct?
The average of the textbook costs sampled was $500
(49) T/F: The Central Limit Theorem guarantees an approximately normal sampling distribution for the sample mean for large sample sizes, so no knowledge about the distribution of the population is necessary for the corresponding interval to be valid.
True
(36) A recent survey found that 78% of all adults over 50 wear glasses for driving. In a random sample of 10 adults over 50, what is the mean and standard deviation of the number who wear glasses?
mean = 7.8 standard deviation = 1.31
(24) A bag of colored candies contains 20 red, 25 yellow, and 35 orange candies. An experiment consists of randomly choosing one candy from the bag and recording its color. What is the sample space for this experiment?
{red, yellow, orange}
(19) For two events, A and B, P(A)=0.5, P(B)=0.5, and P(A|B)=0.4. A. Find P(A∩B). B. Find P(B|A).
A. P(A∩B) = .2 B. P(B|A) = .4
(33) A poll found that 30% of adults do not work at all while on summer vacation. In a random sample of 9 adults, let x represent the number who do not work during summer vacation. A. Find P(x=5) B. Find the probability that 2 or fewer of the 9 adults do not work during summer vacation.
A. P(x=5) = .0735 B. P(x≤2) = .4628
(5) Each month interviewers visit about 50,000 of the 93 million households in the region and question the occupants over 18 years of age about their marriage status. Their responses enable the interviewers to estimate the percentage of people in the labor force who are married. A. Define the population of interest B. What variable is being measured C. Is it qualitative or quantitative D. Is the problem of interest descriptive or inferential?
A. all people in the region who are over 18 years old B. marriage status C. qualitative D. inferential
(43) What is zα/2 when α=0.08?
1.75
(1) What is statistics?
It is the science that deals with collection, classification, analysis, and interpretation of information or data
(3) Explain how populations and samples differ.
A population is a set of units of interest to a study. A sample is a subset of the units of a population
(45) A random sample of 86 observations produced a mean x=25.8 and a standard deviation s=2.4. A. Find a 95% confidence interval for μ. B. Find a 90% confidence interval for μ. C. Find a 99% confidence interval for μ.
A. (25.29, 26.31) B. (25.37, 26.23) C. (25.13, 26.47)
(34) Find the area under the standard normal probability distribution between the following pairs of z-scores. A. z=0 and z=2.00 B. z=0 and z=3.00 C. z=0 and z=1.00 D. z=0 and z=0.74
A. .477 B. .499 C. .341 D. .270
(47) Let t0 be a specific value of t. Use the table of critical values of t below to find t0-values such that the following statements are true. A. P(t≥t0=.025), where df=10 B. P(t≥t0=.01), where df=18 C. P(t≤t0=.005), where df=7 D. P(t≤t0=.05), where df=14
A. 2.228 B. 2.552 C. -3.499 D. -1.761
(20) For two events, A and B, P(A)=.2, P(B)=.2, and P(A∩B)=.1. A. Find P(A|B). B. Find P(B|A). C. Are A and B independent events?
A. P(A|B) = .5 B. P(B|A) = .5 C. No, the events are dependent because P(A|B)≠P(A)
(21) For two independent events, A and B, P(A)=.6 and P(B)=.2. A. Find P(A∩B). B. Find P(A|B). C. Find P(A∪B).
A. P(A∩B) = .12 B. P(A|B) = .6 C. P(A∪B) = .68
(23) Which of the following assignments of probabilities to the sample points A, B, and C is valid if A, B, and C are the only sample points in the experiment?
P(A) = 0 P(B) = 1/12 P(C) = 11/12
(8) Which of the following is not a measure of central tendency? Range Median Mode Mean
Range
(15) Fill in the blank. __________ is a method of interpreting the standard deviation of data that have a mound-shaped, symmetric distribution.
The Empirical Rule
(16) T/F: According to the empirical rule, z-scores of less than -3 or greater than 3 occur very infrequently for data from a mounded and symmetric distribution
True
(17) T/F: If a z-score is 0 or near 0, the measurement is located at or near the mean.
True
(41) T/F: In most situations, the true mean and standard deviation are unknown quantities that have to be estimated.
True
(42) T/F: If x is a good estimator for μ, then we expect the values of x to cluster around μ.
True
(46) Will a large-sample confidence interval be valid if the population from which the sample is taken is not normally distributed?
Yes. As long as a sample is sufficiently large that the Central Limit Theorem applies, the confidence interval will be valid regardless of the shape of the population distribution.
