Download Standard Deviation and Sampling Distribution and more Exams Nursing in PDF only on Docsity!
UCF QMB 3200 Final Exam Test
Questions and Answers (Verified Answers)
- Suppose we have the following data: 12, 17, 13, 25, 16, 21, 30, 14, 16, and
- To find the 10% trimmed mean, what numbers should be deleted from the calculation ANS 12 and 30 2. Which of the following is not resistant to the outliers in a data set? a. Median b. Mean c. Variance d. Interquartile range ANS: B. mean
- The pth percentile is a value such that at least p percent of the observationsare
ANS less than or equal to this value.
4. Which of the following provides a measure of central location for the data? a. Mean b. Variance c. Mode d. Standard deviation ANS: A. mean 5. When testing water for chemical impurities, results are often reported as BDL, that is, below detection limit. The following data set gives the measure- ments of the amount of lead in a series of water samples taken from inner-city households (ppm): 5, 7, 12, BDL, 10, 8, BDL, 20, 6 Which of the following is correct? a. The mean lead level in the water is about 10 ppm. b. The median lead level in the water is 8 ppm. c. The mean lead level in the water is about 8 ppm. d. The median lead level in the water is 7 ppm . ANS: D. The median lead level in thewater is 7 ppm.
ANS sample statistic.
- The measure of location that is most likely to be influenced by extreme values in a data set is the ANS mean 11. A student was performing an experiment that compared a new high protein food to the old food for pigs. He found the mean weight gain for subjects consuming the new food to be 12.8 pounds with a standard deviation of 3.5 pounds. Later, he realized that the scale was out of calibration by 1.5 pounds (meaning that the scale weighed items 1.5 pounds more). What shouldbe the summary measures, mean and standard deviation, for the subjects consuming the new food ANS The mean should be 11.3 and the standard deviationshould remain unchanged.
- When a set of data has suspect outliers, which of the following is the referred measure of central tendency ANS median
16. If the variance of a data set is correctly computed with the formula usingin the denominator, which of the following is true? a. The data set is a population. b. The data set is adjusted for skewness. c. The data set is too small. d. The data set is a sample . ANS: D. The data set is a sample.
- In a sample of size five, the mean is 23 and four of the observations have the following deviations from the mean: - 6, 2, 5, and 3. What is the value of the fifth observation ANS - 4 18. There are three executives in an office with age 56, 57, and 58. If a 57 - year-old executive enters the room, then ANS the mean age will stay the same,but the variance will decrease.
19. The difference between the largest and the smallest data values is the ANS - range
- The interquartile range is ANS the difference between Q3 and Q1, the third andfirst quartiles.
- The standard deviation of a sample was reported to be 20. The report indicated that £x(i-x )^2 = 7200. What is the sample size:? 20 - 1 = 19
- The numerical value of the standard deviation can never be ANS negative
- The interquartile range is used as a measure of variability to overcome the fact that the ANS range is comprised of extreme values. 24. Given the following information: Standard deviation = 8 Coefficient of variation = 64% The mean is: 8 / 64%= 12.
- The sum of deviations of the individual data elements from their meanis ANS always equal to zero
- The correlation coefficient ranges between ANS - 1 and 1 27. A numerical measure of linear association between two variables is the ANS - covariance
- The correlation coefficient between two scores X and Y equals .80. If boththe X scores and the Y scores are converted to z-scores, then the correlation between the z-scores for X and the z-scores for Y would be ANS.
- In a standard normal distribution, what z-score corresponds to the 75th percentile ANS z =. 35. The newest model of smart car is supposed to get excellent gas mileage.A thorough study showed that gas mileage (measured in miles per gallon) is normally distributed with a mean of 75 miles per gallon and a standard deviation of 10 miles per gallon. What is the percentage that, if driven normally,the car will get 100 miles per gallon ANS 100 - 75/10 = 2. The corresponding z score is .6%
- A normal distribution with a mean of zero and a standard deviation of oneis called ANS a standard normal probability distribution.
- A health conscious student faithfully wears a device that tracks his steps. Suppose that the number of steps he takes is normally distributed with a meanof 10,000 and a standard deviation of 1500 steps. How many steps would he have to take to make the cut for the top 5% for his distribution ANS To be at the top 5% of his distribution, he would need a z-score of 1.645. This equates to taking12,467 steps
- Suppose that a basketball player scored, on average, 15 points per game.Also
suppose that the distribution of points scored by this player was normal.If he scores 20 points or more 4.78% of the time, what is his standard devia- tion ANS 100 - 4.78= 95.22 percentile, corresponding z score is 1. 20 - 15= 5 5/1.66= 3
- For the standard normal probability distribution, the area to the left of the mean is ANS. In a standard normal probability distribution, the mean is located at the center of the, curve which means that half of the area is below the mean and half is abovethe mean
- If z is a standard normal random variable, then compute P(z > - 1.75).: Usinga standard normal table, P(z > - 1.75) = .96. 41. The newest model of smart car is supposed to get excellent gas mileage.A thorough study showed that gas mileage (measured in miles per gallon) is normally distributed with a mean of 75 miles per gallon and a standard deviation of 10 miles per gallon. What value represents the 50th percentile ofthis distribution ANS The 50th percentile of a normal distribution is located at its mean = 75
- The center of a normal curve is ANS the mean of the distribution.
ANS numerical characteristics of a population
- When drawing a sample from a population, the goal is for the sampleto ANS match the targeted population.
- For a(n) , it is impossible to construct a sampling frame.: infinite population
- Which of the following is not a symbol for a parameter ANS s
- A random sample of 121 bottles of cologne showed an average contentof 4 ounces. It is known that the standard deviation of the contents (i.e., ofthe population) is .22 ounces. In this problem, the value .22 ounces is ANS a parameter. 53. Which of the following is(are) true? I. The mean of a population depends on the particular sample chosen. II. The standard deviations of two different samples from the same population may be the same. III. Statistical inferences can be used to draw conclusions about the popula- tions based on sample data.: II and III
- A simple random sample of size n from an infinite population is a sample selected such that each element is selected and is selected from the same : independently, population.
- A simple random sample of size n from an infinite population of size N is to be selected. Each possible sample should have ANS the same probability of beingselected.
- A simple random sample of size n from a finite population of size N is a sample selected such that each possible sample of size ANS n has the sameprobability of being selected.
- How many simple random samples of size 5 can be selected from a population of size 8 ANS 8!/5!(8-5)!= 56
- There are 6 children in a family. The number of children defines a popula- tion. The number of simple random samples of size 2 (without replacement) that are possible is equal to ANS 6!/2!(6-2)!
- The medical director of a company looks at the medical records of all 50 employees and finds that the mean systolic blood pressure for these employees is 126.07. The value of 126.07 is ANS a parameter
- The sample statistic characteristic s is the point estimator of ANS Ã
- Which of the following is a point estimator ANS s
- The fact that the sampling distribution of sample means can be approxi- mated by a normal probability distribution whenever the sample size becomes large is based on the ANS central limit theorem.
- A sample of 92 observations is taken from an infinite population. The sampling distribution of is approximately ANS normal because of the central limittheorem.
- In a recent Gallup Poll, the decision was made to increase the size of its random sample of voters from 1500 people to about 4000 people. The purposeof this increase is to ANS reduce the standard error of the estimate.
- As the sample size increases, the standard error of the mean: decreases. 73. Which of the following statements regarding the sampling distribution of sample means is incorrect? a.The standard deviation of the sampling distribution is the standard deviationof the population. b. The sampling distribution is found by taking repeated samples of the same size from the population of interest and computing the mean of each sample. c. The mean of the sampling distribution is the mean of the population. d. The sampling distribution is approximately normal when the population is normal or the sample size is sufficiently large.: The standard deviation of the sampling distribution is the standard deviation of the population.
- The central limit theorem is important in Statistics because it ANS enables reasonably accurate probabilities to be determined for events
involving the sampleaverage when the sample size is large regardless of the distribution of the variable.
- In computing the standard error of the mean, the finite population correc- tion factor is used when ANS n/N >.
- A simple random sample of 100 observations was taken from a large population. The sample mean and the standard deviation were determined tobe 80 and 12, respectively. The standard error of the mean is ANS 12/ sqr rt 100=1.
- The central limit theorem states that ANS if the sample size n is large, then the sampling distribution of the sample mean can be approximated by a normaldistribution.
- Doubling the size of the sample will ANS reduce the standard error of the mean.
- A simple random sample of 64 observations was taken from a large pop- ulation. The sample mean and standard deviation were determined to be 320 and 120, respectively. The standard error of the mean is ANS 120/ square root 64= 15
- The standard deviation of a point estimator is called the ANS standard error
proportion is ANS 150 - 90= 40 sqr rt .40(1-.40)/150=.
- In stratified random sampling ANS randomly selected elements within each of thestrata form the sample.
- A probability sampling method in which we randomly select one of the first k elements and then select every kth element thereafter is ANS systematicsampling.
- Cluster sampling is ANS a probability sampling method.
- Convenience sampling is a ANS nonprobability sampling technique.
- A doctor would like to determine if there is a difference between the blood pressure of people who walk every day for 60 minutes and those who walk one day per week for 60 minutes. Fifty of her patients who report that they have routinely walked 60 minutes every day for the past two years and 50 who report that they have walked 60 minutes only one day per week will be identified. The doctor will examine their medical records and collect their blood pressure readings over this two-year period. This is an example of a(n) ANS observational study. 93. In a survey of public opinion concerning state aid to a particular city, every 40th person registered as a voter was interviewed, beginning with a
person selected at random from among the first 40 listed. This is an exampleof ANS systematic sampling.
- When "s" is used to estimate "Ã,"the margin of error is computed by using the ANS t distribution
- As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution ANS - becomes smaller
- A professor would like to estimate the average number of hours his students spend doing work and studying throughout the semester for the course he teaches. He wants to estimate ¼with 99% confidence and with a margin of error of at most 2 hours. From past experience, he believes that the standard deviation of the number of hours students spent is 8 hours. How many students need to be surveyed to meet these requirements ANS n= (za/2)^2sd^2/E^ (2.576)^2 8^2/ 2^2= 106.17 or 107 (on adaptive test prep)
- In general, higher confidence levels provide larger confidence intervals. One way to have high confidence and a small margin of error is to ANS increasethe sample size
- When the level of confidence decreases, the margin of error ANS becomessmaller
- The value added and subtracted from a point estimate in order to developan interval estimate of the population parameter is known as the ANS margin of error
- population proportion margin of error formula: za/2 sqr rt p bar (1- p bar)/n
