Chpt 6
Which of the following would be information in a question asking you to find the area of a region under the standard normal curve as a solution? Finding z a An percentage is given A distance on the horizontal axis is given A probability is given
A distance on the horizontal axis is given
Which of the following is NOT a procedure for determining whether it is reasonable to assume that sample data are from a normally distributed population? A. Checking that the probability of an event is 0.05 or less B. Identifying outliers C. Constructing a graph called a normal quantile plot D. Visual inspection of a histogram to see if it is roughly bell-shaped
A. Checking that the probability of an event is 0.05 or les
Which of the following statistics are unbiased estimators of population parameters? A. Sample variance used to estimate a population variance. B. Sample standard deviation used to estimate a population standard deviation. C. Sample range used to estimate a population range. D. Sample proportion used to estimate a population proportion. E. Sample median used to estimate a population median. F. Sample mean used to estimate a population mean.
A. Sample variance used to estimate a population variance. D. Sample proportion used to estimate a population proportion. F. Sample mean used to estimate a population mean.
Which of the following is NOT a property of the sampling distribution of the sample mean? A. The expected value of the sample mean is equal to the population mean. B. The distribution of the sample mean tends to be skewed to the right or left. C. The sample means target the value of the population mean. D. The mean of the sample means is the population mean.
B. The distribution of the sample mean tends to be skewed to the right or left.
A researcher collects a simple random sample of grade-point averages of statistics students, and she calculates the mean of this sample. Under what conditions can that sample mean be treated as a value from a population having a normal distribution? A. The researcher collects more than 30 samples. B. The sample has more than 30 grade-point averages. C. If the population of statistics students has a normal distribution. D. If the population of grade-point averages has a normal distribution.
B. The sample has more than 30 grade-point averages. D. If the population of grade-point averages has a normal distribution.
What conditions would produce a negative z-score? A. a z-score corresponding to an area located entirely in the right side of the curve B. a z-score corresponding to an area located entirely in the left side of the curve C. a z-score for a negative area D. an area in the top 10% of the graph
B. a z-score corresponding to an area located entirely in the left side of the curve
Which of the following is NOT true in regards to using a normal quantile plot to determine whether or not a distribution is normal? A. The population distribution is normal if the pattern of points is reasonably close to a straight line. B. The criteria for interpreting a normal quantile plot should be used more strictly for large samples. C. If the plot is bell-shaped, the population distribution is normal. D. The population distribution is not normal if the points show some systematic pattern that is not a straight-line pattern.
C. If the plot is bell-shaped, the population distribution is normal.
If you are asked to find the 85th percentile, you are being asked to find _____. A. an area corresponding to a z-score of 0.85 B. an area corresponding to a z-score of -0.85 C. a data value associated with an area of 0.85 to its left D. a data value associated with an area of 0.85 to its right
C. a data value associated with an area of 0.85 to its left
The _______ tells us that for a population with any distribution, the distribution of the sample means approaches a normal distribution as the sample size increases.
Central Limit Theorem
Which of the following is not true? A. The area in any normal distribution bounded by some score x is the same as the area bounded by the equivalent z-score in the standard normal distribution. B. A z-score is a conversion that standardizes any value from a normal distribution to a standard normal distribution. C. If values are converted to standard z-scores, then procedures for working with all normal distributions are the same as those for the standard normal distribution. D. A z-score is an area under the normal curve.
D. A z-score is an area under the normal curve.
_____________ is the distribution of sample proportions, with all samples having the same sample size n taken from the same population.
The sampling distribution of the proportion
Finding probabilities associated with distributions that are standard normal distributions is equivalent to _______.
finding the area of the shaded region representing that probability.
A _____________ is a graph of points (x,y) where each x-value is from the original set of sample data, and each y-value is the corresponding z-score that is a quantile value expected from the standard normal distribution.
normal quantile plot
The notation P(z<a) denotes _______.
the probability that the z-score is less than a.
A continuous random variable has a _______ distribution if its values are spread evenly over the range of possibilities.
uniform
Which of the following groups of terms can be used interchangeably when working with normal distributions? .areas, probability, and relative frequencies .areas, z-scores, and relative frequencies .areas, z-scores, and probability .z-scores, probability, and relative frequencies
areas, probability, and relative frequencies
Which of the following is not a commonly used practice? A. If the original population is normally distributed, then for any sample size n, the sample means will be normally distributed. B. If the distribution of the sample means is normally distributed, and n > 30, then the population distribution is normally distributed. C. If the original population is not normally distributed and n>30, the distribution of the sample means can be approximated reasonably well by a normal distribution. D. The distribution of sample means gets closer to a normal distribution as the sample size n gets larger.
B. If the distribution of the sample means is normally distributed, and n>30, then the population distribution is normally distributed.
If you select a simple random sample of M&M plain candies and construct a normal quantile plot of their weights, what pattern would you expect in the graphs? A. Not reasonably close to a straight line. B. Approximately a straight line. C. A systematic pattern that is not a straight line.
B. Approximately a straight line.
Which of the following is NOT a conclusion of the Central Limit Theorem? A. The standard deviation of all sample means is the population standard deviation divided by the square root of the sample size. B. The distribution of the sample data will approach a normal distribution as the sample size increases. C. The distribution of the sample means x will, as the sample size increases, approach a normal distribution. D. The mean of all sample means is the population mean u.
B. The distribution of the sample data will approach a normal distribution as the sample size increases.
Annual incomes are known to have a distribution that is skewed to the right instead of being normally distributed. Assume that we collect a large (ngreater than30) random sample of annual incomes. Can the distribution of incomes in that sample be approximated by a normal distribution because the sample is large? Why or why not? A.Yes; the sample size is over 30, so the sample of incomes will be normally distributed. B.No; unless more than 30 samples are collected, the sample of incomes will not be normally distributed. C.No; the population of incomes is not normally distributed, so the sample means will not be normally distributed for any sample size. D. No; the sample means will be normally distributed, but the sample of incomes will be skewed to the right.
D. No; the sample means will be normally distributed, but the sample of incomes will be skewed to the right.
Which of the following is NOT a property of the sampling distribution of the variance? A. The sample variances target the value of the population variance. B. The expected value of the sample variance is equal to the population variance. C. The mean of the sample variances is the population variance. D. The distribution of sample variances tends to be a normal distribution.
D. The distribution of sample variances tends to be a normal distribution.
Where would a value separating the top 15% from the other values on the graph of a normal distribution be found? A. the left side of the horizontal scale of the graph B. on the top of the curve C. the center of the horizontal scale of the graph D. the right side of the horizontal scale of the graph
D. the right side of the horizontal scale of the graph
Which of the following is a biased estimator? That is, which of the following does not target the population parameter? Proportion Variance Median Mean
Median
The _______ states that if, under a given assumption, the probability of a particular observed event is exceptionally small (such as less than 0.05), we conclude that the assumption is probably not correct.
Rare Event Rule for Inferential Statistics
Which of the following is NOT a descriptor of a normal distribution of a random variable? A. The graph is centered around 0. B. The graph is centered around the mean. C. The graph of the distribution is symmetric. D. The graph of the distribution is bell-shaped.
The graph is centered around 0.
Which of the following is NOT a requirement for a density curve? A. The graph is centered around 0. B. The total area under the curve must equal 1. C. Every point on the curve must have a vertical height that is 0 or greater. D. The curve cannot fall below the horizontal axis.
The graph is centered around 0.
Which of the following does NOT describe the standard normal distribution? A. The graph is uniform. B. The total area under the curve must equal 1. C. It is a normal distribution with a mean of 0 and a standard deviation of 1. D. The graph is symmetric.
The graph is uniform.
What requirements are necessary for a normal probability distribution to be a standard normal probability distribution?
The mean =0 and standard deviation =1
_____________ is the distribution of all values of the statistic when all possible samples of the same size n are taken from the same population.
The sampling distribution of a statistic
