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Math Ch.6 Test
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Which of the following is not a descriptor of a normal distribution of a random variable?
a. The graph of the distribution is bell shaped
b. The graph is centered around the mean
c. The graph of the distribution is symmetric
d. The graph is centered around 0
Answer:
a. The graph is centered around 0.
Which of the following groups of terms can be used interchangeably when working with normal distribution?
a. areas, z-scores, and probabilities
b. areas, z-scores, and relative frequencies
c. areas, probabilities, and relative frequencies
d. z-scores, probabilities, and relative frequencies.
Answer:
c. areas, probabilities, and relative frequencies
Fill in the blank: A continuous random variable has a ________ distribution if its values are spread evenly over the range of possibilities.
Answer: uniform distribution
Why?: The graph of a uniform distribution is rectangular because the values are spread evenly over a range. That means every value in the range is equally likely.
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.
Answer:
a. The graph is centered around 0
Which of the following does NOT describe the standard normal distribution?
a. The graph is symmetric
b. The graph is uniform
c. The total area under the curve must equal 1
d. It is a normal distribution with a mean 0 and a standard deviation 1
Answer:
b. The graph is uniform.
Fill in the blank:
The notation P(z<a) denotes
Answer:
The notation P(z<a)
denotes the probability that the z-score is less than a.
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?
a. Finding z(standard deviance subscript)
b. A distance on the horizontal axis is given.
c. A percentage is given
d. A probability is given.
Answer:
b. A distance on the horizontal axis is given
Why?: When given a z-score, you are usually finding the area of the shaded region under the standard normal curve. For the standard normal curve, a z-score is a distance along the horizontal axis.
True or False:
A z-score is an area under the normal curve.
False
Why?: A z-score is not an area under the normal curve. Distances along the horizontal axis are represented by z-scores, while regions under the curve are represented by areas.
Where would a value separating the top 15% from the other values on the graph of a normal distribution be found?
a. The center of the horizontal scale of the graph.
b. the left side of the horizontal scale of the graph
c. the right side of the horizontal scale of the graph
d. on the top of the curve
Answer:
c. The right side of the horizontal scale of the graph
What conditions would produce a negative z-score?
a. A z-score corresponding to an area located entirely in the left side of the curve.
b. A z-score for a negative area
c. An area in the top 10% of the graph
d. A z-score corresponding to an area located entirely in the right side of the curve.
Answer:
a. A z-score corresponding to an area located entirely in the left side of the curve.
Complete the following statement:
If you are asked to find the 85th percentile, you are being asked to find:
Answer:
a data value associated with an area of .85 to its left.
Fill in the blank:
______ is the distribution of all values of the statistic when all possible samples of the same size n are taken.
Answer:
The Sampling Distribution of a Statistic
Why?:
The sampling distribution of a statistic (such as a sample mean or sample proportion) 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 is typically represented as a probability distribution in the format of a table, probability histogram, or formula.)
Which of the following is NOT a property of the sampling distribution of the sampling mean?
a. The distribution of the sample mean tends to be skewed to the right or left.
b. The mean of the sample means is the population mean.
c. The expected value of the sample mean is equal to the population mean.
d.
The sample means target the value of the population mean.
Answer:
a. The distribution of the sample mean tends to be skewed to the right or left.
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 mean of the sample variances is the population variance
c. The distribution of sample variances tends to be a normal distribution
d. The expected value of the sample variance is equal to the population variance.
Answer:
The distribution of sample variances tends to be a normal distribution
Fill in the blank:
_____ is the distribution of the sample proportions, will all the samples having the same sample size n taken from the same population.
Answer:
The sample distribution of the proportion.
Which of the following is a biased estimator? That is which of the following does not target the population parameter?
a. Proportion
b. Mean
c. Median
d. Variance
Answer:
c. Median
Fill in the blank:
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.
Answer:
Central Limit Theorem
Central Limit Theorem
This states that if the sample size is large enough, the distribution of sample means can be approximated by a normal distribution, even if the original population is not normally distributed.
Fill in the blank:
The standard deviation of the distribution of the sample means is:
Answer:
standard deviance over sq rt. of n
Which of the following is NOT a conclusion of the Central Limit Theorem?
a. The distribution of the sample means x overbar
will, as the sample size increases, approach a normal distribution.
b. The mean of all sample means is the population mean.
c. The standard deviation of all sample means is the population standard deviation divided by the square root of the sample size.
d. The distribution of the sample data will approach a normal distribution as the sample size increases.
Answer:
The distribution of the sample data will approach a normal distribution as the sample size increases.
Fill in the blank:
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.
Answer:
The Rare Event Rule for Inferential Statistics.
The Rare Event Rule for Inferential Statistics.
It 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.
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. Constructing a graph called a normal quantile plot
B. Visual inspection of a histogram to see if it is roughly bell-shaped
C. Checking that the probability of an event is 0.05 or less
D. Identifying outliers
Answer:
C. Checking that the probability of an event is 0.05 or less
Why?:
This is a criterion for distinguishing between results occurring by chance and results that are highly unusual.
Fill in the blank.
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.
Answer:
Normal Quantile Plot
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. If the plot is bell-shaped, the population distribution is normal.
C. The criteria for interpreting a normal quantile plot should be used more strictly for large samples.
D. The population distribution is not normal if the points show some systematic pattern that is not a straight-line pattern.
Answer:
B. If the plot is bell-shaped, the population distribution is normal.
Uniform density curve
height x (Max- Min)
Normal distribution
(low range #, high range #, mean, std. deviance)
The Rare Event Rule for Inferential Statistics.
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