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Homework answers / question archive / 1)if events A and B are disjoint, then they are also dependent     if P(A ∪ B)c  = P(Ac ∪ Bc)     probabilities can be less than 0     the P(A ∪ B) + P((A ∪ B)c) = 1     if A and B are mutually exclusive, then P(A|B) = P(B|A)           if two events (A and B) are independent, then the conditional probability of B given A is 1     mutually exclusive events have no simple events in common     the union of events A and B is the event that either A occurs, or B occurs, but not that both occur        if the conditional probability of an event A, given event B, is the same as the probability of event A, then events A and B are independent     the sum of all probabilities in a sample space is <1     if the intersection of A and B is non-zero, then A and B could be independent or dependent         if two events (A and B) are mutually exclusive, then the conditional probability of A given B is 0     independent events cannot occur at the same time     if event A is a subset of event B, then the probability of their intersection is 1     an event is a condition of simple events     the probability of a simple event can be any value between -1 and 1     if two events re independent, then they have no simple events in common     two events, defined on the same sample space, cannot be mutually exclusive     if A and B are independent, then Ac and B are also independent     event A and its complement, Ac are mutually exclusive     A and Ac are independent events     if two events are independent, then their complements are also independent        if the probability of event A is influenced by the occurrence of event B, then the two events are dependent     mutually exclusive events are never independent, but dependent events are not always mutually exclusive     independent events are also known as disjoint events       the P(A ∪ B)c  = P(Ac ∪ Bc)     if P(A) = 0

1)if events A and B are disjoint, then they are also dependent     if P(A ∪ B)c  = P(Ac ∪ Bc)     probabilities can be less than 0     the P(A ∪ B) + P((A ∪ B)c) = 1     if A and B are mutually exclusive, then P(A|B) = P(B|A)           if two events (A and B) are independent, then the conditional probability of B given A is 1     mutually exclusive events have no simple events in common     the union of events A and B is the event that either A occurs, or B occurs, but not that both occur        if the conditional probability of an event A, given event B, is the same as the probability of event A, then events A and B are independent     the sum of all probabilities in a sample space is <1     if the intersection of A and B is non-zero, then A and B could be independent or dependent         if two events (A and B) are mutually exclusive, then the conditional probability of A given B is 0     independent events cannot occur at the same time     if event A is a subset of event B, then the probability of their intersection is 1     an event is a condition of simple events     the probability of a simple event can be any value between -1 and 1     if two events re independent, then they have no simple events in common     two events, defined on the same sample space, cannot be mutually exclusive     if A and B are independent, then Ac and B are also independent     event A and its complement, Ac are mutually exclusive     A and Ac are independent events     if two events are independent, then their complements are also independent        if the probability of event A is influenced by the occurrence of event B, then the two events are dependent     mutually exclusive events are never independent, but dependent events are not always mutually exclusive     independent events are also known as disjoint events       the P(A ∪ B)c  = P(Ac ∪ Bc)     if P(A) = 0

Statistics

1)if events A and B are disjoint, then they are also dependent

 

 

  1. if P(A B)= P(Ac Bc)
 

 

  1. probabilities can be less than 0
 

 

  1. the P(A B) + P((A B)c) = 1

 

 

  1. if A and B are mutually exclusive, then P(A|B) = P(B|A)

 

 

 

 

 

  1. if two events (A and B) are independent, then the conditional probability of B given A is 1
 

 

  1. mutually exclusive events have no simple events in common

 

 

  1. the union of events A and B is the event that either A occurs, or B occurs, but not that both occur   
 

 

  1. if the conditional probability of an event A, given event B, is the same as the probability of event A, then events A and B are independent

 

 

  1. the sum of all probabilities in a sample space is <1
 

 

  1. if the intersection of A and B is non-zero, then A and B could be independent or dependent    

 

 

  1. if two events (A and B) are mutually exclusive, then the conditional probability of A given B is 0

 

 

  1. independent events cannot occur at the same time
 

 

  1. if event A is a subset of event B, then the probability of their intersection is 1
 

 

  1. an event is a condition of simple events

 

 

  1. the probability of a simple event can be any value between -1 and 1
 

 

  1. if two events re independent, then they have no simple events in common

 

 

  1. two events, defined on the same sample space, cannot be mutually exclusive
 

 

  1. if A and B are independent, then Ac and B are also independent

 

 

  1. event A and its complement, Ac are mutually exclusive

 

 

  1. A and Ac are independent events
 

 

  1. if two events are independent, then their complements are also independent

    

 

  1. if the probability of event A is influenced by the occurrence of event B, then the two events are dependent

 

 

  1. mutually exclusive events are never independent, but dependent events are not always mutually exclusive

 

 

  1. independent events are also known as disjoint events

   

 

  1. the P(A B)c  = P(Ac Bc)
 

 

  1. if P(A) = 0.7 and P(B) = 0.5, then the probability of the intersection of A and B is less than 0
 

 

  1. if P(Ac Bc ) = 0, then P(A B) = 1

 

 

  1. if A and B do not intersect, then A and B are independent
 

 

  1. if A is a subset of B, then P(A B) = P(B)

 

 

  1. if A and B are independent, then P(B)*P(A|B) = P(A)*P(B)

 

 

  1. if A and B are mutually exclusive, then their complements are also mutually exclusive

 

 

 

 

 

 

 

 

 

 

  1. The value of a statistic does not vary from sample to sample.
 

 

  1. The value of a parameter does not vary from sample to sample.
 

 

  1. We cannot possibly determine any characteristics of the sampling distribution of a statistic without repeatedly sampling from the population.
 

 

  1. The standard deviation of the sampling distribution of the sample mean depends on the value of μ.
 

 

  1. All else being equal, the standard deviation of the sampling distribution of the sample mean will be smaller for n = 10 than for n = 40.
 

 

  1. The sampling distribution of the sample mean is approximately normal for large sample sizes, and is sometimes approximately normal for small sample sizes.
 

 

  1. If the sampling distribution of the sample mean is approximately normal, then the population from which the samples were drawn must have been normally distributed.
 

 

  1. If we quadruple the sample size, the standard deviation of the sampling distribution of the sample mean would decrease by a factor of 2.
 

 

  1. The sampling distribution of μ is always approximately normal for n > 30.
 

 

  1. Statistics have sampling distributions
 

 

 

 

 

 

 

 

 

 

 

 

 

  1. If the sample sizes are similar, the pooled-variance t procedure will still work relatively well, even if the population variances are not quite the same.
 

 

  1. When applying the paired difference procedure, it is assumed that the differences between pairs of observations constitute a simple random sample from the population of differences.
 

 

  1. The pooled-variance t procedure requires that the two populations be normally distributed, however because the Welch procedure is only an approximate procedure, it does not require this assumption.
 

 

  1. The pooled sample variance used in a pooled-variance t procedure is a weighted average of the sample variances, and tends to be closer to the sample variance with the higher number of observations.
 

 

  1. The pooled-variance t procedure is most appropriate when the observations between the two groups are dependent.
 

 

  1. If the two populations are not normally distributed, then the inference procedures for the difference between two means can still be valid, provided the sample sizes are large.
 

 

  1. The paired difference procedure is less susceptible to the populations being non-normal, since taking the difference between two non-normal populations will result in a normal distribution.

 

 

  1. One problem with taking observations on the same experimental unit, as in a paired difference test, is that it can increase the variability in the experiment.
 

 

  1. The sampling distribution X1 - X2 of is approximately normal, provided the independent sampling distributions of X1 - X2 are themselves approximately normal.
 

 

  1. The results obtained from the pooled-variance t procedure versus the Welch procedure, when applied to the same data set, will always be significantly different.
 

 

 

 

 

 

 

 

 

 

  1. The sum of the observed values in each of the cells can be greater than n, the total number of observations.
 

 

  1. To determine the expected frequency for each cell, we multiply the total number of observations by the probability of an observation being in that particular cell.
 

 

  1. If the null hypothesis is , then large differences between the observed and expected values may exist.
 

 

  1. In a goodness-of-fit test, the null hypothesis is that all of the hypothesized proportions are the same, against the alternate hypothesis that they are all different.
 

 

  1. In a one-way table, each observed value can fall into only one of the given classifications.
 

 

  1. For goodness-of-fit tests, if the chi-square test statistic is greater than 1 then there is significant evidence against the null hypothesis.
 

 

  1. The sum of the hypothesized probabilities must be equal to 1.
 

 

  1. If the null hypothesis is , the chi-square test statistic will follow a chi-square distribution with k degrees of freedom, where k is the number of categories.
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. One of the following random variables has a binomial distribution (or has a distribution that would be closely approximated by the binomial)

 

  1. Suppose we have observed 100 Canada goose nests, counted the number of eggs in each nest, and calculated various summary statistics. quantities would change if we were to add a constant (10, say) to every value in the data set?
  2. mean, median, interquartile range, standard deviation, variance
 

 

  1. Suppose we have a sample data set, and we calculate z-scores for all the values. Consider the following 3 statements:
    1. The mean of the z-scores will be 0.
    2. The z-scores will have a standard deviation of 1.
    3. Typically, the largest z-score will be greater than 100.
  2. Which of these statements are ?
 

 

  1. If P(A) = 0.7 and P(B) = 0.6, then A and B cannot be mutually exclusive.

 

  1. Suppose an animal shelter is currently housing 40 dogs. They are about to draw a simple random sample of 4 dogs to conduct a small stud
  2. Consider the following 3 statements:
    1. Each individual dog at the shelter has a probability of 0.1 of being selected in the sample.
  3. II. There are 82,290 possible samples of size 4 that could be drawn from this group of   40 dogs.
  4. III. Every sample of size 4 has the same chance of being selected.
  5. Which of these statements are ?

 

  1. If the sample size is n = 2, the mean and median will be equal.
 

 

  1. In experiments, the main purpose of randomly assigning experimental units to the treatments is to reduce or eliminate system of the experiment.

 

  1. White Sucker is a species of fish commonly found in the Athabasca River in northern Alberta, and typically grow to an average length of 30 cm. In the health of White Suckers found in the Athabasca River, an environmental consulting agency implements a catch-and-release study in which 50back into the Athabasca. The mean length of the 50 fish is calculated to be 32.4 cm.
  1. Population
  1. Sample
  1. Parameter
  1. Statistic

 

  1. Suppose a university wishes to estimate the average weight of their undergraduate male students. A random sample of 200 undergraduate male students at this university are sampled. It is found that the sample mean weight is 83.3 kg, with a corresponding 95% confidence interval for mu of (81.3, 85.3). Of the following options, which one is the most appropriate interpretation of that interval?

 

  1. Suppose we are sampling from a normally distributed population, and we wish to carry out a test of the null hypothesis that the population mean is 50 against a two-sided alternative hypothesis. Suppose that in reality, the population mean is actually 50.

Consider the following 3 statements:

    1. We cannot possibly make a Type I error in this situation.
    2. We cannot possibly make a Type II error in this situation.
    3. We can be sure the p-value will be greater than 0.05 here.

Which of these statements are ?

 

  1. Suppose we are about to draw a large sample of observations from a distribution that is strongly skewed to the right.

Consider the following 3 statements:

    1. A histogram of these values will usually be strongly skewed to the right.
    2. The sampling distribution of the sample mean will be approximately normal.
    3. The sampling distribution of the population mean will be approximately normal.

Which of these statements are ?

 

 

  1. Suppose we are sampling from a normally distributed population, and we wish to use the t procedure to find a confidence interval for the population mean.

Consider the following 3 statements:

All else being equal, the greater the sample size, the smaller the margin of error.

    1. All else being equal, the greater the confidence level, the greater the margin of error.
    2. All else being equal, the greater the sample variance, the greater the margin of error.

Which of these statements are ?

 

 

 

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