Question

Answer True or False

1. A in a density histogram the area of a region is equivalent to the density of that region_________.
2. Extreme values or “outlier” have a great effect on the Interquartile range than on the standard deviation as the standard deviation is a resistant measure of spread_______.
3. In the events A and B are disjoint they must also be independent_______.
4. For any two events A and B, P (A or B)= P(B)+ P(A and B). ________.
5. If the events A and B are independent, the P (A and B) = P(A)P(B)_________.
6. If the events A and B are disjoint then conditional probabilities P(AB) and P(BA) are both equal to 0______.
7. A random variable that assumes only negative values will have a negative mean ______.
8. A random variable that assumes only negative values will have a negative standard deviation______.
9. A binomial random variable counts the number of “successes” in a fixed number of independent trials where the probability of “success” varies from trial to trial_____.
10. A statistic is a random quantity: different random samples will yield different statistic values______.
11. The mean of sampling distribution of the sample mean is equal to the population mean_____.
12. The standard deviation of the sampling distribution of the the sample mean is generally smaller than the standard deviation of the population_____.
13. If the population is (exactly) normally distributed, the sampling distribution of the sample mean will be (exactly) normal also______.
14. Even if the population distribution is not normal, as long as the sample size is sufficiently large, the sampling distribution of the sample mean will be approximately normal, by central limit theorem______.
15. A 95% Confidence Interval will generally be wider than a 90% Confidence Interval for the same parameter, based on the same data ______.  
16. A 95% Confidence Interval for a population mean will contain at least 95% of the values in the underlying population_______.
17. If we were to take a large number of independent random samples and calculate a A 95% Confidence Interval from about 95% of the resulting intervals would cover the true parameter value______.
18. In hypothesis testing, H₀is a statement about the population that we initially assume to be true________.
19. A P-value close to zero indicated that the observed data are inconsistent with the null hypothesis______.
20. If we reject H₀at the a=0.05 level of significance clearly we would reject a=0.01 as well_______.
21. A P-value less than 0.01 indicates that if H₀ were true, the chance of observing data as extreme as those observed would be less than one out of 100______.
22. In a two-way contingency table, the marginal (row and column) sums of the “expected cell counts” will be equivalent marginal sums of the observed cell counts_______.
23. Evidence against the null hypothesis of independent between row and column variables in a contingency table is provided by a very small value of the chi-square statistic_____.
24. In an r x c contingency table the P-value for a test of row-column is found by comparing the test statistic x^2 to the chi-square distribution with (r-1)(c-1) degrees of freedom______.
25. If two quantitative variable x and y are negatively associated above average values of x will tend to occur with below average values of y and vice versa_______.
26. If a set of data (x₁, y₁) ……. (x_n,y_n) satisfy y_i=4x for each i=1…n then the correlation between the x’s and the y’s is 1______.
27. Correlation is a resistant measure in that it is not sensitive to extreme values or outliers______.
28. Correlation makes a distinction between response variable and explanatory variable______.
29. Least-square regression makes a distinction between response variable and explanatory variable______.
30. The least square regression line always passes through the point(xbar, ybar) ______.

Answer 1

Part A: -

A density histogram is just a modified relative frequency histogram.

A density histogram is defined so that:

• the area of each rectangle equals the relative frequency of the corresponding class, and
• the area of the entire histogram equals 1.

In other words, a histogram represents a frequency distribution by means of rectangles whose widths represent class intervals and whose areas are proportional to the corresponding frequencies: the height of each is the average frequency density for the interval.

Part B: -

False... Outliers impacts more on Standard Deviation than that of Inter-Quartile Range.

Part C: -

Disjoint events aren't independent, unless one event is impossible, which makes the two events trivially independent.

Let's take the simplest situation possible as a counterexample.

Let A be the event that a fair coin lands heads and let B be the event that the coin lands tails.

Part D: -

False

The Solution is that: - For ANY two events A and B, P(A or B) = P(A) + P(B) - P(A and B)

Note: When A and B are disjoint P(A and B) = 0 and the rule reverts to the addition rule of before.

Part E: -

True

Events A and B are independent if the equation P(A∩B) = P(A) P(B) holds true.

Events A and B are independent if: knowing whether A occurs, does not change the probability of B.

Mathematically, can say in two equivalent ways:

P(B|A) = P(B)

P(A and B) = P(A ∩ B) = P(A) × P(B).

It is important to distinguish independence from mutually exclusive which would say A ∩ B is empty (cannot happen).

Part F: -

Events are said to be mutually exclusive if they have no outcomes in common.

In other words, it is impossible that both could occur in a single trial of the experiment.

For mutually exclusive events holds P(A · B) = P(∅) = 0.