Practice Set
1. Let x be a continuous random variable. What is the probability that x assumes a single value, such as a (use numerical value)?
2. The following are the three main characteristics of anormal distribution.
A. The total area under a normal curve equals _____.
B. A normal curveis ..................about the mean . Consequently,50% of the total area under anormal distribution curve lies on the left side of the mean,and 50% lies on the right side of the mean.
C. Fill in the blank. The tails of a normal distribution curve extend indefinitely in both directions without touching or crossing the horizontal axis.Although a normal curve never meets the....................axis,beyondthe pointsrepresentedby µ - 3σ to µ+ 3σ it becomes so close to this axis that the area under the curve beyond these points in both directionsis very close to zero.
3. For the standard normal distribution, find the area within one standard deviation of the
mean that is, the area between μ - σ and μ + σ. Round to four decimal places.
4. Find the area under the standard normal curve. Round to four decimal places.
a) between z = 0 and z = 1.95
b) between z = 0 and z = -2.05
c) between z = 1.15 and z = 2.37
d) from z = -1.53 to z = -2.88
e) from z = -1.67 to z = 2.24
5. The probability distribution of the population data is called the (1) ________.
Table7.2 in the text provides an example of it.The probability distribution of a sample statisticis called its (2) _________.
Table7.5 in the text provides an example it.
A. Probability distribution
B. Population distribution
C. Normal distribution
D. Sampling distribution
6. ___________is the difference between the value of the sample statistic and the value of the corresponding population parameter,assuming that the sample is random and no non-sampling error has been made.
Example7-1 in thetextdisplayssamplingerror.Samplingerroroccursonlyinsample surveys.
7. Consider the following population of 10 numbers. 20 25 13 19 9 15 11 7 17 30
a) Find the population mean. Round to two decimal places.
b) Rich selected one sample of nine numbers from this population. The sample included the numbers 20, 25, 13, 9, 15, 11, 7, 17, and 30. Calculate sampling error for this sample. Round to decimal places.
8. Fill in the blank. The F distribution is________and skewed to the right.The F distribution has two number so f degree s of freedom: df for the numerator and df for the denominator.The unit s of an F distribution,denoted by F,are non negative.
9. Find the critical value of F for the following. Round to two decimal places.
a) df = (3, 3) and area in the right tail = .05
b) df = (3, 10) and area in the right tail = .05
c) df = (3, 30) and area in the right tail = .05
10. The following ANOVA table, based on information obtained for three samples selected from three independent populations that are normally distributed with equal variances, has a few missing values.
|
Source of
Variation
|
Degrees of
Freedom
|
Sum of
Squares
|
Mean
Square
|
Value of the
Test Statistic
|
|
Between
|
2
|
II
|
19.2813
|
|
|
Within
|
-
|
89.3677
|
III
|
F = ___V__ = VII
VI
|
|
Total
|
12
|
IV
|
|
|
a) Find the missing values and complete the ANOVA table. Round to four decimal places.
b) Using α = .01, what is your conclusion for the test with the null hypothesis that the means of the three populations are all equal against the alternative hypothesis that the means of the three populations are not all equal?
Reject H0. Conclude that the means of the three populations are equal.
Reject H0. Conclude that the means of the three populations are not equal.
Do not reject H0. Conclude that the means of the three populations are equal.
Do not reject H0. Conclude that the means are of the three populations are not equal.