PRACTICE EXAM 3- Math 251
Please remember that this is only one of the tools that you can use to prepare yourself for the test. In
addition you should read your text. You can also watch videos listed in βmodulesβ and solve exercises in
your text and quizzes.
Good luck with your work.
I.
Examine the given statement, and then express the null hypothesis and alternative
hypothesis in symbolic form. Do not try to test it.
The mean age of CCP students is greater than 20.
II. Examine the given statement, then express the null hypothesis and alternative hypothesis in
symbolic form. Do not try to test it.
The proportion of people with green eyes is 0.2
III.
Assume that the t-distribution applies and find the critical value(s). The significance
level is 0.05 and alternative hypothesis is: pβ 0.7, sample size 32.
IV.
Assume that the normal distribution applies and find the critical values. The
significance level is 0.00004 and alternative hypothesis is: p<0.7
V.
Assume that the normal distribution applies and find the critical values. The
significance level is 0.00022 and the test is right-tailed.
VI.
Use the given information to find the P-value (normal distribution was used)
The test statistic is a two-tailed test is z=1.78
VII.
Use the given information to find the P-value (normal distribution was used)
The test statistic is z= 3.72, π»0 : π = 5, π»1 : π > 3
VIII.
An economist wants to estimate the mean income for the first year of work for
college graduates. How many such incomes must be found if we want to be 95%
confident that the sample mean is within $500 of the true population mean. Assume
that a previous study has revealed that for such incomes standard deviation is $6250.
IX.
A certain hypothesis was tested at level of significance 0.04. Would you reject it, if pvalue was 0.45?
X.
A certain hypothesis was tested at level of significance 0.01. Would you reject it, if pvalue was 0.0025 ?
XI.
Fill in the missing value in the table in such way that the correlation coefficient
between x and y is -1.
x
y
2
-6
XII.
3
-9
1
-2
3
Find the best predicted value of y given that x=1. The given statistics are summarized
from paired sample data:
r=0.872, n=500, the equation of the regression line is y=-2x+5, and the mean value of y's is 3.
Test if there is a correlation between x and y (use one of the two methods provided). Since we
reject the hypothesis that the correlation is 0, we will use the regression line:
π¦ = β2 Γ 3 + 5 = β1
XIII.
Find the best predicted value of y given that x=1. The given statistics are summarized
from paired sample data:
r=0.02, n=50, the equation of the regression line is y=8x+5, and the mean value of y's is 3.
Test if there is a correlation between x and y (use one of the two methods provided). Since we
fail to reject the hypothesis that the correlation is 0, we will use the mean value of yβs as the
answer.
XIV. What kind of relationship is measured by correlation coefficient?
XV.
Give the definition of p-value
In addition you can learn a lot by solving problems that are given to you in the text (Bluman).
Solve them independently and then compare your solutions with what you have in the text.
Example 7-1, p. 360
Example 7-2, p.360
Example 7-3, p.362
Example 7-4, p. 364
Example 7-6, p.372
Example 7-7, p. 372
Example 7-9, p. 378
Example 7-10, p. 379
Example 8-4, p. 415
Example 8-5, p.416
Example 8-6, p 419
Example 8-7, p. 420
Example 8-12, p. 429
Example 8-13, p430
Example 8-14, p. 430
Example 8-15, p. 431
Example 8-16, p. 432
Example 8-17, p. 438,
Example 8-18, p. 439
Example 8-19, p. 440
Example 8-20, p. 440
Example 10-7, p. 544
Example 10-9, p. 553
Example 10-10, p. 554