Question

A three-digit number is formed from nine numbers (1, 2, 3, 4, 5, 6, 7, 8 & 9). No number can be repeated. How many different three-digit numbers are possible if 1 and 2 will not be chosen together?

Select one:

a. 462

b. 672

c. 336

d. 210

A tire manufacturer claims that the average life of a certain grade of tire is 50,000 miles or more when used under normal driving conditions. A random sample of 20 tires is selected and tested and the sample mean is 49,650 miles. Assume the population of the lives is to be normal with standard deviation of 5,000 miles. At the 5% significance level, the manufacturer’s claim is tested. What is the decision rule in this test?

Select one:

a. Reject H₀ if Z_STAT > +1.96; otherwise, do not reject H₀.

b. Reject H₀ if t_STAT > -1.7291; otherwise, do not reject H₀.

c. Reject H₀ if Z_STAT < -1.645; otherwise, do not reject H₀.

d. Reject H₀ if t_STAT < -2.0930 or t_STAT > +2.0930; otherwise, do not reject H₀.

Jurgen is taking ISOM2002 in the current semester and he suspects that there are not too many students in the course have submitted all the assigned work (online exercises and assignments). He claims that there is no more than 70% of the students have done it. He asked around 20 friends who are also studying ISOM2002 in the current semester, and 15 of them said they had submitted all the assigned work. Suppose Jurgen would like to use hypothesis testing to support his claim, what would be the value of the test statistic?

Select one:

a. 0.516

b. Cannot be determined without the level of significance.

c. 0.488

d. ‒0.516

A report announced that the mean sales price of all new houses sold one year was $272,000. Assume that the population standard deviation of the prices is $100,000. If you select a random sample of 100 new houses, what is the probability that the sample mean sales price will be between $250,000 and $285,000?

Select one:

a. 0.8893

b. 0.2956

c. 0.8034

d. 0.1388

A publisher sends advertising material for a statistics text to 90% of all professors teaching the appropriate statistics course. Twenty-five percent of the professors who received this material adopted the book. Fifteen percent of the professors who did not receive the material also adopted the book. If a professor adopts the book, what is the probability that he has received the advertising material?

Select one:

a. 0.2250

b. 0.9375

c. 0.0375

d. 0.2500

Answer 1

1)

3 numbers can formed by

9C3 * 3!

Now we cannot include 1 and 2 together

Numbers can formed with 1 and 2 together = 7C1 * 3!

Total number of ways = 9C3 * 3! -  7C1 * 3!

= 504 - 42

= 462

2)

c. Reject H₀ if Z_STAT < -1.645; otherwise, do not reject H₀.

............

3)

Ho :   p =    0.7                  
H1 :   p <   0.7       (Left tail test)          
                          
Level of Significance,   α =    0.01                  
Number of Items of Interest,   x =   15                  
Sample Size,   n =    20                  
                          
Sample Proportion ,    p̂ = x/n =    0.7500                  
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.1025                  
Z Test Statistic = ( p̂-p)/SE = (   0.7500   -   0.7   ) /   0.1025   =   0.4880
..............

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