MATH 302 Final Exam MCQs and Problems

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Final Exam_MATH302

 

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Part 1 of 16 -

 

Question 1 of 23                                                                                                                                                                               1.0 Points
The data  presented in the table  below resulted from an experiment in which seeds of 5 different types were planted and the number of seeds that germinated within 5 weeks after planting was recorded for each seed type. At the .01
level of significance, is the proportion  of seeds that germinate dependent on the seed type?

 

 


Seed Type  Observed Frequencies
  Germinated Failed  to Germinate
 1 31 7
 2 57 33
 3 87 60
 4 52 44
 5 10 19

A.Yes, because the test value 16.86  is greater than the critical value of 13.28

B.Yes, because the test value 16.86  is less than the critical value of 14.86

C.No, because the test value 16.86  is greater than the critical value of 13.28

D.No, because the test value 13.28  is less  than the critical value of 16.86
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Question 2 of 23                                                                                                                                                                               1.0 Points
The chi-square goodness-of-fit test can be used to test for:

A.normality

B.significance of sample statistics

C.difference between population variances

D.difference between population means
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Part 2 of 16 -

 

Question 3 of 23                                                                                                                                                                               1.0 Points
A single variable X can  explain a large  percentage of the variation in some other variable  Y when the two variables are:

A.highly correlated

B.directly related

C.mutually  exclusive

D.inversely  related
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1.0 Points
Question 4 of 23
The standard error of the estimate, sest, is essentially the

A.standard deviation of the explanatory variable

B.mean of the explanatory variable

C.mean of the residuals

D.standard deviation  of the residuals
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Question 5 of 23                                                                                                                                                                               1.0 Points
In regression analysis, the variable  we are trying to explain or predict is called the

A.regression variable

B.dependent variable

C.residual variable

D.independent variable
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Part 3 of 16 -

 

Question 6 of 23                                                                                                                                                                               1.0 Points Q-Mart is interested in comparing its male and female  customers. Q-Mart would like to know if the amount of money spent by its female  charge customers differs, on average, from the amount spent by its male charge customers.

To answer this question, an analyst collected random samples of 25 female  customers and 22 male customers. Based on these samples, on average, the 25 women  charge customers spent $102.23 and the 22 men charge customers spent $86.46. Moreover,  the sample standard deviation  of the amount charged by the 25 women  was $93.393, and the sample standard deviation of the amount charged by the 22 men  was $59.695.

Using the procedure advocated by Bluman,   at the 10% level of significance, is there  sufficient evidence for Q-Mart to conclude that, on average, the amount spent by women  charge customers differs from the amount spent by men charge customers.
A.No, the p-value  of this test  is less  than  0.10.

B.Yes, the test value does not exceed the critical value

C.No, the test value does not exceed the critical value.

D.Yes, the p-value  of this test  is greater than 0.10
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Question 7 of 23                                                                                                                                                                               1.0 Points
Two independent samples of sizes n1  = 50 and n2  = 50 are randomly  selected from two populations to test the difference between the population means,    . The sampling distribution of the sample mean
difference,    is:

A.normally distributed

B.chi-squared distributed with 99 degrees of freedom

C.approximately normal

D.t - distributed with 98 degrees of freedom
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Part 4 of 16 -

 

Question 8 of 23                                                                                                                                                                               1.0 Points
You conduct a hypothesis test and you observe values for the sample mean and sample standard deviation  when n =
25 that do not lead to the rejection of H0. You calculate a p-value  of 0.0667. What will happen to the p-value  if you observe the same sample mean and standard deviation  for a sample size larger than 25?
A.The p – value decreases

B.The p – value stays the same

C.The  p – value increases

D.The p – value may increase or decrease
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Question 9 of 23                                                                                                                                                                               1.0 Points
Results from previous studies showed 79% of all high school  seniors from a certain  city plan to attend college  after graduation. A random sample of 200 high school  seniors from this city reveals that 162 plan to attend college. Does  this indicate  that the percentage has increased from that of previous studies? Test at the 5% level of significance.

Compute the z or t value of the sample test  statistic.

A.t = 1.645

B.z = 0.69

C.z = 0.62

D.z = 1.96
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Question 10 of 23                                                                                                                                                                             1.0 Points
In an article appearing in Today’s  Health a writer states that the average number of calories in a serving  of popcorn is
75. To determine if the average number of calories in a serving  of popcorn is different from 75, a nutritionist selected a random sample of 20 servings of popcorn and computed the sample mean number of calories per serving  to be 78 with a sample standard deviation  of 7.

State the null and alternative hypotheses.

 

 

 

 

 

 


Part 5 of 16 -
 
A.H0:     = 75, H1:     ≠ 75

B.H0:     = 75, H1:     > 75

 

Question 11 of 23
 
1.0 Points
A previous study of nickels showed that the standard deviation of the weight of nickels is 150 milligrams. How many nickels does a coin counter manufacturer need to weigh so that she  can  be 98% confident that her sample mean is within 25 milligrams of the true average weight of a nickel?
A.36

B.196

C.239

D.139
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Question 12 of 23                                                                                                                                                                             1.0 Points
From a sample of 500 items,  30 were found to be defective. The point estimate of the population proportion  defective will be:
A..06

B.0.60

C.30

D.16.667
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Part 6 of 16 -

 

Question 13 of 23                                                                                                                                                                             1.0 Points
The mean of a probability distribution is a:

A.measure of relative likelihood

B.measure of variability of the distribution

C.measure of central  location

D.measure of skewness of the distribution
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Part 7 of 16 -

 

Question 14 of 23                                                                                                                                                                             1.0 Points
If a gambler rolls two dice and gets  a sum of 10, he wins $10, and if he gets  a sum of three,  he wins $20. The cost to play the game is $5. What is the expectation of this game?

A.$3.06

B.-$2.78

C.-$3.06

D.$2.78
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Part 8 of 16 -
Question 15 of 23                                                                                                                                                                             1.0 Points
A furniture manufacturer offers bookcases in 5 different sizes and 3 different colors.  If every color is available in every size,  then  the total number of different bookcases is
A.5

B.8

C.15

D.30
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Part 9 of 16 -

 

Question 16 of 23                                                                                                                                                                             3.0 Points Accepted characters: numbers, decimal  point markers (period or comma), sign indicators (-), spaces (e.g.,  as thousands separator, 5 000), "E" or "e" (used in scientific notation).  NOTE: For scientific notation,  a period MUST be used as the decimal point marker.
Complex  numbers should  be in the form (a + bi) where  "a" and "b" need to have  explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.


Staples, a chain of large office supply  stores, sells a line of desktop and laptop computers. Company executives want to know whether the demands for these two types of computers are dependent on one another. Each  day's demand for each type of computers is categorized as Low, Medium-Low, Medium- High, or High. The data  shown  in the table below is based on 200 days  of operation. Based on these data,
can Staples conclude that demands for these two types  of computers are independent? Test  at the 5% level
of significance.

   desktops   
  low med-low med-high high 
 low 3 14 14 4 35
laptops med-low 6 18 17 22 63
 med-high 13 16 11 16 56
 high 8 14 15 9 46
  30 62 57 51 200


What is the test  value for this hypothesis test?


Answer:  Round  your answer to two decimal places. What is the critical value for this hypothesis test?
Answer:  Round  your answer to two decimal places. What is the conclusion for this hypothesis test?  Choose one.
1.  At the .05 level of significance, Staples can conclude that demands for these two types of computers are
independent.
2. At the .05 level of significance, Staples can conclude that demands for these two types  of computers are dependent.


Answer:                                     Enter only a 1 or 2 for your answer.
Part 10 of 16 -

 

Question 17 of 23                                                                                                                                                                             1.0 Points Accepted characters: numbers, decimal  point markers (period or comma), sign indicators (-), spaces (e.g.,  as thousands separator, 5 000), "E" or "e" (used in scientific notation).  NOTE: For scientific notation,  a period MUST be used as the decimal point marker.
Complex  numbers should  be in the form (a + bi) where  "a" and "b" need to have  explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

The  marketing manager of a large  supermarket chain  would like to determine the  effect  of shelf  space (in feet) on the weekly sales of international food (in hundreds of dollars).  A random sample of 12 equal –sized stores is selected, with the following results:

Store Shelf Space(X) Weekly Sales(Y)
1 10 2.0
2 10 2.6
3 10 1.8
4 15 2.3
5 15 2.8
6 15 3.0
7 20 2.7
8 20 3.1
9 20 3.2
10 25 3.0
11 25 3.3
12 25 3.5


Using the equation of the regression line for these data, predict the average weekly sales (in hundreds of dollars) of international food for stores with 13 feet of shelf space for international food.

Place your answer, rounded to 3 decimal  places , in the blank.  Do not use  a dollar sign.  For example, 2.345  would be a legitimate  entry.

 

 


Part 11 of 16 -

 

Question 18 of 23                                                                                                                                                                             1.0 Points Accepted characters: numbers, decimal  point markers (period or comma), sign indicators (-), spaces (e.g.,  as thousands separator, 5 000), "E" or "e" (used in scientific notation).  NOTE: For scientific notation,  a period MUST be used as the decimal point marker.
Complex  numbers should  be in the form (a + bi) where  "a" and "b" need to have  explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.


Q-Mart is interested in comparing its male and female  customers. Q-Mart would like to know if the amount of money spent by its female  charge customers differs, on average, from the amount spent by its male charge customers.
To answer this question, an analyst collected random samples of 25 female  customers and 22 male customers. Based on these samples, on average, the 25 women  charge customers spent $102.23 and the 22 men charge customers spent $86.46. Moreover,  the sample standard deviation  of the amount charged by the 25 women  was $93.393, and the sample standard deviation of the amount charged by the 22 men  was $59.695.

Suppose, using a 10% level of significance, you wish to know if there  is sufficient evidence for Q-Mart to conclude that, on average, the amount spent by women  charge customers differs from the amount spent by men  charge customers. That is suppose you wish to test

H0:     versus H1:  


Assuming that the amounts spent by female  and male charge customers at Q-Mart are normally distributed, based on the procedure advocated by Bluman,  what is/are  the critical values that you would use  to conduct this test of hypothesis? Place your answer, rounded to 3 decimal  places, in the blank. If there  are two critical values, place  only the
positive value in the blank. For example, 2.035  would be a legitimate entry.

 

Part 12 of 16 -

 

Question 19 of 23                                                                                                                                                                             1.0 Points Accepted characters: numbers, decimal  point markers (period or comma), sign indicators (-), spaces (e.g.,  as thousands separator, 5 000), "E" or "e" (used in scientific notation).  NOTE: For scientific notation,  a period MUST be used as the decimal point marker.
Complex  numbers should  be in the form (a + bi) where  "a" and "b" need to have  explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

Mrs. Smith's  reading class can read  a mean of 175 words per minute  with a standard deviation  of 20 words per minute.  The top 3% of the class is to receive a special award. Assuming that the distribution of words read  per minute  are normally distributed, what is the minimum number of words per minute a student would have  to read  in order to get the award? Place your answer, rounded to the nearest whole number,  in the
blank.                           When entering your answer do not use  any labels  or
symbols. Simply provide the numerical value.  For example, 123 would be a legitimate entry.

 

Part 13 of 16 -

 

Question 20 of 23                                                                                                                                                                             1.0 Points Accepted characters: numbers, decimal  point markers (period or comma), sign indicators (-), spaces (e.g.,  as thousands separator, 5 000), "E" or "e" (used in scientific notation).  NOTE: For scientific notation,  a period MUST be used as the decimal point marker.
Complex  numbers should  be in the form (a + bi) where  "a" and "b" need to have  explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.


The manufacturer of a new compact car claims the miles per gallon (mpg) for the gasoline consumption is mound- shaped and symmetric with a mean of 24.6 mpg and a standard deviation  of 11.2 mpg.  If 30 such  cars  are tested, what is the probability the average mpg achieved by these 30 cars  will be greater than 27?

Answer:                                     Round  your answer to 4 decimal places as necessary. For example, 0.1357 would be a legitimate  entry.
Part 14 of 16 -

 

Question 21 of 23                                                                                                                                                                             1.0 Points Accepted characters: numbers, decimal  point markers (period or comma), sign indicators (-), spaces (e.g.,  as thousands separator, 5 000), "E" or "e" (used in scientific notation).  NOTE: For scientific notation,  a period MUST be used as the decimal point marker.
Complex  numbers should  be in the form (a + bi) where  "a" and "b" need to have  explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.


Find the expected value of the following probability distribution.

X 1 2 3 4 5
P(X) 0.05 0.20 0.35 0.25 0.15

Round  your answer to two decimal  place as necessary. For example, 4.56 would be a legitimate entry.


Expected value =

 


Part 15 of 16 -

 

Question 22 of 23                                                                                                                                                                             1.0 Points Accepted characters: numbers, decimal  point markers (period or comma), sign indicators (-), spaces (e.g.,  as thousands separator, 5 000), "E" or "e" (used in scientific notation).  NOTE: For scientific notation,  a period MUST be used as the decimal point marker.
Complex  numbers should  be in the form (a + bi) where  "a" and "b" need to have  explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.


A survey  determines that mint chocolate chip is the favorite ice cream flavor of 6% of consumers. An ice cream shop determines that of 240 customers, 18 customers stated their preference for mint chocolate chip.

Find the P-value that would be used to determine if the percentage of customers who prefer mint chocolate chip ice has increased at a 5% level of significance.

P-value:                              Round  your answer to four decimal  places as necessary.

 

Part 16 of 16 -

 

Question 23 of 23                                                                                                                                                                             1.0 Points Accepted characters: numbers, decimal  point markers (period or comma), sign indicators (-), spaces (e.g.,  as thousands separator, 5 000), "E" or "e" (used in scientific notation).  NOTE: For scientific notation,  a period MUST be used as the decimal point marker.
Complex  numbers should  be in the form (a + bi) where  "a" and "b" need to have  explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.


A jar contains four white marbles, five red marbles, and six black marbles. If a marble  was selected at random, find the probability that it is white or black. Place your answer, rounded to 2 decimal places in the blank. For example 0.23 would be a legitimate entry.
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