## MATH 302 -Final Exam

Question 1 of 23

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?

Observed Frequencies

Germinated

Failed to Germinate

1

7

57

33

3

87

60

4

52

44

5

Seed Type

31

2

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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1.0 Points

Question 5 of 23

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 –

1.0 Points

Question 6 of 23

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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1.0 Points

Question 7 of 23

Two independent samples of sizes n1 = 50 and n2 = 50 are randomly selected from two populations to test the

difference between the population means,

difference,

. The sampling distribution of the sample mean

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 –

1.0 Points

Question 8 of 23

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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1.0 Points

Question 9 of 23

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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1.0 Points

Question 10 of 23

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.

A.H0:

= 75, H1:

≠ 75

B.H0:

= 75, H1:

> 75

C.H0:

75, H1:

< 75

D.H0:

75, H1:

> 75

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Part 5 of 16 –

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 –

3.0 Points

Question 16 of 23

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, MediumHigh, 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-high

high

low

3

14

14

4

35

med-low

6

18

17

22

63

med-high

13

16

11

16

56

high

8

14

15

9

46

30

laptops

med-low

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 –

1.0 Points

Question 17 of 23

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 moundshaped 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:

legitimate entry.

Round your answer to 4 decimal places as necessary. For example, 0.1357 would be a

Part 14 of 16 –

1.0 Points

Question 21 of 23

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 –

1.0 Points

Question 22 of 23

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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