Stats Assignment 8

Question 1 of 23 1.0 Points

The chi-square goodness-of-fit test can be used to test for:

A.difference between population means

B.normality

C.significance of sample statistics

D.difference between population variances

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Question 2 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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Part 2 of 16 -

Question 3 of 23 1.0 Points

In a simple linear regression analysis, the following sum of squares are produced:

= 400

= 80

= 320

The proportion of the variation in Y that is explained by the variation in X is:

A.80%

B.25%

C.20%

D.50%

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Question 4 of 23 1.0 Points

The marketing manager of a large supermarket chain would like to use shelf space to predict the sales of

pet food. For a random sample of 12 similar stores, she gathered the following information regarding the

shelf space, in feet, devoted to pet food and the weekly sales in hundreds of dollars. .

Store 1 2 3 4 5 6

Shelf Space 5 5 5 10 10 10

Weekly Sales 1.6 2.2 1.4 1.9 2.4 2.6

Store 7 8 9 10 11 12

Shelf Space 15 15 15 20 20 20

Weekly Sales 2.3 2.7 2.8 2.6 2.9 3.1

Compute the value of the sample correlation coefficient between weekly sales and shelf space.

A.0.308

B.0.827

C.0.652

D.0.684

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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.independent variable

C.dependent variable

D.residual variable

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Part 3 of 16 -

Question 6 of 23 1.0 Points

An investor wants to compare the risks associated with two different stocks. One way to measure the risk

of a given stock is to measure the variation in the stock’s daily price changes.

In an effort to test the claim that the variance in the daily stock price changes for stock 1 is different from

the variance in the daily stock price changes for stock 2, the investor obtains a random sample of 21

daily price changes for stock 1 and 21 daily price changes for stock 2.

The summary statistics associated with these samples are: n1 = 21, s1 = .725, n2 = 21, s2 = .529.

If you compute the test value by placing the larger variance in the numerator, at the .05 level of

significance, would you conclude that the risks associated with these two stocks are different?

A.No, the test value of 1.371 does not exceed the critical value of 2.12

B.No, the p-value associated with this test is 0.0528

C.No, the test value of 1.879 does not exceed the critical value of 2.46

D.Yes, the p-value associated with this test is 0.0264

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Question 7 of 23 1.0 Points

Some defendants in criminal proceedings plead guilty and are sentenced without a trial, whereas others who

plead innocent are subsequently found guilty and then are sentenced. In recent years, legal scholars

have speculated as to whether sentences of those who plead guilty differ in severity from sentences for

those who plead innocent and are subsequently judged guilty. Consider the data given below on

defendants accused of robbery, all of whom, by the way, had previous prison records. At the .01 level of

significance, do these data suggest that the proportion of all defendants in these circumstances who

plead guilty and are sent to prison differs from the proportion who are sent to prison after pleading

innocent and being found guilty?

Plea

Guilty Not Guilty

Number judged guilty n1 = 191 n2 = 64

Number sentenced to prison x1 = 101 x2 = 56

Sample proportion .529 .875

A.No, because the test value -1.96 is inside the interval (-2.58, 2.58)

B.Yes, because the test value 2.58 is inside the interval (-4.94, 4.94)

C.No, because the test value -4.94 is outside the interval (-1.96, 1.96)

D.Yes, because the test value -4.94 is outside the interval (-2.58, 2.58)

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Part 4 of 16 -

Question 8 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.

A.H0: 75, H1: < 75

B.H0: = 75, H1: ≠ 75

C.H0: = 75, H1: > 75

D.H0: 75, H1: > 75

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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.

What is your conclusion?

A.Reject H0. There is enough evidence to support the claim that the proportion of students planning

to go to college is now greater than .79.

B.Cannot determine

C.Do not reject H0. There is not enough evidence to support the claim that the proportion of

students planning to go to college is greater than .79.

D.More seniors are going to college

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Question 10 of 23 1.0 Points

A type II error occurs when:

A.the null hypothesis is incorrectly rejected when it is true

B.the sample mean differs from the population mean

C.the test is biased

D.the null hypothesis is incorrectly accepted when it is false

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Part 5 of 16 -

Question 11 of 23 1.0 Points

Compute where t15 has a t-distribution with 15 degrees of freedom.

A.0.93606

B.0.7639

C.0.03197

D.0.96803

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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 standard normal distribution has a mean of ___ and standard deviation of ___, respectively.

A.1 and 0

B.0 and 1

C.1 and 1

D.0 and 0

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Part 7 of 16 -

Question 14 of 23 1.0 Points

Find the variance of the following probability distribution.

X P(X)

1 0.10

2 0.20

3 0.35

4 0.30

5 0.05

A.1.1

B.1.21

C.1.05

D.1.02

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Part 8 of 16 -

Question 15 of 23 1.0 Points

In a recent study, the following data were obtained in response to the question, “Do you favor recycling in

your neighborhood?”

Yes No No Opinion

Males 25 15 10

Females 30 10 10

If a person is picked at random, what is the probability that the person is either male or has no opinion

regarding recycling?

A.3/5

B.3/10

C.4/5

D.7/10

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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.

Two teams of workers assemble automobile engines at a manufacturing plant in Michigan. A random

sample of 145 assemblies from team 1 shows 15 unacceptable assemblies. A similar random sample of

125 assemblies from team 2 shows 8 unacceptable assemblies.

If you are interested in determining if there is sufficient evidence to conclude, at the 10% significance

level, that the two teams differ with respect to their proportions of unacceptable assemblies, what is the

p-value associated with such a test of hypothesis?

Place your answer, rounded to 4 decimal places, in the blank. For example, .0123 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.

A set of final exam scores in an organic chemistry course was found to be normally distributed, with a

mean of 73 and a standard deviation of 8.

What is the probability of getting a score of 68 or less on this exam? Place your answer, rounded to 4

decimal places in the blank. For example, 0.3456 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 25.9 mpg and a standard deviation of 9.5 mpg. If 30

such cars are tested, what is the probability the average mpg achieved by these 30 cars will be greater

than 28?

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.

It has been observed that electrical connectors manufactured by Jolt Electrical Supply Company last an

average of 18.2 months and follow a normal distribution with a standard deviation of 1.7 months. Jolt

agrees to replace any connector that fails within 19 months. Out of 500 connectors sold, how many does

Jolt expect to replace, on average? Place your answer, rounded to the nearest whole number, in the

blank. For example, 123 would be a legitimate answer.

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.

At a university, the average cost of books per student has been $550 per student per semester. The

Dean of Students believes that the costs are increasing and that the average is now greater than $550.

He surveys a sample of 40 students and finds that for the most recent semester their average cost was

$630 with a standard deviation of $120. What is the test value for this hypothesis test?

Test value: Round your answer to two 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 particular brand of women's jeans is available in seven different sizes, three different colors, and three

different styles. How many different jeans does the store manager need to order to have one pair of each

type of jean? Place your answer in the blank. Do not use any decimal places or commas. For example,

45 would be a legitimate entry.