# Statistics & probability timed exam quiz

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

Question 2 of 23 1.0 Points
A company operates four machines during three shifts each day. From production records, the data in the table below were collected. At the .05 level of significance test to determine if the number of breakdowns is independent of the shift.

Machine
Shift A B C D
1 41 20 12 16
2 31 11 9 14
3 15 17 16 10

A.The number of breakdowns is dependent on the shift, because the test value 11.649 is less than the critical value of 12.592.
B.The claim that the number of breakdowns is independent of the shift cannot be rejected, because the test value 11.649 is less than the critical value of 12.592.
C.The number of breakdowns is dependent on the shift, because the p-value is .07.
D.The number of breakdowns is independent of the shift, because the test value 12.592 is greater than the critical value of 11.649.

Part 2 of 16 –

Question 3 of 23 1.0 Points
Outliers are observations that

A.disrupt the entire linear trend

B.render the study useless

C.lie outside the sample

D.lie outside the typical pattern of points

Question 4 of 23 1.0 Points
If an estimated regression line has a Y-intercept of –7.5 and a slope of 2.5, then when X = 3, the actual value of Y is:

A.10

B.0

C.unknown
D.5

Question 5 of 23 1.0 Points
Data for a sample of 25 apartments in a particular neighborhood are provided in the worksheet Apartments in the Excel workbook Apartments.xlsx.  Using that data, find the estimated regression equation which can be used to estimate the monthly rent for apartments in this neighborhood using size as the predictor variable.

A. 177.12 + 0.8500(size)

B. 1.065 + 177.12(size)

C.     177.12 + 1.065(size)

D. 197.12 + 2.065(size)

Part 3 of 16 –

Question 6 of 23 1.0 Points
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.

Is there sufficient evidence to conclude, at the 10% significance level, that the two teams differ with respect to their proportions of unacceptable assemblies?

A.No, since the p-value is less than 0.10

B.No, since the test value exceeds the critical value

C.No, since the test value does not exceed the critical value
D.Yes, since the p-value is greater than 0.10

Question 7 of 23 1.0 Points
Multiple myeloma or blood plasma cancer is characterized by increased blood vessel formulation in the bone marrow that is a prognostic factor in survival. One treatment approach used for multiple myeloma is stem cell transplantation with the patient’s own stem cells. The following data represent the bone marrow microvessel density for a sample of 7 patients who had a complete response to a stem cell transplant as measured by blood and urine tests. Two measurements were taken: the first immediately prior to the stem cell transplant, and the second at the time of the complete response.

Patient 1 2 3 4 5 6 7
Before 158 189 202 353 416 426 441
After 284 214 101 227 290 176 290

Suppose you wanted to conduct a test of hypothesis to determine if there is sufficient evidence to conclude that the mean bone marrow microvessel density is higher before the stem cell transplant than after the stem cell transplant?  What is the p-value associated with the test of hypothesis you would conduct?

A.p = .057493

B.p = .942597

C.p = .885014

D.p = .114986

Part 4 of 16 –

Question 8 of 23 1.0 Points
A two-tailed test is one where:

A.negative sample means lead to rejection of the null hypothesis

B.results in only one direction can lead to rejection of the null hypothesis

D.results in either of two directions can lead to rejection of the null hypothesis

Question 9 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 stays the same

B.The p – value may increase or decrease

C.The p – value decreases

D.The p – value increases

Question 10 of 23 1.0 Points
A type II error occurs when:

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

B.the sample mean differs from the population mean

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

D.the test is biased

Part 5 of 16 –

Question 11 of 23 1.0 Points
In constructing a confidence interval estimate for a population mean, when we replace   with the sample standard deviation (s), we introduce a new source of variability and the sampling distribution we use is:

A.F- distribution

B.the normal distribution

C.chi-square distribution

D.t -distribution

Question 12 of 23 1.0 Points
If you are constructing a confidence interval for a single mean, the confidence interval will___________ with an increase in the sample size.

A.increase

B.decrease

C.stay the same

D.increase or decrease, depending on the sample data

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 1
B.0 and 0

C.0 and 1

D.1 and 0

Part 7 of 16 –

Question 14 of 23 1.0 Points
One of the requirements for a binomial experiment is that there must be a(n) _____ number of trials.

A.infinite

B.fixed

C.odd

D.random

Part 8 of 16 –

Question 15 of 23 1.0 Points
If 25 tickets are sold and 2 prizes are to be awarded, find the probability that one person will win both prizes if that person buys exactly 2 tickets.

A.1/600

B.1/700

C.1/2300

D.1/300

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.

A sport preference poll yielded the following data for men and women. Use a 5% significance level and test to determine if sport preference and gender are independent.
Sport Preferences of Men and Women
Men 20 25 30 75
Women 18 12 15 45
38 37 45 120

What is the test value for this hypothesis test?

What is the critical value for this hypothesis test?

What is the conclusion for this hypothesis test?  Choose one.

1.  There is sufficient evidence to support the claim that one’s sport preference is dependent on one’s gender.
2. There is not sufficient evidence to support the claim that one’s sport preference is dependent on one’s gender.

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.

A company has observed that there is a linear relationship between indirect labor expense (ILE) , in dollars, and direct labor hours (DLH). Data for direct labor hours and indirect labor expense for 18 months are given in the file ILE_and_DLH.xlsx

Treating ILE as the response variable, use regression to fit a straight line to all 18 data points. What values for the intercept (a)  and slope (b) do you obtain?

Place your answers, rounded to 3 decimal places, in the blanks provided.  Do not use any stray punctuation marks.  For example, 34.567 would be a legitimate entry.

intercept (a) =
slope(b) =

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 test value you would use to conduct such a test of hypothesis?

Place your answer, rounded to 2 decimal places, in the blank. For example, 2.34 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.
In a particular region of Cape Cod, it is known that lobstermen trap on average of 32 pounds of lobster per day with a standard deviation of four pounds. If a random sample of 30 lobster fishermen is selected, what is the probability that their average catch is less than 31.5 pounds?

Place your answer, rounded to four decimal places, in the blank.      When entering your answer do not use any labels or symbols other than a decimal point. Simply provide the numerical value. For example, 0.1234 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 personnel department of a large corporation wants to estimate the family dental expenses of its employees to determine the feasibility of providing a dental insurance plan. A random sample of 12 employees reveals the following family dental expenses (in dollars): 115, 370, 250, 593, 540, 225, 177, 425, 318, 182, 275, and 228.

Construct a 99% confidence interval estimate for the standard deviation of family dental expenses for all employees of this corporation.

Place your LOWER limit, in dollars rounded to 1 decimal place, in the first blank. Do not use a dollar sign, a comma, or any other stray mark. For example, 98.4 would be a legitimate entry.

Place your UPPER limit, in dollars rounded to 1 decimal place, in the second blank. Do not use a dollar sign, a comma, or any other stray mark. For example, 567.8 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.

In a survey, 55% of the voters support a particular referendum. If 40 voters are chosen at random, and X is the number of voters that support this referendum, find the mean and variance of X. Place the mean in the first blank   and place the variance in the second blank.

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 260 customers, 20 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.

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.

If a set of six books is to be placed on a shelf, in how many ways can the six books be arranged? Place your answer in the blank. Do not use any decimal places or commas. For example, 45 would be a legitimate entry.

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