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
Reset Selection
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
Reset Selection
Part 2 of 16 -
Question 3 of 23
1.0 Points
In a simple linear regression analysis, the following sum of squares are produced:
= 500
= 100
= 400
The proportion of the variation in Y that is explained by the variation in X is:
Reset Selection
Question 4 of 23
1.0 Points
In regression analysis, the variable we are trying to explain or predict is called the
Reset Selection
Question 5 of 23
1.0 Points
In choosing the “best-fitting” line through a set of points in linear regression, we choose the one with the:
Reset Selection
Part 3 of 16 -
Question 6 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
Perform an appropriate test of hypothesis to determine if there is evidence, at the .05 level of significance, to support the claim that the mean bone marrow microvessel density is higher before the stem cell transplant than after the stem cell transplant? What is the value of the sample test statistic?
Reset Selection
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?
Reset Selection
Part 4 of 16 -
Question 8 of 23
1.0 Points
A lab technician is tested for her consistency by taking multiple measurements of cholesterol levels from the same blood sample. The target accuracy is a variance in measurements of 1.2 or less. If the lab technician takes 16 measurements and the variance of the measurements in the sample is 2.2, does this provide enough evidence to reject the claim that the lab technician’s accuracy is within the target accuracy?
At thea = .01 level of significance, what is your conclusion?
Reset Selection
Question 9 of 23
1.0 Points
A null hypothesis can only be rejected at the 5% significance level if and only if:
Reset Selection
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. At thea = .05 level of significance, does the nutritionist have enough evidence to reject the writer’s claim?
Reset Selection
Part 5 of 16 -
Question 11 of 23
1.0 Points
The t- distribution for developing a confidence interval for a mean has _____ degrees of freedom.
Reset Selection
Question 12 of 23
1.0 Points
In order to be accepted into a top university, applicants must score within the top 5% on the SAT exam. Given that SAT test scores are normally distributed with a mean of 1000 and a standard deviation of 200, what is the lowest possible score a student needs to qualify for acceptance into the university?
Reset Selection
Part 6 of 16 -
Question 13 of 23
1.0 Points
If the value of the standard normal random variable Z is positive, then the original score is where in relationship to the mean?
Reset Selection
Part 7 of 16 -
Question 14 of 23
1.0 Points
In a small town, 60% of the households have dogs. If 5 households are randomly selected, what is the probability that at least 4 of them have dogs?
Reset Selection
Part 8 of 16 -
Question 15 of 23
1.0 Points
If events A and B are mutually exclusive, then the probability of both events occurring simultaneously is equal to
Reset Selection
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
Basketball
Football
Soccer
Men
20
25
30
75
Women
18
12
15
45
38
37
45
120
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. 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.
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.
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.
A school determines that the number of children X in the families who attend the school follows the distribution below:
Number of children X
1
2
3
4
5
Probability P(X)
0.20
0.35
0.25
0.15
0.05
What is the mean number of children per family? Round your answer to one decimal place as necessary. For example, 4.5 would be a legitimate entry.
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.
The ABC battery company claims that their batteries last at least 100 hours, on average. Your experience with their batteries has been somewhat different, so you decide to conduct a test to see if the company's claim is true. You believe that the mean life is actually less than the 100 hours the company claims. You decide to collect data on the average battery life (in hours) of a random sample of n = 20 batteries. Some of the information related to the hypothesis test is presented below.
Test of H0: 100 versus H1: 100 Sample mean 98.5 Std error of mean 0.777
Assuming the life length of batteries is normally distributed, what is the p-value associated with this test? Place your answer, rounded to 3 decimal places in the blank. For example, 0.234 would be a legitimate entry.
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.
Suppose that a marketing firm sends questionnaires to two different companies. Based on historical evidence, the marketing research firm believes that each company, independently of the other, will return the questionnaire with a probability of 0.30. What is the probability that both questionnaires will be returned? Place your answer, rounded to 2 decimal places, in the blank. For example, 0.23 is a legitimate entry.
Solution: apu math302 final exam solution