Mathematics questions
1.0/ 1.0 Points
A manufacturer of flashlight batteries took a sample of 13 batteries from a day’s production and used them continuously until they failed to work. The life lengths of the batteries, in hours, until they failed were: 342, 426, 317, 545, 264, 451, 1049, 631, 512, 266, 492, 562, and 298.
At the .05 level of significance, is there evidence to suggest that the mean life length of the batteries produced by this manufacturer is more than 400 hours?
A.No, because the p-value for this test is equal to .1164
B.Yes, because the test value 1.257 is less than the critical value 1.782
C.Yes, because the test value 1.257 is less than the critical value 2.179
D.No, because the test value 1.257 is greater than the critical value 1.115
Answer Key:
Question 2 of 20
1.0/ 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 increases
D.The p – value decreases
Answer Key:
Question 3 of 20
1.0/ 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.
State the null and alternative hypotheses.
A.H0: m = .79, H1: m > .79
B.H0: p ≤ .79, H1: p > .79
C.H0: p = .79, H1: p ≠ .79
D.
H0: = .79, H1: > .79
Answer Key:
Question 4 of 20
1.0/ 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 = 0.62
C.z = 1.96
D.z = 0.69
Answer Key:
Question 5 of 20
1.0/ 1.0 Points
A severe storm has an average peak wave height of 16.4 feet for waves hitting the shore. Suppose that a storm is in progress with a severe storm class rating. Let us say that we want to set up a statistical test to see if the wave action (i.e., height) is dying down or getting worse. If you wanted to test the hypothesis that the waves are dying down, what would you use for the alternate hypothesis? Is the P-value area on the left, right, or on both sides of the mean?
A.H1: is greater than 16.4 feet; the P-value area is on the left of the mean
B.H1: is greater than 16.4 feet; the P-value area is on both sides of the mean
C.H1: is less than 16.4 feet; the P-value area is on the left of the mean
D.H1: is not equal to 16.4 feet; the P-value area is on the right of the mean
Answer Key:
Question 6 of 20
1.0/ 1.0 Points
Which of the following statements are true of the null and alternative hypotheses?
A.It is possible for neither hypothesis to be true
B.Both hypotheses must be true
C.Exactly one hypothesis must be true
D.It is possible for both hypotheses to be true
Answer Key:
Question 7 of 20
1.0/ 1.0 Points
The alternative hypothesis is also known as the:
A.optional hypothesis
B.elective hypothesis
C.research hypothesis
D.null hypothesis
Answer Key:
Question 8 of 20
1.0/ 1.0 Points
Which of the following values is not typically used for ?
A.0.01
B.0.50
C.0.10
D.0.05
Answer Key:
Question 9 of 20
1.0/ 1.0 Points
Smaller p-values indicate more evidence in support of the:
A.the reduction of variance
B.null hypothesis
C.alternative hypothesis
D.quality of the researcher
Answer Key:
Question 10 of 20
1.0/ 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?
Compute the value of the appropriate test statistic.
A.z = 1.65
B.= 27.50
C. = 30.58
D.t = 27.50
Answer Key:
Question 11 of 20
0.0/ 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 the a = .01 level of significance, what is your conclusion?
A.
Reject H0. At the = .01 level of significance, there is not enough evidence to support the claim that this technician’s true variance is larger than the target accuracy.
B.Do not reject H0. At the = .01 level of significance there is not sufficient evidence to suggest that this technician’s true variance is greater than the target accuracy.
C.Cannot determine
D.Reject H0. At the = .01 level of significance, there is enough evidence to support the claim that this technician’s variance is larger than the target accuracy.
Answer Key:
Comment: 2.2 > 1.2 outside the rejection area
Part 2 of 3 –
5.0/ 6.0 Points
Question 12 of 20
0.0/ 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 firm that produces light bulbs claims that their lightbulbs last 1500 hours, on average. You wonder if the average might differ from the 1500 hours that the firm claims. To explore this possibility you take a random sample of n = 25 light bulbs purchased from this firm and record the lifetime (in hours) of each bulb. You then conduct an appopriate test of hypothesis. Some of the information related to the hypothesis test is presented below.
Test of H0: = 1500 versus H1: 1500
Sample mean 1509.5
Sample Standard Deviation 24.27
Assuming the life length of this type of lightbulb 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. 0.031
Answer Key:
Comment: multiply by two, you have a two tailed test
Question 13 of 20
1.0/ 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. 0.34
Answer Key:
Question 14 of 20
1.0/ 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 $400 per student per semester. The Dean of Students believes that the costs are increasing and that the average is now greater than $400. He surveys a sample of 40 students and finds that for the most recent semester their average cost was $430 with a standard deviation of $80. What is the test value for this hypothesis test?
Test value: 2.36 Round your answer to two decimal places as necessary.
Answer Key:
Question 15 of 20
1.0/ 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 100 hours, on average. You decide to conduct a test to see if the company’s claim is true. You believe that the mean life may be different from 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, if you wish to conduct this test at the 0.05 level of significance, what are the critical values that you should use? Place the smaller critical value, rounded to 3 decimal places, in the first blank. For example, -1.234 would be a legitimate entry. -2.093 . Place the larger critical value, rounded to 3 decimal places, in the second blank. For example, 1.234 would be a legitimate entry. 2.093
Answer Key:
Question 16 of 20
1.0/ 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, if you wish to conduct this test using a .05 level of significance, what is the critical value that you should use? Place your answer, rounded to 3 decimal places in the blank. For example, -1.234 would be a legitimate entry. -1.729
Answer Key:
Question 17 of 20
1.0/ 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 190 customers, 15 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: 0.1357 Round your answer to four decimal places as necessary.
Answer Key:
Part 3 of 3 –
2.0/ 3.0 Points
Question 18 of 20
1.0/ 1.0 Points
Using the confidence interval when conducting a two-tailed test for the population mean, we do not reject the null hypothesis if the hypothesized value for falls between the lower and upper confidence limits.
True
False
Answer Key:
Question 19 of 20
1.0/ 1.0 Points
A low p–value provides evidence for accepting the null hypothesis and rejecting the alternative.
True
False
Answer Key:
Question 20 of 20
0.0/ 1.0 Points
If a null hypothesis about a population mean is rejected at the 0.025 level of significance, then it must also be rejected at the 0.01 level.
True
False
Answer Key:
"Not answered?"
