MATHEMATICS

Question 1 of 20 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. Compute the z or t value of the sample test statistic.

A.z = 1.645
B.t = 1.916
C.z = 1.916
D.t = -1.916

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Question 2 of 20

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.\f$\chi ^{2}\f$ = 30.58
B.z = 1.65
C.t = 27.50
D.\f$\chi ^{2}\f$= 27.50

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Question 3 of 20

1.0 Points

The form of the alternative hypothesis can be:

A.one or two-tailed
B.neither one nor two-tailed
C.two-tailed
D.one-tailed

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Question 4 of 20

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 = 1.96
C.z = 0.69
D.z = 0.62

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Question 5 of 20

1.0 Points

Suppose that the mean time for a certain car to go from 0 to 60 miles per hour was 7.7 seconds. Suppose that you want to test the claim that the average time to accelerate from 0 to 60 miles per hour is longer than 7.7 seconds. What would you use for the alternative hypothesis?

A.H1: \f$\mu \f$< 7.7 seconds
B.H1: \f$\mu \f$ > 7.7 seconds
C.H1: \f$\mu \f$ = 7.7 seconds
D.H1: \f$\mu \geq \f$7.7 seconds

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Question 6 of 20

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: \f$\hat{p}\f$   = .79, H1: \f$\hat{p}\f$ > .79

B.H0:  = .79, H1:  > .79
C.H0: p = .79, H1: p ≠ .79
D.H0: p ≤ .79, H1: p > .79

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Question 7 of 20

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: \f$\mu \f$ = 75, H1: \f$\mu \f$ ≠ 75
B.H0: \f$\mu \f$ \f$\geq \f$ 75, H1: \f$\mu \f$ < 75
C.H0: \f$\mu \f$= 75, H1: \f$\mu \f$ > 75
D.H0: \f$\mu \f$ \f$\leq \f$ 75, H1: \f$\mu \f$ > 75

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Question 8 of 20

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.More seniors are going to college
B.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.
C.Cannot determine
D.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.

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Question 9 of 20

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 may increase or decrease
B.The p – value decreases
C.The p – value increases
D.The p – value stays the same

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Question 10 of 20

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 test value 1.257 is greater than the critical value 1.115
B.Yes, because the test value 1.257 is less than the critical value 2.179
C.No, because the p-value for this test is equal to .1164
D.Yes, because the test value 1.257 is less than the critical value 1.782

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Question 11 of 20

1.0 Points

Which of the following statements are true of the null and alternative hypotheses?

A.Both hypotheses must be true
B.Exactly one hypothesis must be true
C.It is possible for neither hypothesis to be true
D.It is possible for both hypotheses to be true

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Part 2 of 3 –
Question 12 of 20

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 statistician wishes to test the claim that the standard deviation of the weights of firemen is greater than 25 pounds. To do so, she selected a random sample of 20 firemen and found s = 27.2 pounds. Assuming that the weights of firemen are normally distributed, to test her research hypothesis the statistician would use a chi-square test. In that case, what is the computed test value? Place your answer, rounded to 3 decimal places, in the blank. For example, 23.456 would be a legitimate entry.

Question 13 of 20

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:  f$mu geq f$ 100 versus H1: f$mu< f$  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.

Question 14 of 20

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 a firm that produces light bulbs wants to know whether it can say that its light bulbs typically last more than 1500 hours. Hoping to find support for their claim, the firm collects a random sample of n = 25 light bulbs and records the lifetime (in hours) of each bulb. The information related to the hypothesis test is presented below. Test of H0: f$mu leq f$ 1500 versus H1:f$mu f$  > 1500 Sample mean 1509.5 Std error of mean 4.854 What is the test value that you would use to conduct this test? Place your answer, rounded to 3 decimal places in the blank. For example, 1.234 would be a legitimate entry.

Question 15 of 20

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 a firm that produces light bulbs wants to know whether it can say that its light bulbs typically last more than 1500 hours. Hoping to find support for their claim, the firm collects a random sample of n = 25 light bulbs and records the lifetime (in hours) of each bulb. The information related to the hypothesis test is presented below. Test of H0: f$mu leq f$ 1500 versus H1: f$mu  f$> 1500 Sample mean 1509.5 Std error of mean 4.854 Assuming the life length of this type of lightbulb 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.

Question 16 of 20

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 medical doctor wishes to test the claim that the standard deviation of the systolic blood pressure of deep sea divers is less than 450. To do so, she selected a random sample of 20 divers and found s = 432. Assuming that the systolic blood pressures of deep sea divers are normally distributed, if the doctor wanted to test her research hypothesis at the .01 level of significance, what is the critical value? Place your answer, rounded to 3 decimal places, in the blank. For example, 4.567 would be a legitimate entry.

Question 17 of 20

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 CEO of a software company is committed to expanding the proportion of highly qualified women in the organization’s staff of salespersons. He believes that the proportion of women in similar sales positions across the country is less than 45%. Hoping to find support for his belief, he directs you to test H0: p  f$geq f$ .45 vs H1: p < .45. In doing so, you collect a random sample of 50 salespersons employed by his company, which is thought to be representative of sales staffs of competing organizations in the industry. The collected random sample of size 50 showed that only 18 were women. What is the smallest level of significance at which you could reject the null in favor of the alternative hypothesis? Place your answer, rounded to 4 decimal places, in the blank. For example, 0.1234 would be a legitimate entry.

Part 3 of 3 –
Question 18 of 20

1.0 Points

If a null hypothesis about a population proportion p is rejected at the 0.025 level of significance, then it must also be rejected it at the 0.05 level.

True
False

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Question 19 of 20

1.0 Points

In order to determine the p-value, it is unnecessary to know the level of significance.

True
False

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Question 20 of 20

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 f$mu f$ falls between the lower and upper confidence limits.

True
False

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