# Mathematics

 Question 1 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.z = 1.96 B.z = 0.69 C.t = 1.645 D.z = 0.62

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 Question 2 of 20 1.0 Points

A null hypothesis can only be rejected at the 5% significance level if and only if:

 A.a 95% confidence interval does not include the hypothesized value of the parameter B.the null hypotheses includes sampling error C.a 95% confidence interval includes the hypothesized value of the parameter D.the null hypothesis is biased

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 Question 3 of 20 1.0 Points

A type II error occurs when:

 A.the sample mean differs from the population mean B.the test is biased C.the null hypothesis is incorrectly rejected when it is true D.the null hypothesis is incorrectly accepted when it is false

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 Question 4 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:   75, H1:  > 75 B.H0:   75, H1:  < 75 C.H0:  = 75, H1:  ≠ 75 D.H0:  = 75, H1:  > 75

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 Question 5 of 20 1.0 Points

If a teacher is trying to prove that a new method of teaching economics is more effective than a traditional one, he/she will conduct a:

 A.two-tailed test B.one-tailed test C.confidence interval D.point estimate of the population parameter

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 Question 6 of 20 1.0 Points

The form of the alternative hypothesis can be:

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

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 Question 7 of 20 1.0 Points

Smaller p-values indicate more evidence in support of the:

 A.quality of the researcher B.the reduction of variance C.alternative hypothesis D.null hypothesis

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 Question 8 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.z = 1.65 B. = 30.58 C.t = 27.50 D.= 27.50

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 Question 9 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? At the  = .01 level of significance, what is your conclusion?

 A.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. 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 not enough evidence to support the claim that this technician’s true variance is larger than the target accuracy.

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 Question 10 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:    = .79, H1:  > .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 11 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 = 1.916 B.t = -1.916 C.z = 1.645 D.t = 1.916

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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 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.  P-value:  Round your answer to four decimal places as necessary.

 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.  A medical doctor wishes to test the claim that the standard deviation of the systolic blood pressure of deep sea divers is greater than 450. To do so, she selected a random sample of 25 divers and found s = 468.  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, 34.567 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.  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, 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.

 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:  1500 versus H1:  > 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 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.  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:  Round your answer to two decimal places as necessary.

 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.  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.

 Part 3 of 3 –
 Question 18 of 20 1.0 Points

An alternative or research hypothesis is usually the hypothesis a researcher wants to prove.

 True False

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 Question 19 of 20 1.0 Points

A low p–value provides evidence for accepting the null hypothesis and rejecting the alternative.

 True False

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 Question 20 of 20 1.0 Points

Sample evidence is statistically significant at the  level only if the p–value is larger than  .

 True False

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