# 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.

At the a = .05 level of significance, does the nutritionist have enough evidence to reject the writer’s claim?

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##### Question 2 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.

 H0: = .79, H1: > .79

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##### Question 3 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.

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##### Question 4 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 a = .01 level of significance, what is your conclusion?

 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 5 of 20
1.0 Points
The “Pizza Hot” manager commits a Type I error if he/she is

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##### Question 6 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?

State the null and alternative hypotheses.

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##### Question 7 of 20
1.0 Points
A two-tailed test is one where:

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##### Question 8 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.

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##### Question 9 of 20
1.0 Points
A type II error occurs when:

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##### Question 10 of 20
1.0 Points
The alternative hypothesis is also known as the:

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##### Question 11 of 20
1.0 Points
The form of the alternative hypothesis can be:

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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 less than 25 pounds. To do so, she selected a random sample of 20 firemen and found s = 23.2 pounds.

Assuming that the weights of firemen are normally distributed, if the statistician wanted to test her research hypothesis at the .05 level of significance, what is the critical value?

Place your answer, rounded to 3 decimal places, in the blank. For example, 12.345 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.

A survey determines that mint chocolate chip is the favorite ice cream flavor of 6% of consumers. An ice cream shop determines that of 240 customers, 18 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.

##### 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.

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 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.

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.

##### 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 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
Std error of mean 4.854

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.

##### 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 .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.

Compute the p-value associated with this test. Place your answer, rounded to 4 decimal places, in the blank. For example, 0.3456 would be a legitimate entry.

 Part 3 of 3 –
##### Question 18 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 falls between the lower and upper confidence limits.

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##### Question 19 of 20
1.0 Points
An alternative or research hypothesis is usually the hypothesis a researcher wants to prove.

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##### Question 20 of 20
1.0 Points
The smaller the p–value, the more evidence there is in favor of the alternative hypothesis.

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