# Multiple choice questions | Numerical analysis homework help

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$leq f$ 75, H1: f$mu f$ > 75

C.H0: f$mu f$ f$geq f$ 75, H1: f$mu f$ < 75

D.H0: f$mu f$ = 75, H1: f$mu f$ > 75 Reset Selection

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?

State the null and alternative hypotheses.

A.H0: s2 < 1.2, H1: s2 ≠ 1.2

B.H0: s2 ≥ 1.2, H1: s2 ≠ 1.2

C.H0: s2 ≠ 1.2, H1: s2 = 1.2

D.H0: s2 ≤ 1.2, H1: s2 > 1.2

Question 3 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?

A.Cannot Determine

B.No

C.Yes

Question 4 of 20

1.0 Points

The form of the alternative hypothesis can be:

A.one-tailed

B.one or two-tailed

C.neither one nor two-tailed

D.two-tailed

Question 5 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. Reset Selection

Question 6 of 20

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: f$mu f$ is greater than 16.4 feet; the P-value area is on the left of the mean

B.H1: f$mu f$ is less than 16.4 feet; the P-value area is on the left of the mean

C.H1: f$mu f$ is greater than 16.4 feet; the P-value area is on both sides of the mean

D.H1: f$mu f$ is not equal to 16.4 feet; the P-value area is on the right of the mean Reset Selection

Question 7 of 20

1.0 Points

The “Pizza Hot” manager commits a Type I error if he/she is

A.switching to new style when it is better than old style

B.staying with old style when new style is better

C.switching to new style when it is no better than old style

D.staying with old style when new style is no better than old style Reset Selection

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 the p-value associated with your test of hypothesis?

A.0.6874

B.0.7563

C.0.4874

D.0.2437

Question 9 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.null hypothesis

D.alternative hypothesis

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.

Compute the z or t value of the sample test statistic.

A.t = 1.645

B.z = 0.69

C.z = 0.62

D.z = 1.96

Question 11 of 20

1.0 Points

The null and alternative hypotheses divide all possibilities into:

A.two sets that may or may not overlap

B.as many sets as necessary to cover all possibilities

C.two sets that overlap

D.two non-overlapping sets

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 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: f$mu f$ = 1500 versus H1: f$mu

eq 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 are the critical values that you should use? Place the smallest critical value, rounded to 3 decimal places, in the first blank. For example, -1.234 would be a legitimate entry. . Place the larger critical value, rounded to 3 decimal places, in the second blank. For example, 1.234 would be a legitimate entry. -2.064 and 2.064

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.

Let x be a random variable representing dividend yield of Australian bank stocks. We may assume that x has a normal distribution with f$sigma f$ = 2.8%. A random sample of 16 Australian bank stocks has a sample mean dividend yield of 8.91%. For the entire Australian stock market, the mean dividend yield is f$mu f$ = 6.4%. If you wanted to test to determine if these data indicate that the dividend yield of all Australian bank stocks is higher than 6.4%, what is the value of the test statistic? Place your answer, rounded to 3 decimal places, in the blank. For example, 2.345 would be a legitimate entry. 3.586

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

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. 1.711

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.

Let x be a random variable representing dividend yield of Australian bank stocks. We may assume that x has a normal distribution with f$sigma f$ = 2.8%. A random sample of 16 Australian bank stocks has a sample mean dividend yield of 8.91%. For the entire Australian stock market, the mean dividend yield is f$mu f$ = 6.4%. If you wanted to test, at a .05 level of significance, to determine if these data indicate that the dividend yield of all Australian bank stocks is higher than 6.4% what is the critical value that you would use? Place your answer, rounded to 2 decimal places, in the blank. For example, 2.345 would be a legitimate entry. 1.645

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.

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, what is the p-value associated with this test? Place your answer, rounded to 3 decimal places in the blank. For example, .123 would be a legitimate entry. 0.025

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 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? 10.117

Place your answer, rounded to 3 decimal places, in the blank. For example, 12.345 would be a legitimate entry.

Part 3 of 3 –

Question 18 of 20

1.0 Points

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

True

False

Reset Selection

Question 19 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

Question 20 of 20

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

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