apu math 302 quiz 4

Question 1 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?

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

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

C.H1: \f$\mu \f$ is greater than 16.4 feet; the P-value area is on the left 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

Answer Key:

Question 2 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?

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

Correct D.H0: s2 ? 1.2, H1: s2 > 1.2

Answer Key:

Question 3 of 20

0.0/ 1.0 Points

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

Incorrect A.the null hypotheses includes sampling error

B.a 95% confidence interval includes the hypothesized value of the parameter

C.a 95% confidence interval does not include the hypothesized value of the parameter

D.the null hypothesis is biased

Answer Key:

Question 4 of 20

1.0/ 1.0 Points

The alternative hypothesis is also known as the:

A.optional hypothesis

Correct B.research hypothesis

C.null hypothesis

D.elective hypothesis

Answer Key:

Question 5 of 20

1.0/ 1.0 Points

The null and alternative hypotheses divide all possibilities into:

A.two sets that overlap

B.two sets that may or may not overlap

Correct C.two non-overlapping sets

D.as many sets as necessary to cover all possibilities

Answer Key:

Question 6 of 20

1.0/ 1.0 Points

A type I error occurs when the:

Correct A.null hypothesis is incorrectly rejected when it is true

B.sample mean differs from the population mean

C.null hypothesis is incorrectly accepted when it is false

D.test is biased

Answer Key:

Question 7 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 \f$\alpha \f$ = .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.

Incorrect B.Reject H0. At the \f$\alpha \f$ = .01 level of significance, there is enough evidence to support the claim that this technician’s variance is larger than the target accuracy.

C.Do not reject H0. At the \f$\alpha \f$ = .01 level of significance there is not sufficient evidence to suggest that this technician’s true variance is greater than the target accuracy.

D.Cannot determine

Answer Key:

Question 8 of 20

1.0/ 1.0 Points

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

Correct A.alternative hypothesis

B.quality of the researcher

C.null hypothesis

D.the reduction of variance

Answer Key:

Question 9 of 20

1.0/ 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$\mu \f$ \f$\leq \f$ 75, H1: \f$\mu \f$ > 75

Correct B.H0: \f$\mu \f$ = 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

Answer Key:

Question 10 of 20

1.0/ 1.0 Points

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

A.staying with old style when new style is better

B.staying with old style when new style is no better than old style

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

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

Answer Key:

Question 11 of 20

0.0/ 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 increases

B.The p – value decreases

Incorrect C.The p – value may increase or decrease

D.The p – value stays the same

Answer Key:

Part 2 of 3 - 3.0/ 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 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.

P-value: Correct.3278 Round your answer to four decimal places as necessary.

Answer Key: 0.1635|0.1639

Feedback: This is a right-tail hypothesis test with a test statistic of z = 0.978492.

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 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: f$mu f$ = 100 versus H1: f$mu

eq 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 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. Correct-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. Correct2.093

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.

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. Correct7.633

Answer Key:

Question 15 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.

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. Correct1.711

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: 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, what is the p-value associated with this test? Place your answer, rounded to 3 decimal places in the blank. For example, 0.0234 would be a legitimate entry. Correct.0344

Answer Key:

Question 17 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 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 30 firemen and found s = 27.2 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, 23.456 would be a legitimate entry. Correct34.329

Answer Key:

Part 3 of 3 - 3.0/ 3.0 Points

Question 18 of 20

1.0/ 1.0 Points

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

Correct

True

False

Answer Key:

Question 19 of 20

1.0/ 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.

Correct

True

False

Answer Key:

Question 20 of 20

1.0/ 1.0 Points

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

Correct

True

False

Answer Key: