USA Today reported that about 47% of the general consumer population in the United States is loyal to the automobile manufacturer of their choice. Suppose Chevrolet did a study of a random sample of 1009 Chevrolet owners and found that 482 said they would buy another Chevrolet. Does this indicate that the population proportion of consumers loyal to Chevrolet is more than 47%? Use α = 0.01.

(a) What is the level of significance?

State the null and alternate hypotheses.

(b) What sampling distribution will you use?

What is the value of the sample test statistic? (Round your answer to two decimal places.)
(c) Find the P-value of the test statistic. (Round your answer to four decimal places.)

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

(e) Interpret your conclusion in the context of the application.

New York City is the most expensive city in the United States for lodging. The mean hotel room rate is $205 per night (USA Today, April 30, 2012). Assume that room rates are normally distributed with a standard deviation of $55. Use Table 1 in Appendix B.

a. What is the probability that a hotel room costs $227 or more per night (to 4 decimals)?

b. What is the probability that a hotel room costs less than $143 per night (to 4 decimals)?

c. What is the probability that a hotel room costs between $201 and $299 per night (to 4 decimals)?

d. What is the cost of the 20% most expensive hotel rooms in New York City? Round up to the next dollar.
$ or - Select your answer -more less

Snow avalanches can be a real problem for travelers in the western United States and Canada. A very common type of avalanche is called the slab avalanche. These have been studied extensively by David McClung, a professor of civil engineering at the University of British Columbia. Suppose slab avalanches studied in a region of Canada had an average thickness of μ = 68 cm. The ski patrol at Vail, Colorado, is studying slab avalanches in its region. A random sample of avalanches in spring gave the following thicknesses (in cm).

(i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)

(ii) Assume the slab thickness has an approximately normal distribution. Use a 1% level of significance to test the claim that the mean slab thickness in the Vail region is different from that in the region of Canada.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: μ < 68; H₁: μ = 68 H₀: μ ≠ 68; H₁: μ = 68     H₀: μ = 68; H₁: μ > 68 H₀: μ = 68; H₁: μ < 68 H₀: μ = 68; H₁: μ ≠ 68

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since we assume that x has a normal distribution and σ is known. The standard normal, since we assume that x has a normal distribution and σ is unknown.     The Student's t, since we assume that x has a normal distribution and σ is unknown. The Student's t, since we assume that x has a normal distribution and σ is known.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

In the current tax year, IRS, the internal revenue service of the United States, estimates that five persons of the many high network individual tax returns would be fraudulent. That is, they will contain errors that are purposely made to cheat the government. Although these errors are often well concealed, let us suppose that a thorough IRS audit will uncover them.

Given this information, if a random sample of 100 such tax returns are audited, what is the probability that exactly five fraudulent returns will be uncovered? Here, the number of trials is n=100. And p=0.05 is the probability of a tax return will be fraudulent. Answer the following questions.

1. What is the probability that five fraudulent returns will be uncovered based on 100 IRS audits ? (n=100, p=0.05)
2. If a random sample of 250 high net worth tax returns are audited, what is the probability that the IRS will uncover at least 15 fraudulent errors? (n=250 and P= 0.05)
3. If a random sample of 250 high net worth tax returns are audited, what is the probability that the IRS would uncover at least 15 fraudulent returns but at most 20 fraudulent returns? (n=250 and P= 0.05)
4. What is the probability that out of the 250 randomly selected high net worth tax returns no fraudulent return is uncovered? (n=250 and P= 0.05)
5. Aside from the ethics of tax fraud and based solely on your answers to questions 1-4, do you think it would be advisable to cheat on your tax return? Do you need more information to decide? What type of information?

The mean cost of domestic airfares in the United States rose to an all-time high of $385 per ticket (Bureau of Transportation Statistics website, November 2, 2012 ). Airfares were based on the total ticket value, which consisted of the price charged by the airlines plus any additional taxes and fees. Assume domestic airfares are normally distributed with a standard deviation of $110.

a. What is the probability that a domestic airfare is $550 or more (to 4 decimals)?

b. What is the probability that a domestic airfare is $250 or less (to 4 decimals)?

c. What if the probability that a domestic airfare is between $300 and $500 (to 4 decimals)?

d. What is the cost for the 3% highest domestic airfares? (rounded to nearest dollar)

A survey shows that 81% of households in the United States own a computer. You randomly select 12 households and ask if they own a computer. Answer the following questions. 1) Identify n 2) Identify p 3) Calculate 1 - p 4) Find the probability that exactly 6 of them respond yes 5) Find the probability that at least 6 of them respond yes 6) Find the probability that fewer than 6 of them respond yes 7) Find the probability that between 5 and 10 of them (inclusive) respond yes 8) Find the probability that no more than 8 of them respond yes 9) Find the probability that more than 9 of them respond yes 10) What is the expected (mean) number of “yes” response? 11) What is the standard deviation of the expected (mean) number of “yes” response?

According to a recent study annual per capita consumption of milk in the United States is 21.5 gallons. Being from the Midwest, you believe milk consumption is higher there and wish to test your hypothesis. A sample of 14 individuals from the Midwestern town of Webster City was selected and then each person's milk consumption was entered into the Microsoft Excel Online file below. Use the data to set up your spreadsheet and test your hypothesis. 24.8 23.84 25.25 21.3 17.52 19.61 19.83 26.18 34.97 29.9 28.59 20.57 26.94 27.24 What is a point estimate of the difference between mean annual consumption in Webster City and the national mean? (2 decimals). At ? = 0.05, test for a significant difference by completing the following. Calculate the value of the test statistic (2 decimals). The p-value is (4 decimals).

The mean cost of domestic airfares in the United States rose to an all-time high of $400 per ticket. Airfares were based on the total ticket value, which consisted of the price charged by the airlines plus any additional taxes and fees. Assume domestic airfares are normally distributed with a standard deviation of $120. Use Table 1 in Appendix B.

  What is the probability that a domestic airfare is $530 or more (to 4 decimals)?

b. What is the probability that a domestic airfare is $260 or less (to 4 decimals)?

c. What if the probability that a domestic airfare is between $320 and $490 (to 4 decimals)?

d. What is the cost for the 4% highest domestic airfares? (rounded to nearest dollar)

In the current tax year, IRS, the internal revenue service of the United States, estimates that five persons of the many high network individual tax returns would be fraudulent. That is, they will contain errors that are purposely made to cheat the government. Although these errors are often well concealed, let us suppose that a thorough IRS audit will uncover them.

Given this information, if a random sample of 100 such tax returns are audited, what is the probability that exactly five fraudulent returns will be uncovered? Here, the number of trials is n=100. And p=0.05 is the probability of a tax return will be fraudulent. Answer the following questions.

1. What is the probability that five fraudulent returns will be uncovered based on 100 IRS audits ? (n=100, p=0.05)
2. If a random sample of 250 high net worth tax returns are audited, what is the probability that the IRS will uncover at least 15 fraudulent errors? (n=250 and P= 0.05)
3. If a random sample of 250 high net worth tax returns are audited, what is the probability that the IRS would uncover at least 15 fraudulent returns but at most 20 fraudulent returns? (n=250 and P= 0.05)
4. What is the probability that out of the 250 randomly selected high net worth tax returns no fraudulent return is uncovered? (n=250 and P= 0.05)
5. Aside from the ethics of tax fraud and based solely on your answers to questions 1-4, do you think it would be advisable to cheat on your tax return? Do you need more information to decide? What type of information?

Snow avalanches can be a real problem for travelers in the western United States and Canada. A very common type of avalanche is called the slab avalanche. These have been studied extensively by David McClung, a professor of civil engineering at the University of British Columbia. Suppose slab avalanches studied in a region of Canada had an average thickness of μ = 68 cm. The ski patrol at Vail, Colorado, is studying slab avalanches in its region. A random sample of avalanches in spring gave the following thicknesses (in cm).

(i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)

(ii) Assume the slab thickness has an approximately normal distribution. Use a 1% level of significance to test the claim that the mean slab thickness in the Vail region is different from that in the region of Canada.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: μ < 68; H₁: μ = 68H₀: μ = 68; H₁: μ ≠ 68    H₀: μ ≠ 68; H₁: μ = 68H₀: μ = 68; H₁: μ > 68H₀: μ = 68; H₁: μ < 68

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The Student's t, since we assume that x has a normal distribution and σ is unknown.

The Student's t, since we assume that x has a normal distribution and σ is known.    

The standard normal, since we assume that x has a normal distribution and σ is unknown.

The standard normal, since we assume that x has a normal distribution and σ is known.

What is the value of the sample test statistic? (Round your answer to three decimal places.)


(c) Estimate the P-value.

P-value > 0.2500.100 < P-value < 0.250    0.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010

Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant

.At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.    

At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.01 level to conclude that the mean slab thickness in the Vail region is different from that in the region of Canada.

There is insufficient evidence at the 0.01 level to conclude that the mean slab thickness in the Vail region is different from that in the region of Canada.