stats final: 3

A medical laboratory claims that 85% of all COVID-19 tests that it performs yield results in 2 days or less. A government agency randomly samples 150 such tests, and finds that 82% of the sampled tests gave results in 2 days or less. The agency wishes to test the following hypotheses: H 0 : p = 0.85 , H a : p < 0.85. In this scenario, p^ = ____, p0= _____

0.82,0.85

A genetic engineering company claims that it has developed a genetically modified tomato plant that yields on average more tomatoes than other varieties. A farmer wants to test the claim on a small scale before committing to a full-scale planting. The farmer grows 19 genetically modified tomato plants, and has an average yield of 24 pounds. The farmer tests the following hypotheses: H 0 : μ = 20 , H a : μ > 20. In this scenario x bar= _____, mu0 = _____.

24,20

A diabetic claims that the average cost of insulin per year for a Type 1 diabetic is $5,705. She takes a sample of 100 Type 1 diabetics and finds their average cost is $5,912 with a standard deviation of $300. Use α = 0.05 to test the claim. Which function in Excel finds the test statistic? A. =NORM.DIST(5912, 5705, 300, TRUE) B. =(5705-5912)/(300/SQRT(100)) C. =NORM.DIST(5705, 5912, 300, TRUE) D. =NORM.INV((5705-5912)/(300/SQRT(100))

B

Let p be the proportion of all adults who are in favor of outlawing cigarettes. A researcher testing the hypotheses: H 0 : p = 0.23 , H a : p ≠ 0.23 calculates a p-value of 0.489. The researcher will likely A. reject the null hypothesis B. fail to reject the null hypothesis C. make a type I error D. fail to reject the alternative hypothesis

B

The "significance level" of a test, α, is also A. the probability of making a Type I error B. the probability of making a Type II error C. called "the power of the test"

a

An English professor is studying the use of semicolons over time. She estimates that in the Georgian era, authors used more than 8 semicolons per page. It is well known in her field that the standard deviation of semicolons in this era is 2. She randomly selects 25 pages from different books and finds the average amount of semicolons is 8.5. Assume the population is normally distributed and use α = 0.05 to test the claim. What distribution should be used? A. t-distribution B. p-distribution C. c-distribution D. z-distribution

d

If Ha: p < 0.77 then H0

p ≥ 0.77

True or false: If α > p-value, we reject Ha

false

A researcher uses α = 0.10 and finds a p-value = 0.01. What should their decision be? A. Fail to support H a B. More information on the claim is needed C. Fail to reject H 0 D. Reject H 0 E. Support H a

D

A standard painkiller is known to bring relief in 3.5 minutes on average (μ). A new painkiller is hypothesized to bring faster relief to patients. A sample of 40 patients are given the new painkillers. The sample yields a mean of 2.8 minutes and a standard deviation of 1.1 minutes. To test H0: mu = 3.5 vs Ha: mu < 3.5 the researchers should use a A. Type 3 Error Test B. Z-test C. Armadillo Cheesecake Test D. T-test

b

A diabetic claims that the average cost of insulin per year for a Type 1 diabetic is $5,705. She takes a sample of 100 Type 1 diabetics and finds their average cost is $5, 912 with a standard deviation of $300. Use α = 0.05 to test the claim. Suppose the test statistic is 1.65. Which function in Excel finds the p-value? A. =2*NORM.DIST(1.65, 0, 1, TRUE) B. =2*NORM.DIST(1-1.65, 0, 1, TRUE) C. =2*(1-NORM.DIST(1.65, 0, 1, TRUE)) D. =NORM.DIST(1-1.65, 0, 1, TRUE) E. =1-NORM.DIST(1.65, 0, 1, TRUE) F. =NORM.DIST(1.65, 0, 1, TRUE) G. =2*NORM.DIST(-1.65, 0, 1, TRUE)

c

A diabetic claims that the average cost of insulin per year for a Type 1 diabetic is $5,705. She takes a sample of 100 Type 1 diabetics and finds their average cost is $5, 912 with a standard deviation of $300. Use α = 0.05 to test the claim. If the decision is to reject H0 what should the interpretation be? there is a large enough n to ____ ____

reject the claim

Which of the following comes after finding the p-value in the p-value method? A. Finding the test statistic B. Marking the claim C. Making a decision about H 0 D. Finding the descriptive statistics

C

Which of the following is not a step that must be conducted each time you use the p-value method? A. Finding the test statistic B. Marking the claim C. Multiplying the test statistic by -1 D. Providing an interpretation

C

A medical laboratory claims that 85% of all COVID-19 tests that it performs yield results in 2 days or less. A government agency randomly samples 150 such tests, and finds that 82% of the sampled tests gave results in 2 days or less. The agency wishes to test the following hypotheses: H 0 : p = 0.85 , H a : p < 0.85. In this scenario, the appropriate test statistic is: A. Z= p^-p0/√(p0q0/n) B. Z= x bar-μ0/s/√(n) C. T= x bar-μ0/s/√(n)

A

A university administrator wishes to know if there is a difference in average starting salary for graduates with master's degrees in engineering and those with master's degrees in business. The average starting salary for graduates with master's degrees in engineering $83,000. The administrator samples 32 former students with master's degrees in business and finds an average starting salary of $61,000. The administrator tests the following hypotheses: H 0 : μ = 83000 , H a : μ < 83000-X bar = 61000, μ0= 83000. In this scenario the appropriate test statistic is: A. Z= p^-p0/√p0q0/n B. Z= x̄ -μ0/s/√n C. T= x̄ -μ0/s/√n

A

If H 0: μ ≤ 100, then the test will be _____________. A. Two-tailed B. Right-tailed C. Left-tailed D. Unable to tell given the current information

C

A sociologist wishes to test H 0 : μ = 42 vs. H a : μ ≠ 42. The sociologist takes a sample of size 100 and calculates a standardized test statistic of -2.34. To calculate a p-value for the test in Excel, the sociologist should use: A. =NORM.DIST(-2.34, 0, 1, TRUE) B. =1-T.DIST(-2.34, 99, TRUE) C. =2*NORM.DIST(-2.34, 0, 1, TRUE) D. =2*(1-T.DIST(-2.34, 99, TRUE)) E. =T.DIST(-2.34, 99, TRUE) F. =1-NORM.DIST(-2.34, 0, 1, TRUE)

C

A diabetic claims that the average cost of insulin per year for a Type 1 diabetic is $5,705. She takes a sample of 100 Type 1 diabetics and finds their average cost is $5, 800 with a standard deviation of $575. Use α = 0.05 to test the claim. Which distribution should be used? A. t-distribution B. z-distribution C. p-distribution D. c-distribution

b

Let μ be the average starting salary for graduates with a master's degree in business. A university administrator tests the following hypotheses: H 0 : μ = 83000 , H a : μ < 83000, and calculates a p-value of 0.004. At the 5% level of significance, the administrator should conclude that: A. the average starting salary is less than $83000 B. the average starting salary is NOT less than $83000

a

The average yield per acre for all types of corn in a recent year was 161.9 bushels. An economist believes that the average yield per acre is lower this year. In this scenario, a Type I error would be: (a) Deciding that the yield is lower when it isn't. (b) Deciding that the yield is not lower when it is.

a

A veterinarian reads that 15% of dogs are allergic to chicken. However, he claims that the actual proportion is less than this. He randomly selects 15 of his customers and asks them if their dog is allergic to chicken. 3 of them say yes. Assume the population is normally distributed and use α = 0.01. Which distribution should be used? A. c-distribution B. t-distribution C. p-distribution D. z-distribution

answer needed, is not B

If Ha μ > 0.85 then H0

μ ≤ 0.85

Which of the following statements are true in hypothesis testing? (i) if we reject H0 when H0 is in fact true we make a Type I error. (ii) is we reject H0 when H0 is in fact false we make a Type II Error. (iii) one will reject H0 if the P value is smaller than the significance level

(i) and (iii)

A fashion company releases a new line of prom dresses that are all under $100. They claim this is a bargain because the average cost of a prom dress is over $300. A customer decides to test this, and takes a random sample of 25 dresses. She finds the mean is $250 with a standard deviation of $10. Assume the population is normally distributed and use α = 0.05 to test the claim. Which function in Excel finds the test statistic? A. =T.INV(250, 24, TRUE) B. =(250-300)/(10/SQRT(25)) C. =1-((250-300)/(10/SQRT(25))) D. =NORM.DIST(250, 300, 10, TRUE)

B

A test is made of H0: μ = 20 versus Ha: μ ≠ 20. Suppose the true value of μ is 25, and H0 is rejected. Determine whether the outcome is a Type I error, a Type II error, or a correct decision. A. Type I Error B. Correct Decision C. Type I Error D. Insufficient information to decide E. Both Type I and II Errors

B

A university administrator wishes to know if there is a difference in average starting salary for graduates with master's degrees in engineering and those with master's degrees in business. The average starting salary for graduates with master's degrees in engineering $83,000. The administrator samples 32 former students with master's degrees in business and finds an average starting salary of $61,000. The administrator tests the following hypotheses: H 0 : μ = 83000 , H a : μ < 83000-X bar = 61000, mu0= 83000 A. Z= p^-p0/ √(p0q0/n) B. Z= x bar -μ0/s/√(n) C. T= x bar -μ0/s/√(n)

B

If the claim is that the population mean is equal to 8,000,000 and the decision is to reject H0, what should the interpretation be? A. There is not enough evidence to support the claim. B. There is not enough evidence to reject the claim. C. There is enough evidence to reject the claim. D. There is enough evidence to support the claim.

C

A fashion company releases a new line of prom dresses that are all under $100. They claim this is a bargain because the average cost of a prom dress is over $300. A customer decides to test this, and takes a random sample of 25 dresses. She finds the mean is $250 with a standard deviation of $10. Assume the population is normally distributed and use α = 0.05 to test the claim.Suppose the test statistic is -1.02. Which function in Excel finds the p-value? A. = 1-T.DIST(-1.02, 24, TRUE) B. = NORM.DIST(1.02, 0, 1, TRUE) C. = NORM.DIST(-1.02, 0, 1, TRUE) D. = T.DIST(1.02, 24, TRUE) E. = T.DIST(-1.02, 24, TRUE) F. = 1-NORMDIST(-1.02, 0, 1, TRUE)

D

The level of significance is ____________. A. when a result is very unlikely to have happened given the null hypothesis. B. the maximum allowable probability of getting results as extreme as the actual observed values. C. the maximum allowable probability of not rejecting the null hypothesis when it's false. D. the maximum allowable probability of rejecting the null hypothesis when it's true.

D

The null hypothesis for a problem is that the population proportion is at least 0.60. What is the alternative hypothesis? A. H a: p ≥ 0.60 B. H a: p > 0.40 C. H a: p < 0.40 D. H a: p < 0.60 E. H a: p ≥ 0.40 F. H a: p ≤ 0.40 G. H a: p > 0.60 H. H a: p ≤ 0.60

D

The null and alternative hypotheses are statements about: A. a population parameter B. a sample statistic C. It depends -sometimes a parameter and sometimes a statistic

a

The average room rate in hotels in a certain region is $82.53. A travel agent believes that the average in a particular resort area is different. The agent tests H 0 : μ = 82.53 ,H a : μ ≠ 82.53, and calculates a p-value of 0.063. At a 5% level of significance, the agent should _____ the null hypothesis. There ____ sufficient evidence to claim that the average in the resort area differs from that of the region.

answer needed

The null hypothesis for a problem is that the population proportion is at least 0.22. Which type of test will be used? A. Two-tailed test B. Right-tailed test C. Left-tailed test D. Unable to tell given the current information

b

The recommended daily allowance of iron for females aged 19-50 is 18 mg/day. A dietitian believes that elderly women (on average) get less than 18 mg/day. The dietitian uses hypothesis testing to check this belief. In this scenario, a Type 2 error would be: (a) Deciding that elderly women get less than the recommended allowance when they don't. (b) Deciding that elderly women get at least the recommended allowance when they don't.

b

A fashion company releases a new line of prom dresses that are all under $100. They claim this is a bargain because the average cost of a prom dress is over $300. A customer decides to test this, and takes a random sample of 25 dresses. She finds the mean is $250 with a standard deviation of $10. Assume the population is normally distributed and use α = 0.05 to test the claim. Which distribution should be used to test the claim? A. z-distribution B. c-distribution C. t-distribution D. p-distribution

c

A genetic engineering company claims that it has developed a genetically modified tomato plant that yields on average more tomatoes than other varieties. A farmer wants to test the claim on a small scale before committing to a full-scale planting. The farmer grows 19 genetically modified tomato plants, and has an average yield of 24 pounds. The farmer tests the following hypotheses: H 0 : μ = 20 , H a : μ > 20. In this scenario the appropriate test statistic is A. Z= p^-p0/√(p0q0/n) B. Z= x bar -μ0/s/√(n) C. T= x bar -μ0/s/√(n)

c

A sociologist wishes to test H 0 : μ = 42 vs. H a : μ < 42. The sociologist takes a sample of size 100 and calculates a standardized test statistic of -2.34. To calculate a p-value for the test in Excel, the sociologist should use: A. =1-NORM.DIST(-2.34, 0, 1, TRUE) B. =1-T.DIST(-2.34, 99, TRUE) C. =NORM.DIST(-2.34, 0, 1, TRUE) D. =2*NORM.DIST(-2.34, 0, 1, TRUE) E. =T.DIST(-2.34, 99, TRUE) F. =2*(1-T.DIST(-2.34, 99, TRUE))

c

If H a: p ≠ 1.00, then H 0: A. μ ≤ 1.00 B. μ ≥ 1.00 C. μ = 1.00 D. μ < 1.00 E. The number in H a is too large to be a proportion.

c

Let p be the proportion of all adults who are in favor of outlawing cigarettes. A researcher testing the hypotheses: H 0 : p = 0.23, H a : p ≠ 0.23 calculates a p-value of 0.00003. The researcher will likely A. Make a type II error B. Reject the alternative hypothesis C. Fail to reject the null hypothesis. D. Reject the null hypothesis.

c

Which of the following is not a step that must be conducted each time you use the p-value method? A. finding the test statistic B. providing an interpretation C. multiplying the test statistic by -1 D. marking the claim

c

A certain type of fiber optic cable transmits light a mean distance of 58 km. A research team wishes to investigate if a modification in the manufacturing process will increase the mean acceptable transmission distance. A sample of 20 batches of cable produced under the new process are tested. The sample mean is 60.3 km with sample standard deviation 2.31 km. Assume the population is normally distributed.To test H 0 : μ = 58 versus H a : μ > 58, the team should use a: A. Z-test B. SASS Test C. Blue Baker Test D. T-test

d

A veterinarian reads that 15% of dogs are allergic to chicken. However, he claims that the actual proportion is less than this. He randomly selects 15 of his customers and asks them if their dog is allergic to chicken. 3 of them say yes. Assume the population is normally distributed and use α = 0.01.Which function in Excel finds the test statistic?(Note: 3/15 = 0.20) A. = NORM.INV(0.20, 0, 1) B. = NORM.DIST(0.20, 0, 1, TRUE) C. =1-((0.20-0.15)/SQRT(0.15*0.85/15)) D. =(0.20-0.15)/SQRT(0.15*0.85/15)

d

An English professor is studying the use of semicolons over time. She estimates that in the Georgian era, authors used more than 8 semicolons per page. It is well known in her field that the standard deviation of semicolons in this era is 2. She randomly selects 25 pages from different books and finds the average amount of semicolons is 8.5. Assume the population is normally distributed and use α = 0.05 to test the claim. Also suppose that the test statistic equals 0.85. Which formula in Excel finds the p-value? A. =1 -T.DIST(0.85, 25, TRUE) B. =T.DIST(0.85, 25, TRUE) C. =T.DIST(0.85, 24, TRUE) D. =NORM.DIST(0.85, 0, 1, TRUE) E. =1-NORM.DIST(0.85, 0, 1, TRUE) F. =1 -T.DIST(0.85, 24, TRUE)

e

A fashion company releases a new line of prom dresses that are all under $100. They claim this is a bargain because the average cost of a prom dress is over $300. A customer decides to test this, and takes a random sample of 25 dresses. She finds the mean is $250 with a standard deviation of $10. Assume the population is normally distributed and use α = 0.05 to test the claim. State the hypothesis. A. H0: μ = 300 (claim), Ha: μ ≠ 300 B. H0: μ ≥ 300 (claim), Ha: μ < 300 C. H0: μ = 100, Ha: μ ≠ 100 (claim) D. H0: μ ≤ 100 (claim), Ha: μ > 100 E. H0: μ ≥ 100, Ha: μ < 100 (claim) F. H0: μ ≤ 300, Ha: μ > 300 (claim)

f

An English professor is studying the use of semicolons over time. She estimates that in the Georgian era, authors used more than 8 semicolons per page. It is well known in her field that the standard deviation of semicolons in this era is 2. She randomly selects 25 pages from different books and finds the average amount of semicolons is 8.5. Assume the population is normally distributed and use α = 0.05 to test the claim. Suppose the decision is to fail to reject H0, the interpretation would be there ____ enough evidence to ____ the claim

is not, support

A forensic anthropologist claims that 80% of female skeletons have a sub-pubic angle less than the often-cited 90 degrees. She randomly selects 200 skeletons and finds that 150 have an angle less than 90 degrees. Use α = 0.10 to test the claim. Suppose the decision is to fail to reject H 0.Then the interpretation would be: There ____ enough evidence to ____ the claim.

is, reject

A nutritionist claims that the average amount of sugar in a 16 oz soda is at least 50 g. He randomly samples 10 sodas and finds they contain an average of 54 g of sugar with a standard deviation of 3 g. Assume the population is normally distributed and use α = 0.10 to test the claim. Suppose the decision is to reject H0 then the interpretation would be there ____ enough evidence to ____ the claim.

is, reject