Final Statistics Exam

a. H0: (𝜇W − 𝜇D) = 0 versus Ha: (𝜇W − 𝜇D) ≠ 0 z= 11.04 z>1.96 z<-1.96 1. H0 is rejected. There is sufficient evidence to indicate that there is a difference in the average room rates for the Westin and the Doubletree hotels. $152.10 to $137.90 2. Since zero is not in the interval, it is not likely that the two means are the same which confirms the conclusion in part (a).

(a) Do the data provide sufficient evidence to indicate a difference in the average room rates for the Westin and the Doubletree hotel chains? Use 𝛼 = 0.05. State the null and alternative hypothesis. (Use 𝜇W for the Westin hotel and Use 𝜇D for the Doubletree hotel.) H0: (𝜇W − 𝜇D) ≠ 0 versus Ha: (𝜇W − 𝜇D) = 0 H0: (𝜇W − 𝜇D) = 0 versus Ha: (𝜇W − 𝜇D) < 0 H0: (𝜇W − 𝜇D) = 0 versus Ha: (𝜇W − 𝜇D) ≠ 0 H0: (𝜇W − 𝜇D) = 0 versus Ha: (𝜇W − 𝜇D) > 0 H0: (𝜇W − 𝜇D) < 0 versus Ha: (𝜇W − 𝜇D) > 0 Find the test statistic and rejection region. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.) State your conclusion. 1. H0 is rejected. There is sufficient evidence to indicate that there is a difference in the average room rates for the Westin and the Doubletree hotels. 2. H0 is rejected. There is insufficient evidence to indicate that there is a difference in the average room rates for the Westin and the Doubletree hotels. 3. H0 is not rejected. There is sufficient evidence to indicate that there is a difference in the average room rates for the Westin and the Doubletree hotels. 4. H0 is not rejected. There is insufficient evidence to indicate that there is a difference in the average room rates for the Westin and the Doubletree hotels. (b) Construct a 95% confidence interval for the difference in the average room rates for the two chains. (Round your answers to the nearest cent.) Does this interval confirm your conclusion in part (a)? 1. Since zero is in the interval, it is possible that the two means are the same which confirms the conclusion in part (a). 2. Since zero is not in the interval, it is not likely that the two means are the same which confirms the conclusion in part (a). 3. Since zero is not in the interval, it is not likely that the two means are the same which contradicts the conclusion in part (a). 4. Since zero is in the interval, it is possible that the two means are the same which contradicts the conclusion in part (a).

5. The results are not statistically significant. H0 is not rejected.

(a) A right-tailed test with observed z = 1.14 and p-value 0.1271 1. The results are statistically significant at the 1% level. H0 is rejected. 2. The results are statistically significant at the 1% level. H0 is not rejected. 3. The results are statistically significant at the 5% level, but not at the 1% level. H0 is rejected at the 5% level. 4. The results are statistically significant at the 5% level, but not at the 1% level. H0 is not rejected at the 5% level. 5. The results are not statistically significant. H0 is not rejected.

H0: p = 0.5 versus Ha: p > 0.5 z= 3.24 1. H0 is rejected. There is sufficient evidence to indicate that p is greater than 0.5.

A random sample of 110 observations was selected from a binomial population, and 72 successes were observed. Do the data provide sufficient evidence to indicate that p is greater than 0.5? Use one of the two methods of testing presented in this section, and explain your conclusions. (Let 𝛼 = 0.05.) State the null and alternative hypotheses. H0: p ≠ 0.5 versus Ha: p = 0.5 H0: p = 0.5 versus Ha: p > 0.5 H0: p < 0.5 versus Ha: p > 0.5 H0: p = 0.5 versus Ha: p < 0.5 H0: p = 0.5 versus Ha: p ≠ 0.5 Find the test statistic. (Round your answer to two decimal places.) Explain your conclusion. 1. H0 is rejected. There is sufficient evidence to indicate that p is greater than 0.5. 2. H0 is rejected. There is insufficient evidence to indicate that p is greater than 0.5. 3. H0 is not rejected. There is sufficient evidence to indicate that p is greater than 0.5. 4. H0 is not rejected. There is insufficient evidence to indicate that p is greater than 0.5.

0.171 to 0.869

A random sample of n = 10 observations was selected from a normal population. The sample mean and variance were x = 3.94 and s2 = 0.3212. Find a 90% confidence interval for the population variance 𝜎2. (Round your answers to three decimal places.)

H0: 𝜎2 = 15 versus Ha: 𝜎2 > 15 𝜒2 =35.333 𝜒2>37.6525 𝜒2<NONE 2. H0 is not rejected. There is insufficient evidence to indicate that the population variance is greater than 15.

A random sample of n = 26 observations from a normal population produced a sample variance equal to 21.2. Do these data provide sufficient evidence to indicate that 𝜎2 > 15? Test using 𝛼 = 0.05. State the null and alternative hypotheses. H0: 𝜎2 = 0 versus Ha: 𝜎2 < 0 H0: 𝜎2 = 0 versus Ha: 𝜎2 > 0 H0: 𝜎2 = 15 versus Ha: 𝜎2 > 15 H0: 𝜎2 = 15 versus Ha: 𝜎2 ≠ 15 H0: 𝜎2 ≠ 15 versus Ha: 𝜎2 = 15 Calculate the test statistic. (Round your answer to three decimal places.) State the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.) State your conclusion. 1. H0 is not rejected. There is sufficient evidence to indicate that the population variance is greater than 15. 2. H0 is not rejected. There is insufficient evidence to indicate that the population variance is greater than 15. 3. H0 is rejected. There is insufficient evidence to indicate that the population variance is greater than 15. 4. H0 is rejected. There is sufficient evidence to indicate that the population variance is greater than 15.

p̂ =0.275 0.044

A random sample of n = 400 observations from a binomial population produced x = 110 successes. Give the best point estimate for the binomial proportion p. (Round your answer to three decimal places.) Calculate the 95% margin of error. (Round your answer to three decimal places.)

d. 984

A recent survey indicates that the proportion of season ticket holders for Ferris State University hockey team that renew their seats is about .80. Using this information, the sample size that is needed to estimate the true proportion that plan to renew their seats using 95% confidence and a margin of error of ± .025 is about: a. 689 b. 1,179 c. 810 d. 984 e. 697

a. E1, E4 b. E1, E3, E4 c. E2

A sample space consists of S = E1, E2, E3, E4. Consider the following events A and B. A = E1, E4 and B = E1, E3, E4 List the simple events in each of the following. (Enter your answers as comma-separated lists.) a. both A and B b. A or B or both c. not B

P(A)= 0.6

A sample space consists of five simple events with P(E1) = P(E2) = 0.3, P(E3) = 0.1, P(E4) = 0.2, and P(E5) = 0.1. Find the probability of the event A = {E1, E3, E4}.

d= {1, 2, 3}

A single six-sided die is tossed. List the simple events in D. (Enter your answers as a comma-separated list. If D contains no simple events, enter NONE.) D: observe a number less than 4

a. 0.98 b. 0.02

A smoke-detector system uses two devices, A and B. If smoke is present, the probability that it will be detected by device A is 0.94; by device B, 0.97; and by both devices, 0.93. (a) If smoke is present, find the probability that the smoke will be detected by device A or device B or both devices. (b) Find the probability that the smoke will not be detected.

e. the student did relatively better on the statistics exam than on the chemistry exam, compared to the other students in the two classes

A student took a chemistry exam where the exam scores were mound-shaped with a mean score of 90 and a standard deviation of 64. She also took a statistics exam where the scores were mound-shaped, the mean score was 70 and the standard deviation was 16. If the student's grades were 102 on the chemistry exam and 77 on the statistics exam, then: a. the student's scores on both exams are comparable, when accounting for the scores of the other students in the two classes b. it is impossible to say which of the student's exam scores indicates the better performance c. the student did relatively better on the chemistry exam than on the statistics exam, compared to the other students in each class d. the student did relatively the same on both exams e. the student did relatively better on the statistics exam than on the chemistry exam, compared to the other students in the two classes

a. 0.1587 b. 99.43

Allen Shoemaker derived a distribution of human body temperatures, which has a distinct mound-shape.† Suppose we assume that the temperatures of healthy humans is approximately normal with a mean of 98.6 degrees and a standard deviation of 0.8 degrees. (a) If a healthy person is selected at random, what is the probability that the person has a temperature above 99.4 degrees? (Round your answer to four decimal places.) (b) What is the 85th percentile for the body temperatures (in °) of healthy humans? (Round your answer to two decimal places.)

graph #1 e. The data is approximately mound shaped with no obvious outliers.

Also, Describe the shape of the distribution and look for any outliers. a. The data is skewed right with no obvious outliers. b. The data is skewed left with one unusually small outlier. c. The data is skewed right with one unusually large outlier. d. The data is skewed left with no obvious outliers. e. The data is approximately mound shaped with no obvious outliers.

Graph #1 b. The distribution is U shaped with large relative frequencies in the first and fifth classes and lower relative frequencies in the middle.

Also, How would you describe the shape of the distribution? a. The distribution is relatively mound shaped. b. The distribution is U shaped with large relative frequencies in the first and fifth classes and lower relative frequencies in the middle. c. The distribution is relatively flat with all classes having roughly the same relative frequencies. d. The distribution is skewed to the left. e. The distribution is skewed to the right.

2.7

Also, use the stem and leaf plot to find the smallest observation.

H0: 𝜇 = 7.4 versus Ha: 𝜇 > 7.4 z=2.63 p-value=0.0043 𝛼 = 0.01 3. You could claim that you work significantly more hours than those without a college education. 3. If you were not a college graduate, you might just report that you work an average of more than 7.4 hours per week.

An article describing various aspects of American life indicated that higher educational achievement pays off! College grads work 7.4 hours per day, fewer than those with less than a college education. Suppose that the average work day for a random sample of n = 100 individuals who had less than a 4-year college education was calculated to be x = 7.9 hours with a standard deviation of s = 1.9 hours. (a) Use the p-value approach to test the hypothesis that the average number of hours worked by individuals having less than a college degree is greater than individuals having a college degree. H0: 𝜇 = 7.4 versus Ha: 𝜇 ≠ 7.4 H0: 𝜇 = 7.4 versus Ha: 𝜇 > 7.4 H0: 𝜇 < 7.4 versus Ha: 𝜇 > 7.4 H0: 𝜇 = 7.4 versus Ha: 𝜇 < 7.4 H0: 𝜇 ≠ 7.4 versus Ha: 𝜇 = 7.4 Find the test statistic and the p-value. (Round your test statistic to two decimal places and your p-value to four decimal places.) What is the smallest level at which you can reject H0? 𝛼 = 0.01 𝛼 = 0.05 𝛼 = 0.10 If you were a college graduate, how would you state your conclusion to put yourself in the best possible light? 1. You could claim that you work significantly more hours than those with a college education. 2. You could claim that you work significantly fewer hours than those with a college education. 3. You could claim that you work significantly more hours than those without a college education. 4. You could claim that you work significantly fewer hours than those without a college education. If you were not a college graduate, how might you state your conclusion? 1. If you were not a college graduate, you might just report that you work an average of less than 7.4 hours per week. 2. If you were not a college graduate, you might just report that you work an average of more than 7.9 hours per week. 3. If you were not a college graduate, you might just report that you work an average of more than 7.4 hours per week. 4. If you were not a college graduate, you might just report that you work an average of less than 7.9 hours per week.

0.4286

Assume that the heights of American men are normally distributed with a mean of 69.4 inches and a standard deviation of 3.1 inches. What is the probability that a randomly selected man will be between 5'9" and 6'1" tall? (Round your answer to four decimal places.)

t = 2.631 0.020 < p-value < 0.050 2. At the 1% level of significance, H0 is not rejected. 3. At the 5% level of significance, H0 is rejected. 5. At the 10% level of significance, H0 is rejected.

Calculate the observed value of the t statistic for testing the difference between the two population means using paired data. (Round your answer to three decimal places.) d = 0.3, sd2 = 0.13, n1 = n2 = 10, Ha: (𝜇1 − 𝜇2) ≠ 0 Approximate the p-value for the test. p-value < 0.010 0.010 < p-value < 0.020 0.020 < p-value < 0.050 0.050 < p-value < 0.100 0.100 < p-value < 0.200 p-value > 0.200 Which of the following could be appropriate conclusions based on your p-value? (Select all that apply.) 1. At the 1% level of significance, H0 is rejected. 2. At the 1% level of significance, H0 is not rejected. 3. At the 5% level of significance, H0 is rejected. 4. At the 5% level of significance, H0 is not rejected. 5. At the 10% level of significance, H0 is rejected. 6. At the 10% level of significance, H0 is not rejected.

d= 2 sd= 5.099

Calculate the values for d and sd. (Round your answer for sd to three decimal places.)

a. 3.4818 b. 2.1330 c. -1.21 d. 1.98 2. Since neither z-score exceeds 2 in absolute value, none of the observations are unusually small or large.

Consider the given data set. n = 11 measurements: 2.4, 0.9, 2.0, 6.4, 2.7, 7.7, 1.8, 2.8, 4.5, 5.0, 2.1 a. Find the mean. (Round your answer to four decimal places.) b. Find the standard deviation. (Round your answer to four decimal places.) c. Find the z-score corresponding to the minimum in the data set. (Round your answers to two decimal places.) d. Find the z-score corresponding to the maximum in the data set. (Round your answers to two decimal places.) Do the z-scores indicate that there are possible outliers in this data set? 1. Since the z-score for the smaller observation is larger than 2 in absolute value, the smaller value is unusually small. 2. Since neither z-score exceeds 2 in absolute value, none of the observations are unusually small or large. 3. Since both z-scores exceed 2 in absolute value, both of the observations are unusual. 4. Since the z-score for the larger observation is larger than 2 in absolute value, the larger value is unusually large.

min= 11 Q1= 21 Median=26 Q3= 27 Max= 29 IQR=6 Outlier: 11

Consider the given data set. n = 11 measurements: 26, 21, 27, 22, 26, 27, 29, 17, 26, 23, 11 Calculate the five-number summary and the interquartile range. Min Q1 Median Q3 Max IQR Identify any outliers. (Enter your answers as a comma-separated list. If there are no outliers, enter NONE.)

a. discrete b. continuous c. continuous 4. discrete

Identify each variable as continuous or discrete. (a)number of cars for sale by an automobile dealership (b) height of an underpass on a highway (c) total elapsed time for an operator to pick up at an emergency call center (d) number of trains arriving at Grand Central Terminal in New York City in a given day

a. quantitative b. quantitative c. qualitative d. qualitative

Identify each variable as quantitative or qualitative. (a) amount of time it takes to assemble a simple puzzle (b) number of students in a first-grade classroom (c) rating of a newly elected politician (excellent, good, fair, poor) (d) state in which a person lives

continuous

Identify the random variable as either discrete or continuous. height of the ocean's tide at a given location

discrete

Identify the random variable as either discrete or continuous. total number of points scored in a football game

2. convenience

Identify the sampling plan as judgment, convenience, or quota sampling. A student waits until Sunday night to complete a survey for his sociology class. He asks 12 of his fraternity brothers to participate. 1. judgement 2. convenience 3. quota

x, y

Identify which of the two variables is the independent variable x and which is the dependent variable y. number of hours spent studying and grade on a history test The number of hours spent studying is (x/y) and the grade on a history test is (x/y)

0.0273

Let x have an exponential distribution with 𝜆 = 0.4. Find the probability. (Round your answer to four decimal places.) P(x > 9)

Yes, np and nq are both greater than 5. 0.0297

Random samples of size n = 200 were selected from a binomial population with p = 0.1. Is it appropriate to use the normal distribution to approximate the sampling distribution of p̂? Yes, np and nq are both greater than 5. No, np is less than 5. No, nq is less than 5. No, np and nq are both less than 5. Use this result to find the probability. (Round your answer to four decimal places.) p̂ > 0.14

greater than, can Mean= 38 standard error= 0.2582

Random samples of size n were selected from a nonnormal population with the means and variances given here. n = 90, 𝜇 = 38, 𝜎2 = 6 What can be said about the sampling distribution of the sample mean? Since the sample size is (greater/less) than 30, we (can/ cannot) assume that the distribution of x is approximately normal. Find the mean and standard error for this distribution. (Round your standard error to four decimal places.)

a. 0.2 b. A and B are not mutually exclusive c. A and B are independent.

Suppose that P(A) = 0.3 and P(A ∩ B) = 0.06. (a) Find P(B|A). (b) Are events A and B mutually exclusive? (c) If P(B) = 0.2, are events A and B independent?

fail to reject H0

The critical boundaries for a hypothesis test are z = +1.96 and -1.96. If the z-score for the sample data is z = −1.90, then what is the correct statistical decision? reject H0 reject H1 fail to reject H1 fail to reject H0

e. 171

The sample size needed to estimate a population mean within 1.5 units with a 95% confidence when the population standard deviation equals 10 is: a. 88 b. 54 c. 121 d. 13 e. 171

a. 0.24 b. 0.4 c. 0.68

The thickness in microns (µ) of a protective coating applied to a conductor designed to work in corrosive conditions is uniformly distributed on the interval from 25 to 50. (a) What is the probability that the thickness of the coating is greater than 44 microns? (b) What is the probability that the thickness of the coating is between 34 and 44 microns? (c) What is the probability that the thickness of the coating is less than 42 microns?

a. 2. Select three people and record each person's gender (F or M). b. {(M, M, M), (M, M, F), (M, F, M), (M, F, F), (F, M, M), (F, M, F), (F, F, M), (F, F, F)} c. 0.125 d. 0.375 e. 0.125

Three people are randomly selected to report for jury duty. The gender of each person is noted by the county clerk. (a) Define the experiment. 1. Select three people and record each person's name. 2. Select three people and record each person's gender (F or M). 3. Select three people and record each person's name and gender (F or M). (b) List the simple events in S. (Enter your answer as a comma-separated list. Enter each simple event in the format (G1, G2, G3) where Gi is the gender of the ith person. Use M for male and F for female.) (c) If each person is just as likely to be a man as a woman, what probability do you assign to each simple event? (d) What is the probability that only one of the three is a woman? (e) What is the probability that all three are women?

a. 69, 50.769 b. 18.231 to 119.769, 1. The data suggest that there is a difference in the average test scores of the two states since zero is not contained in the interval.

(a) Find a point estimate for the difference in mean test scores for state 1 and state 2. (Use state 1 − state 2.) What is the 95% margin of error for the point estimate you found? (Round your answer to three decimal places.) (b) Find a 95% confidence interval estimate for the difference in mean test scores for these two states. (Use state 1 − state 2. Round your answers to three decimal places.) Does it appear that there is a significant difference in the average test scores? 1. The data suggest that there is a difference in the average test scores of the two states since zero is not contained in the interval. 2. The data do not suggest that there is a difference in the average test scores of the two states since zero is contained in the interval. 3. The data suggest that there is a difference in the average test scores of the two states since zero is contained in the interval. 4. The data do not suggest that there is a difference in the average test scores of the two states since zero is not contained in the interval.

a. 0.8079 b. 0.9082

(a) Find the probability that z is greater than −0.87. (Round your answer to four decimal places.) (b) Find the probability that z is less than 1.33. (Round your answer to four decimal places.)

1. The results are statistically significant at the 1% level. H0 is rejected.

(b) A two-tailed test with observed z = −2.71 and p-value 0.0067 1. The results are statistically significant at the 1% level. H0 is rejected. 2. The results are statistically significant at the 1% level. H0 is not rejected. 3. The results are statistically significant at the 5% level, but not at the 1% level. H0 is rejected at the 5% level. 4. The results are statistically significant at the 5% level, but not at the 1% level. H0 is not rejected at the 5% level. 5. The results are not statistically significant. H0 is not rejected.

3. The results are statistically significant at the 5% level, but not at the 1% level. H0 is rejected at the 5% level.

(c) A left-tailed test with observed z = −2.01 and p-value 0.0222 1. The results are statistically significant at the 1% level. H0 is rejected. 2. The results are statistically significant at the 1% level. H0 is not rejected. 3. The results are statistically significant at the 5% level, but not at the 1% level. H0 is rejected at the 5% level. 4. The results are statistically significant at the 5% level, but not at the 1% level. H0 is not rejected at the 5% level. 5. The results are not statistically significant. H0 is not rejected.

H0: 𝜇 = 16 versus Ha: 𝜇 < 16 t = -1.333 t>NONE t<-1.753 4. H0 is not rejected. There is insufficient evidence to conclude that the mean weight is less than that claimed on the label.

A cannery prints "weight 16 ounces" on its label. The quality control supervisor selects sixteen cans at random and weighs them. She finds x = 15.8 and s = 0.6. Do the data present sufficient evidence to indicate that the mean weight is less than that claimed on the label? (Use 𝛼 = 0.05.) State the null and alternative hypotheses. H0: 𝜇 = 16 versus Ha: 𝜇 < 16 H0: 𝜇 = 16 versus Ha: 𝜇 ≠ 16 H0: 𝜇 ≠ 16 versus Ha: 𝜇 = 16 H0: 𝜇 < 16 versus Ha: 𝜇 > 16 H0: 𝜇 < 16 versus Ha: 𝜇 = 16 State the test statistic. (Round your answer to three decimal places.) State the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.) State the conclusion. 1. H0 is rejected. There is insufficient evidence to conclude that the mean weight is less than that claimed on the label. 2. H0 is not rejected. There is sufficient evidence to conclude that the mean weight is less than that claimed on the label. 3. H0 is rejected. There is sufficient evidence to conclude that the mean weight is less than that claimed on the label. 4. H0 is not rejected. There is insufficient evidence to conclude that the mean weight is less than that claimed on the label.

a. 0.4987 b. 0.0013 c. 0000

A certain type of automobile battery is known to last an average of 1,180 days with a standard deviation of 40 days. If 100 of these batteries are selected, find the following probabilities for the average length of life of the selected batteries. (Round your answers to four decimal places.) (a) The average is between 1,168 and 1,180. (b) The average is greater than 1,192. (c) The average is less than 930.

a. 0.19, 3/4, 0.15 b. 68%, 0.2, 0.15 c. would not, would not be suitable

A chemist wanted to determine the number of moles of cupric ions in a given volume of solution. The solution was divided into n = 30 portions of 0.2 milliliter each, and each of the portions was tested. The average number of moles of cupric ions for the n = 30 portions was found to be 0.18 mole; the standard deviation was 0.01 mole. (a) Describe the distribution of the measurements for the n = 30 portions of the solution using Tchebysheff's Theorem. Using Tchebysheff's Theorem, at least 0 of the measurements fall in the interval 0.17 to _____ . At least ____proportion___ of the measurements fall in the interval 0.16 to 0.2, and at least 8/9 of the measurements fall in the interval ___ to 0.21. (b) Describe the distribution of the measurements for the n = 30 portions of the solution using the Empirical Rule. (Do you expect the Empirical Rule to be suitable for describing these data?) Using the Empirical Rule, approximately ____% of the measurements fall in the interval 0.17 to 0.19. Approximately 95% of the measurements fall in the interval 0.16 to ____ , and approximately 99.7% of the measurements fall in the interval ____ to 0.21. (c) Suppose the chemist had used only n = 4 portions of the solution for the experiment and obtained the readings 0.15, 0.19, 0.17, and 0.15. Would the Empirical Rule be suitable for describing the n = 4 measurements? Why? With n = 4 measurements, the histogram (would/would not) be mound-shaped. Therefore, the Empirical Rule (would/ would not be suitable) for describing the set of data.

a. 6 b. (1, 3), (1, 4), (1, 5), (3, 4), (3, 5), (4, 5) c. 2.0, 2.5, 3.0, 3.5, 4.0, 4.5 d. p(x) = 1/6 for all values of x e. 𝜇 = 3.25

A finite population consists of four elements: 5, 1, 4, 3. (a) How many different samples of size n = 2 can be selected from this population if you sample without replacement? (Sampling is said to be without replacement if an element cannot be selected twice for the same sample.) (b) List the possible samples of size n = 2. (Enter your samples as a comma-separated list. Use parentheses around each sample. For each sample, enter the elements as a comma-separated list from smallest to largest.) (c) Compute the sample mean for each of the samples given in part (b). (Enter your answers as a comma-separated list.) (d) Find the sampling distribution of x. p(x) = 1/3 for all values of x p(x) = 1/2 for x = 1, 2, 3, 4, 5, 6 p(x) = 1/2 for x = 1, 2 p(x) = 1/6 for all values of x p(x) = 1/6 for x = 1, 2, 3, 4, 5, 6 e. If all four population values are equally likely, calculate the value of the population mean 𝜇. (Enter your answer to two decimal places.) Do any of the samples listed in part (b) produce a value of x exactly equal to 𝜇?

a. 0.328 b. 0.205 c. 0.007 1. It would be very unlikely for a team with a success rate of 80% to have fewer than two successful procedures out of five. Therefore, these results would lead one to question the skill of this surgical team.

A new surgical procedure is said to be successful 80% of the time. Suppose the operation is performed five times and the results are assumed to be independent of one another. (Round your answers to three decimal places.) (a) What is the probability that all five operations are successful? (b) What is the probability that exactly three are successful? (c) What is the probability that less than two are successful? (d) If less than two operations were successful, how would you feel about the performance of the surgical team? 1. It would be very unlikely for a team with a success rate of 80% to have fewer than two successful procedures out of five. Therefore, these results would lead one to question the skill of this surgical team. 2. It would be fairly common for a team with a success rate of 80% to have fewer than two successful procedures out of five. Therefore, these results would lead one to question the skill of this surgical team. 3. It would be fairly common for a team with a success rate of 80% to have fewer than two successful procedures out of five. Therefore, these results would not lead one to question the skill of this surgical team. 4. It would be very unlikely for a team with a success rate of 80% to have fewer than two successful procedures out of five. Therefore, these results would not lead one to question the skill of this surgical team.

0.0016

A paper reports that approximately 25% of cell phone owners walked into someone or something while they were talking on their cell phone. In a random sample of n = 200 cell phone owners, what is the probability that the sample proportion of cell phone owners who have walked into someone or something while they were on the phone would be less than 0.16? (Round your answer to four decimal places.)

2.56 to 2.70

Find the necessary confidence interval for a population mean 𝜇 for the following values. (Round your answers to two decimal places.) a 95% confidence interval, n = 81, x = 2.63, s2 = 0.1057 Interpret the interval that you have constructed. a. In repeated sampling, 5% of all intervals constructed in this manner will enclose the population mean. b. In repeated sampling, 95% of all intervals constructed in this manner will enclose the population mean. c. There is a 5% chance that an individual sample mean will fall within the interval. d. There is a 95% chance that an individual sample mean will fall within the interval. e. 95% of all values will fall within the interval.

0.8812

Find the probability that z lies between z = −1.56 and z = 1.56. (Round your answer to four decimal places.)

𝜒2= 18.31

Find the tabled value for a 𝜒2 variable based on n − 1 degrees of freedom with an area of a to its right. (Round your answer to two decimal places.) n = 11, a = 0.05

z = ±2.58

For a regular two-tailed test with 𝛼 = .01, the boundaries for the critical region would be defined by the following z-scores. z = ±2.33 z = ±1.96 z = ±3.30 z = ±2.58

H0: μ=6 Ha: μ<6

For the situation described below, state the null and alternative hypotheses to be tested. (Enter != for ≠ as needed.) A researcher wishes to show that a modified treatment decreases the mean time to recovery 𝜇, which is currently 6 days.

b. 1.645

If the population standard deviation 𝜎 is known and we wish to estimate the population mean 𝜇 with 90% confidence, what is the appropriate critical value z to use? a. 2.33 b. 1.645 c. 1.28 d. 2.58 e. 1.96

105

In how many ways can you select two people from a group of 15 if the order of selection is not important?

a. p = 0.4 b. 𝜇=8 days, 𝜎=2.19 days c. z = 0.46 2. The observed event is less than 2 standard deviations above the mean, so it is not unlikely assuming p is accurate.

To check the accuracy of a particular weather forecaster, records were checked only for those days when the forecaster predicted rain "with 40% probability." A check of 20 of those days indicated that it rained on 9 of the 20. (a)If the forecaster is accurate, what is the appropriate value of p, the probability of rain on one of the 20 days? (b) What are the mean 𝜇 and standard deviation 𝜎 of x, the number of days on which it rained, assuming that the forecaster is accurate? (Round your standard deviation to two decimal places.) (c) Calculate the z-score for the observed value, x = 9. [HINT: Recall that z-score = (x − 𝜇)/𝜎.] (Round your answer to two decimal places.) (d) Do these data disagree with the forecast of a "40% probability of rain"? Explain. 1. The observed event is more than 2 standard deviations above the mean, so it is unlikely assuming p is accurate. 2. The observed event is less than 2 standard deviations above the mean, so it is not unlikely assuming p is accurate. 3. The observed event is less than 2 standard deviations above the mean, so it is very unlikely assuming p is accurate. 4. The observed event is more than 2 standard deviations above the mean, so it is not unlikely assuming p is accurate.

a. t = 1.782 b. |t| = 2.306 c. t = -2.650

Use Table 4 in Appendix I or using SALT to find the following critical values. (Round your answers to three decimal places.) (a) An upper one-tailed rejection region with 𝛼 = 0.05 and 12 df. (b) A two-tailed rejection region with 𝛼 = 0.05 and 8 df. (c) A lower one-tailed rejection region with 𝛼 = 0.01 and 13 df.

sxy= -1.97 r = -0.9838 y= 6.153-0.563x

Use the given set of bivariate data. x 1, 2, 3, 4, 5, 6 y 5.8, 4.7, 4.6, 3.8, 3.4, 2.8 Calculate the covariance sxy Calculate the correlation coefficient r. (Round your answer to four decimal places.) Calculate the equation of the regression line. (Round your numeric values to three decimal places.) Also, find the right graph.

32

Use the mn Rule to find the number of items in the following exercise. Five coins are tossed. How many simple events are in the sample space?

mean= 2.31 variance= 1.4739 SD= 1.214

Use the probability distribution for the random variable x to answer the question. x 0, 1, 2, 3, 4 p(x) 0.12, 0.15, 0.15, 0.46, 0.12 Calculate the population mean, variance, and standard deviation. (Round your standard deviation to three decimal places.)

0.88

Use the probability distribution for the random variable x to answer the question. x 0, 1, 2, 3, 4 p(x) 0.12, 0.2, 0.2, 0.36, 0.12 What is the probability that x is 3 or less?

d. The 79th percentile implies that 79% of all students scored below your score.

What is the percentile given below and what does it mean in practical terms? You scored 77 which was the 79th percentile on a placement test. a. The 79th percentile implies that your score was 79%, but does not provide information for comparison with other students. b. The 79th percentile implies that 79 students scored below your score. c. The 79th percentile implies that 21 students scored below your score. d. The 79th percentile implies that 79% of all students scored below your score. e. The 79th percentile implies that 21% of all students scored below your score.

3. 1-in-8

What survey design is used in the situation described below? Every 8th car on an assembly line is checked for defects in its paint job. 1. cluster 2. convenience 3. 1-in-8 4. simple random 5. stratified

a. 0.414 to 0.646 b. 1. Since the confidence interval includes the value of p given by the survey, there is no reason to doubt the claim of the survey.

Will there be a time when hiring decisions will be done using a computer algorithm, and without any human involvement? A survey found that 60% of the adults surveyed were worried about the development of algorithms that can evaluate and hire job candidates. To check this claim, a random sample of n = 100 U.S. adults was selected, with 53 saying they were worried about this issue. (a) Construct a 98% confidence interval for the true proportion of adults that are worried about being "hired by a robot." (Round your answer to three decimal places.) (b) Does the confidence interval constructed in part (a) confirm the claim of the Pew Research survey? Why or why not? 1. Since the confidence interval includes the value of p given by the survey, there is no reason to doubt the claim of the survey. 2. Since the confidence interval does not include the value of p given by the survey, there is no reason to doubt the claim of the survey. 3. The confidence interval cannot be used to assess the value from the survey. 4. Since the confidence interval does not include the value of p given by the survey, there is good reason to doubt the claim of the survey. 5. Since the confidence interval includes the value of p given by the survey, there is good reason to doubt the claim of the survey.

a. 8.8 b. m=8.5 c. 8,9

You are given n = 10 measurements: 6, 8, 7, 9, 13, 8, 9, 12, 5, 11. (a) Calculate x. (b) Find m. (c) Find the mode. (If there is more than one mode, enter your answer as a comma-separated list.)

a. 2. Yes. The value 𝜇1 − 𝜇2 = 0 is not in the interval which suggests that there is likely a difference between 𝜇1 and 𝜇2. b. 1. No. The value 𝜇1 − 𝜇2 = 0 is in the interval which does not suggest that there is a difference between 𝜇1 and 𝜇2.

a. Can you conclude with 90% confidence that there is a difference in the means for the two populations? 1. No. The value 𝜇1 − 𝜇2 = 0 is in the interval which does not suggest that there is a difference between 𝜇1 and 𝜇2. 2. Yes. The value 𝜇1 − 𝜇2 = 0 is not in the interval which suggests that there is likely a difference between 𝜇1 and 𝜇2. 3. No. The value 𝜇1 − 𝜇2 = 0 is not in the interval which does not suggest that there is a difference between 𝜇1 and 𝜇2. 4. Yes. The value 𝜇1 − 𝜇2 = 0 is in the interval which suggests that there is likely a difference between 𝜇1 and 𝜇2. b. Can you conclude with 99% confidence that there is a difference in the means for the two populations? 1. No. The value 𝜇1 − 𝜇2 = 0 is in the interval which does not suggest that there is a difference between 𝜇1 and 𝜇2. 2. Yes. The value 𝜇1 − 𝜇2 = 0 is not in the interval which suggests that there is likely a difference between 𝜇1 and 𝜇2. 3. No. The value 𝜇1 − 𝜇2 = 0 is not in the interval which does not suggest that there is a difference between 𝜇1 and 𝜇2. 4. Yes. The value 𝜇1 − 𝜇2 = 0 is in the interval which suggests that there is likely a difference between 𝜇1 and 𝜇2.