Identify whether the variable in the information below is qualitative or quantitative. Government agencies carefully monitor water quality and its effect on wetlands
Question 1 Identify whether the variable in the information below is qualitative or quantitative. Government agencies carefully monitor water quality and its effect on wetlands (Reference: Environment Protection Agency Wetland Report EPA 832-R-93-005). Of particular concern is the concentration of nitrogen in water draining from fertilized lands. Too much nitrogen can kill fish and wildlife. Twenty-eight samples of water were taken at random from a lake. The nitrogen concentration (milligrams of nitrogen per liter of water) was determined for each sample.
Question options:
quantitative
qualitative
qualitative as well as quantitative
neither qualitative nor quantitative
Information does not have any variable
Question 2 Wetlands offer a diversity of benefits. They provide habitat for wildlife, spawning grounds for U.S. commercial fish, and renewable timber resources. In the last 200 years the United States has lost more than half its wetlands. Suppose Environmental Almanac gives the percentage of wet lands lost in each state in the last 200 years as noted in the table below.
The distribution of the percentage loss of wetlands per state is approximately mound shaped.
Question options:
false
true
Question 3 In a biology class, the final grade is based on several things: a lab score, score on two major tests, and the score on the final exam. There are 100 points available for each score. However, the lab score is worth 30% of your total grade, each major test is worth 22.5%, and the final exam is worth 25%. Compute the weighted average for the following scores: 90 on the lab, 82 on the first major test, 91 on the second major test, and 84 on the final exam. Round your answer to the nearest hundredth.
Question options:
88.42
85.12
86.62
86.92
84.90
Question 4 Finish times (to the nearest hour) for 59 dogsled teams are provided. Draw a relative frequency histogram. Use five classes.
261 270 236 244 278 296 284 297 287 287 250 256
338 360 341 333 261 267 287 296 313 311 309 309
299 303 277 283 304 305 286 290 286 287 297 299
332 330 309 329 309 329 285 291 295 298 306 315
310 318 318 320 333 321 323 324 327 302 319
Question options:
Question 5 Given the sample data, 13, 32, 28, 13, 12, 23, compute the sample standard deviation.
Question options:
8.71
24.20
63.14
75.77
7.95
Question 6 Given the values of x: 24, 17, 12, 34, and 28, find the sample variance. Round your answer to the nearest hundredth and place it in the blank. For example, 62.70 is a legitimate answer.______
Question 7 Let x be a random variable representing annual percent return for the Vanguard Total Stock Index (all Stocks). Let y be a random variable representing annual return for the Vanguard Balanced Index (60% stock and 40% bond). Given data for the past several years, compute the coefficient of variation for each fund. Round your answers to the nearest tenth.
Question options:
for x-values: 119.7%, and for y-values: 133.2%
for x-values: 205.5%, and for y-values: 133.2%
for x-values: 133.2%, and for y-values: 205.5%
for x-values: 119.7%, and for y-values: 225.5%
for x-values: 205.5%, and for y-values: 225.5%
Question 8 At Center Hospital there is some concern about the high turnover of nurses. A survey was done to determine how long (in months) nurses had been in their current positions. The responses (in months) of 20 nurses were generated. Using the procedure specified by Brase and Brase, find the interquartile range, rounded to one decimal place.
27 3 7 20 28 38 31 45 19 11
9 11 35 30 33 16 25 37 13 38
Question options:
46.5
17.5
22.0
48.5
31.5
Question 9Given box plots for the annual premium for urban customers in three states, which state has the smallest range of premiums for urban customers?
Question options:
Texas has the smallest range of premiums.
California has the smallest range of premiums.
Texas as well as Pennsylvania have the smallest range.
Pennsylvania has the smallest range of premiums.
none of these choices
Question 10 Given box plots for the annual premium for urban customers in three states, which state has the highest median premium for urban customers?
Question options:
Pennsylvania has the highest median premium.
Texas has the highest median premium.
Texas as well as California have the highest median premium.
California has the highest median premium.
none of these choices
MATH530 Applied Statistics
Quiz 2
Question 1 Assuming that the heights of college women are normally distributed with mean 65 inches and standard deviation 2.5 inches, what percentage of women are taller than 67.5 inches?
Question options:
0.1%
15.9%
97.7%
50.0%
84.1%
Question 2 Find the area under the standard normal curve between z = -1.9 and z = 1.8.
Question options:
0.036
0.471
0.029
0.964
0.935
Question 3 Let z be a random variable with a standard normal distribution. Find P(-2.9 < z < 0.4).
Question options:
0.994
0.654
0.002
0.498
0.155
Question 4 Assume that X has a normal distribution, with mean, , and standard deviation, . Find P(7 < X < 18).
Question options:
0.999
0.369
0.001
0.630
1.000
Question 5 A certain company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a battery is normally distributed, with a mean of 56 months and a standard deviation of 6 months. If the company does not want to make refunds for more than 10% of its batteries under a full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?
Question options:
56 months
67 months
48 months
44 months
63 months
Question 6 A cement truck delivers mixed cement to a large construction site. Let X represent the cycle time in minutes for the truck to leave the construction site, go back to the cement plant, fill up, and return to the construction site with another load of cement. From past experiences, it is known that the mean cycle time is 41 minutes with a standard deviation of 13 minutes and that cycle times are normally distributed. What is the probability that the cycle time will exceed 48 minutes, given that it has exceeded 39 minutes?
Question options:
0.526
0.297
0.565
0.295
0.561
Question 7Assume that 55% of all customers will take free samples. Furthermore, of those who take the free samples, assume that about 32% will buy what they have sampled. Suppose that you set up a counter in a supermarket offering free samples of a new product and that the day you were offering free samples, 347 customers passed by your counter. What is the probability that a customer will take a free sample and buy the product?
Question options:
0.320
0.582
0.230
0.176
0.550
Question 8The heights of 18-year-old men are approximately normally distributed with mean 68 inches and standard deviation 3 inches. What is the probability that the average height of a sample of twenty 18-year-old men will be less than 69 inches?
Question options:
0.0968
0.4032
0.8064
0.9320
0.4516
Question 9A mechanical press is used to mold shapes for plastic toys. When the machine is adjusted and working well, it still produces about 8% defective toys. The toys are manufactured in lots of n = 100. Let r be a random variable representing the number of defective toys in a lot. Then is the proportion of defective toys in a lot. Find . Round your answer to four decimal places.
Question options:
0.2719
0.7719
0.2281
0.2085
0.2876
Question 10 A mechanical press is used to mold shapes for plastic toys. When the machine is adjusted and working well, it still produces about 8% defective toys. The toys are manufactured in lots of n = 100. Let r be a random variable representing the number of defective toys in a lot. Find the probability that between 7 and 9 defective toys are produced in a lot of n = 100 toys. That is, find .
Question options:
0.2719
0.7719
0.4188
0.2085
0.5812
MATH530 Applied Statistics
Quiz 3
Question 1 Suppose that the mean time for a certain car to go from 0 to 60 miles per hour was 6.7 seconds. Suppose that you want to set up a statistical test to challenge the claim of 6.7 seconds. What would you use for the null hypothesis?
Question options:
f$mu > 6.7 secondsf$
f$mu = 6.7 secondsf$
f$mu < 6.7 secondsf$
f$mu neq 6.7 secondsf$
Question 2 Let X be a random variable representing the dividend yield of Australian bank stocks. We may assume that X has a normal distribution with standard deviation f$sigma =f$ 2.8%. Now, suppose we wish to test the null hypothesis that f$mu =f$ 6.4% against the alternative that f$mu >f$ 6.4% using a level of significance of f$alpha =f$ .05. To do so, a random sample of 16 Australian bank stocks is observed and has a sample mean of f$bar{x} =f$ 8.91%.What is the value of the test statistic?
Question options:
-0.224
-3.586
3.586
0.896
Question 3 Let X be a random variable representing the dividend yield of Australian bank stocks. We may assume that X has a normal distribution with standard deviation f$sigma =f$ 2.8%. Now, suppose we wish to test the null hypothesis that f$mu =f$ 6.4% against the alternative that f$mu >f$ 6.4% using a level of significance of f$alpha =f$ .05. To do so, a random sample of 16 Australian bank stocks is observed and has a sample mean of f$bar{x} = f$ 8.91%. What is the p-value associated with this test?
Question options:
.0002
.0500
.0100
.0068
Question 4 Let X be a random variable representing dividend yield of Australian bank stocks. We may assume that X has a normal distribution with standard deviation f$sigma = 2.4f$ % . A random sample of 19 Australian bank stocks has a sample mean of f$bar{x} f$ = 8.71%. For the entire Australian stock market, the mean dividend yield is f$mu f$ = 5.9%. Do these data indicate that the dividend yield of all Australian bank stocks is higher than 5.9%? Use f$alpha f$ = .05. Are the data statistically significant at the given level of significance? Based on your answers, will you reject or fail to reject the null hypothesis?
Question options:
The p-value is less than the level of significance and so the data are not statistically significant. Thus, we reject the null hypothesis.
The p-value is less than the level of significance and so the data are statistically significant. Thus, we fail to reject the null hypothesis.
The p-value is greater than the level of significance and so the data are statistically significant. Thus, we fail to reject the null hypothesis.
The p-value is greater than the level of significance and so the data are not statistically significant. Thus, we reject the null hypothesis.
The p-value is less than the level of significance and so the data are statistically significant. Thus, we reject the null hypothesis.
Question 5 Benford’s Law claims that numbers chosen from very large data files tend to have “1” as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with “1” as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 397 numerical entries from the file and r = 110 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using f$alpha =f$ 0.1. What is the value of the test statistic?
Question options:
20.704
0.052
-20.704
-0.052
-1.039
Question 6 Benford’s Law claims that numbers chosen from very large data files tend to have “1” as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with “1” as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 463 numerical entries from the file and r = 122 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using f$alpha =f$ 0.1. What is the P-value of the test statistic?
Question options:
0.921
0.039
0.020
0.961
0.079
Question 7 A random sample of n1 = 16 communities in western Kansas gave the following rates of hay fever per 1000 population for people under 25 years of age.
121
115
124
99
134
121
110
116
113
96
116
116
135
96
96
116
A random sample of n2 = 14 communities in western Kansas gave the following rates of hay fever per 1000 population for people over 50 years old.
113
86
106
102
113
94
94
108
103
99
78
105
88
100
Assume that the hay fever rate in each age group has an approximately normal distribution. Using the method outlined in Brase and Brase, do the data indicate that the age group over 50 has a lower rate of hay fever? Use f$alpha =f$ 0,05. Do you reject or fail to reject the null hypothesis? Are the data statistically significant at the f$alpha =f$ 0.05 level of significance?
Question options:
Since the p-value is greater than the level of significance, the data are not statistically significant. Thus, we fail to reject the null hypothesis.
Since the p-value is less than the level of significance, the data are not statistically significant. Thus, we fail to reject the null hypothesis.
Since the p-value is greater than the level of significance, the data are statistically significant. Thus, we fail to reject the null hypothesis.
Since the p-value is less than the level of significance, the data are statistically significant. Thus, we reject the null hypothesis.
Since the p-value is greater than the level of significance, the data are not statistically significant. Thus, we reject the null hypothesis.
Question 8 It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) for an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. Suppose that the following data were obtained for a collection of archaeological sites in New Mexico:
x
5.25
5.50
5.75
6.25
6.50
y
12
38
38
42
59
Find the equation of the least squares line f$hat{y} = a + bxf$
Question options:
y^=−130.081+28.698x
y^=130.081−28.698x
y^=130.081+28.698x
y^=28.698−130.081x
Question 9 It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) for an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. Suppose that the following data were obtained for a collection of archaeological sites in New Mexico:
x
5.25
5.50
5.75
6.25
6.50
y
12
38
38
42
59
What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line?
Question options:
0.6%
2.3%
78.2%
84.8%
7.9%
Question 10 It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) for an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. Suppose that the following data were obtained for a collection of archaeological sites in New Mexico:
x
5.25
5.50
5.75
6.25
6.50
y
12
38
38
42
59
Calculate the sample correlation coefficient r.
Question options:
-0.884
-0.821
0.884
0.091
0.909
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