A researcher wants to determine the impact of soil type on the growth of a certain type of plant. She grows three plants in each of four different types of soil and measures the growth in inches for each plant after one month resulting in the data below.
Inches |
Soil |
12.2 |
1 |
12.8 |
1 |
11.9 |
1 |
10.8 |
2 |
12.2 |
2 |
12.3 |
2 |
9.3 |
3 |
9.9 |
3 |
10.8 |
3 |
13 |
4 |
11.8 |
4 |
11.9 |
4 |
a) What null hypothesis is the researcher testing if she runs an ANOVA with this data?
The mean growth of the plant is different in each type of soil.
The variability in growth of the plant in each type of soil is the same.
The mean growth of the plant in each type of soil is the same.
One type of soil has a higher mean growth for the plant than the others.
Soil 3 provides a lower mean growth for the plant than the other types of soil.
b) What is the SS_{trt} for the ANOVA? Give your answer to
at least three decimal places.
c) What is DF_{err} for the ANOVA?
d) What is the value of the F statistic for the ANOVA? Give your
answer to at least three decimal places.
e) Using a 0.1 level of significance, what conclusion should the
researcher reach?
There is not enough evidence to reject the claim that the mean growth of the plant is the same in each type of soil.
Soil 3 has a lower mean growth for the plant than the other types of soil.
Soil 1 has a higher mean growth for the plant than the other types of soil.
The mean growth of the plant is not the same for all soil types.
In: Math
A marketing research firm wishes to study the relationship
between wine consumption and whether a person likes to watch
professional tennis on television. One hundred randomly selected
people are asked whether they drink wine and whether they watch
tennis. The following results are obtained:
Watch Tennis |
Do Not Watch Tennis |
Totals | |
Drink Wine | 10 | 36 | 46 |
Do Not Drink Wine | 10 | 44 | 54 |
Totals | 20 | 80 | 100 |
(a) For each row and column total, calculate the corresponding row or column percentage.
Row 1 | % |
Row 2 | % |
Column 1 | % |
Column 2 | % |
(b) For each cell, calculate the corresponding
cell, row, and column percentages. (Round your answers to
the nearest whole number.)
Watch Tennis |
Do Not Watch Tennis |
||
Drink Wine | Cell= % | Cell= % | |
Row= % | Row= % | ||
Column= % | Column= % | ||
Do Not Drink Wine | Cell= % | Cell= % | |
Row= % | Row= % | ||
Column= % | Column= % | ||
(c) Test the hypothesis that whether people drink wine is independent of whether people watch tennis. Set α = .05. (Round your answer to 3 decimal places.)
χ2χ2 =
In: Math
An advertising executive claims that there is a difference in the mean household income for credit cardholders of Visa Gold and of MasterCard Gold. A random survey of 8 Visa Gold cardholders resulted in a mean household income of $78,320 with a standard deviation of $11,100. A random survey of 12 MasterCard Gold cardholders resulted in a mean household income of $68,070 with a standard deviation of $10,700. Is there enough evidence to support the executive's claim? Let μ1 be the true mean household income for Visa Gold cardholders and μ2 be the true mean household income for MasterCard Gold cardholders. Use a significance level of α=0.05α=0.05 for the test. Assume that the population variances are not equal and that the two populations are normally distributed.
Step 1 of 4: State the null and alternative hypotheses for the test.
Step 2 of 4: Compute the value of the t test statistic. Round your answer to three decimal places.
Step 3 of 4: Determine the decision rule for rejecting the null hypothesis H0H0. Round your answer to three decimal places.
Step 4 of 4: State the test's conclusion.
....reject null hypothesis...fail to reject null hypothesis
In: Math
(1) Symposium is part of a larger work referred to as Plato's Dialogues. Wishart and Leach† found that about 21.4% of five-syllable sequences in Symposium are of the type in which four are short and one is long. Suppose an antiquities store in Athens has a very old manuscript that the owner claims is part of Plato's Dialogues. A random sample of 488 five-syllable sequences from this manuscript showed that 128 were of the type four short and one long. Do the data indicate that the population proportion of this type of five-syllable sequence is higher than that found in Plato's Symposium? Use α = 0.01.
(a) What is the level of significance? _________
(b) 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.) ________
(2) Prose rhythm is characterized as the occurrence of five-syllable sequences in long passages of text. This characterization may be used to assess the similarity among passages of text and sometimes the identity of authors. The following information is based on an article by D. Wishart and S. V. Leach appearing in Computer Studies of the Humanities and Verbal Behavior (Vol. 3, pp. 90-99). Syllables were categorized as long or short. On analyzing Plato's Republic, Wishart and Leach found that about 26.1% of the five-syllable sequences are of the type in which two are short and three are long. Suppose that Greek archaeologists have found an ancient manuscript dating back to Plato's time (about 427 - 347 B.C.). A random sample of 316 five-syllable sequences from the newly discovered manuscript showed that 61 are of the type two short and three long. Do the data indicate that the population proportion of this type of five syllable sequence is different (either way) from the text of Plato's Republic? Use α = 0.01.
(a) What is the level of significance? _____________
(b) 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.)
In: Math
Let X and Y have the joint pdf f(x, y) = 8xy, 0 ≤ x ≤ y ≤ 1. (i) Find the conditional means of X given Y, and Y given X. (ii) Find the conditional variance of X given Y. (iii) Find the correlation coefficient between X and Y.
In: Math
3. Take the mean and standard deviation of data set A calculated in problem 1 and assume that they are population parameters (μ and σ) known for the variable fish length in a population of rainbow trouts in the Coldwater River. Imagine that data set B is a sample obtained from a different population in Red River (Chapter 6 problem!). a) Conduct a hypothesis test to see if the mean fish length in the Red River population is different from the population in Coldwater River. b) Conduct a hypothesis test to see if the variance in fish length is different in the Red River population compared to the variance in the Coldwater population.
• Data set A: total= 677.98, mean= 67.798, n= 10, variance= 0.663084, std devition= 0.814299972
• Data set B: total= 574.24, mean=71.78, n=8, variance= 0.727143, std devition= 0.852726719
Do not use excel function for p value. Show all your work
In: Math
QUESTION 7
The Federal Reserve Board of Governors recently changed the reporting of its stance on monetary policy from what they termed a "policy bias" to a "balance of risks". A researcher wished to see whether there had been a change in the way financial analysts were interpreting the change in reporting. When the "policy bias" reporting method was used, it was known that only 35% of the Board's decisions were correctly anticipated by analysts in their reports. For the "balance of risks" method, the researcher took a random sample of 56 analysts' reports and found that 26 of these correctly anticipated the Board's decision. Assume that the test is to be carried out at the 10% level.
1. State the direction of the alternative hypothesis used to
test whether the proportion of analysts correctly anticipating the
Board's decision had changed. Type gt (greater than), ge (greater
than or equal to), lt (less than), le (less than or equal to) or ne
(not equal to) as appropriate in the box.
2. Calculate the test statistic, reporting your answer to two
decimal places.
3. Use the tables in the textbook to determine the p-value for the
test (answer to 4 decimal places)
4. Is the null hypothesis rejected for this test? Type yes or
no.
5. Disregarding your answer for 4, if the null hypothesis was
rejected at the 10% level, would the predictive accuracy of the
claims in analysts' reports appear to have changed under the new
system? Type yes or no.
In: Math
Refer to the Baseball 2016 data, which reports information on the 2016 Major League Baseball season. Let attendance be the dependent variable and total team salary be the independent variable. Determine the regression equation and answer the following questions.
Draw a scatter diagram. From the diagram, does there seem to be a direct relationship between the two variables?
What is the expected attendance for a team with a salary of $100.0 million?
If the owners pay an additional $30 million, how many more people could they expect to attend?
At the .05 significance level, can we conclude that the slope of the regression line is positive? Conduct the appropriate test of hypothesis.
What percentage of the variation in attendance is accounted for by salary?
Determine the correlation between attendance and team batting average and between attendance and team ERA. Which is stronger? Conduct an appropriate test of hypothesis for each set of variables.
Show all work in Excel
Team | League | Year Opened | Team Salary | Attendance | Wins | ERA | BA | HR | Year | Average salary | ||
Arizona | National | 1998 | 65.80 | 2080145 | 79 | 4.04 | 0.264 | 154 | 2000 | 1988034 | ||
Atlanta | National | 1996 | 89.60 | 2001392 | 67 | 4.41 | 0.251 | 100 | 2001 | 2264403 | ||
Baltimore | American | 1992 | 118.90 | 2281202 | 81 | 4.05 | 0.250 | 217 | 2002 | 2383235 | ||
Boston | American | 1912 | 168.70 | 2880694 | 78 | 4.31 | 0.265 | 161 | 2003 | 2555476 | ||
Chicago Cubs | National | 1914 | 117.20 | 2959812 | 97 | 3.36 | 0.244 | 171 | 2004 | 2486609 | ||
Chicago Sox | American | 1991 | 110.70 | 1755810 | 76 | 3.98 | 0.250 | 136 | 2005 | 2632655 | ||
Cincinnati | National | 2003 | 117.70 | 2419506 | 64 | 4.33 | 0.248 | 167 | 2006 | 2866544 | ||
Cleveland | American | 1994 | 87.70 | 1388905 | 81 | 3.67 | 0.256 | 141 | 2007 | 2944556 | ||
Colorado | National | 1995 | 98.30 | 2506789 | 68 | 5.04 | 0.265 | 186 | 2008 | 3154845 | ||
Detroit | American | 2000 | 172.80 | 2726048 | 74 | 4.64 | 0.270 | 151 | 2009 | 3240206 | ||
Houston | American | 2000 | 69.10 | 2153585 | 86 | 3.57 | 0.250 | 230 | 2010 | 3297828 | ||
Kansas City | American | 1973 | 112.90 | 2708549 | 95 | 3.73 | 0.269 | 139 | 2011 | 3305393 | ||
LA Angels | American | 1966 | 146.40 | 3012765 | 85 | 3.94 | 0.246 | 176 | 2012 | 3440000 | ||
LA Dodgers | National | 1962 | 230.40 | 3764815 | 92 | 3.44 | 0.250 | 187 | 2013 | 3650000 | ||
Miami | National | 2012 | 84.60 | 1752235 | 71 | 4.02 | 0.260 | 120 | 2014 | 3950000 | ||
Milwaukee | National | 2001 | 98.70 | 2542558 | 68 | 4.28 | 0.251 | 145 | 2015 | 4250000 | ||
Minnesota | American | 2010 | 108.30 | 2220054 | 83 | 4.07 | 0.247 | 156 | ||||
NY Mets | National | 2009 | 100.10 | 2569753 | 90 | 3.43 | 0.244 | 177 | ||||
NY Yankees | American | 2009 | 213.50 | 3193795 | 87 | 4.05 | 0.251 | 212 | ||||
Oakland | American | 1966 | 80.80 | 1768175 | 68 | 4.14 | 0.251 | 146 | ||||
Philadelphia | National | 2004 | 133.00 | 1831080 | 63 | 4.69 | 0.249 | 130 | ||||
Pittsburgh | National | 2001 | 85.90 | 2498596 | 98 | 3.21 | 0.260 | 140 | ||||
San Diego | National | 2004 | 126.60 | 2459742 | 74 | 4.09 | 0.243 | 148 | ||||
San Francisco | National | 2000 | 166.50 | 3375882 | 84 | 3.72 | 0.267 | 136 | ||||
Seattle | American | 1999 | 123.20 | 2193581 | 76 | 4.16 | 0.249 | 198 | ||||
St. Louis | National | 2006 | 120.30 | 3520889 | 100 | 2.94 | 0.253 | 137 | ||||
Tampa Bay | American | 1990 | 74.80 | 1287054 | 80 | 3.74 | 0.252 | 167 | ||||
Texas | American | 1994 | 144.80 | 2491875 | 88 | 4.24 | 0.257 | 172 | ||||
Toronto | American | 1989 | 116.40 | 2794891 | 93 | 3.8 | 0.269 | 232 | ||||
Washington | National | 2008 | 174.50 | 2619843 | 83 | 3.62 | 0.251 | 177 |
In: Math
Carleton Chemical claims that they can produce an average of
more than 800 tons of meladone
per week. A random sample of 36 weeks of production yielded a
sample mean of 823 tons, with
a standard deviation of 79.8 tons.
Does the sample data provide sufficient evidence to support the
claim
made by Carleton Chemical? Use a significance level of
α = .05.
In: Math
1. What is the z-score associated with the 75th percentile?
2. What z-scores bound the middle 50% of a normal distribution?
3. What z-score has 10% of the distribution above it?
4. What z-score has 20% of the distribution below it?
5. Reading comprehension scores for junior high students are
normally distributed with a mean of80.0 and a standard deviation of
5.0.
a. What percent of students have scores greater than 87.5?
b. What percent of students have scores between 75 and 85
In: Math
The New Jersey Department of Public Health offers psychological support programs for substance abuse patients with depression. It is suggested that the type of depression varies by the type of substance abuse. If so, such a relationship might help the department better target treatments. They random sample 75 medically declared substance abusers with depression. (C15PROB7.SAV) (χ2 = 5.12, p=.077; V=0.26; Lambdarow= 0.11, p > .05
Substance Abuse | Clinical | Dysthymic | Manic |
Alcohol | 20 | 10 | 8 |
Drugs | 10 | 15 | 12 |
Select and justify the best test(s). The chi-square, Phi, Yates, or Lambda (or even a combination) might be best for a problem given the data and research question. Do not assume the independent is always on the row.
Provide the null and alternative hypotheses in formal and plain language for the appropriate test at the 0.05 significance level.
Do the math and reject/retain null at a=.05. State your critical value.
Explain the results in plain language.
In: Math
A researcher wishes to determine whether there is a significant relationship between the gender of psychology students and the refreshment drink they prefer. The results obtained from a survey of students are presented in the following table: Preferred Drink Gender Water Coffee Soda Total Male 46 29 40 115 Female 29 36 70 135 Total 75 65 110 250.
Perform an appropriate two-tailed hypothesis test at α = 0.05. If a significant result is obtained, determine the strength of the relationship. Show all four decision making steps. (20)
In: Math
Determine the sample size n needed to construct a 90% confidence interval to estimate the population proportion for the following sample proportions when the margin of error equals 8%.
a. p over bar equals 0.10
b. p over bar equals 0.20
c. p over bar equals 0.30
Click the icon to view a table of standard normal cumulative probabilities.
In: Math
At a university the historical mean of scholarship examination scores for freshman applications is 800. A historical population standard deviation σ = 150 is assumed known. Each year, the assistant dean uses a sample of applications to determine whether the mean examination score for the new freshman applications has changed.
(a) State the hypotheses.
(b) What is the 95% confidence interval estimate of the population mean examination score if a sample of 90 applications provided a sample mean x = 834?
(c) Use the confidence interval to conduct a hypothesis test. Using α = 0.05, what is your conclusion?
(d) What is the test statistic? What is the p-value?
In: Math
Refer to the Lincolnville School District bus data.
Conduct a test of hypothesis to reveal whether the mean maintenance cost is equal for each of the bus manufacturers. Use the .01 significance level.
Conduct a test of hypothesis to determine whether the mean miles traveled since the last maintenance is equal for each bus manufacturer. Use the .05 significance level.
Show work in Excel.
ID | Manufacturer | Engine Type | Engine Type (0=diesel) | Capacity | Maintenance cost | Age | Odometer Miles | Miles |
122 | Bluebird | Gasoline | 1 | 55 | 9394 | 10 | 116580 | 11967 |
279 | Bluebird | Diesel | 0 | 55 | 1008 | 2 | 22672 | 11925 |
500 | Bluebird | Gasoline | 1 | 55 | 5329 | 5 | 50765 | 11922 |
520 | Bluebird | Diesel | 0 | 55 | 4794 | 10 | 119130 | 11896 |
714 | Bluebird | Diesel | 0 | 42 | 3742 | 7 | 73703 | 11837 |
875 | Bluebird | Diesel | 0 | 55 | 4376 | 9 | 97947 | 11814 |
600 | Bluebird | Diesel | 0 | 55 | 4832 | 10 | 119860 | 11800 |
953 | Bluebird | Diesel | 0 | 55 | 5160 | 10 | 117700 | 11798 |
101 | Bluebird | Diesel | 0 | 55 | 1955 | 4 | 41096 | 11789 |
358 | Bluebird | Diesel | 0 | 55 | 2775 | 6 | 70086 | 11782 |
29 | Bluebird | Gasoline | 1 | 55 | 5352 | 6 | 69438 | 11781 |
686 | Bluebird | Diesel | 0 | 55 | 1569 | 3 | 34674 | 11757 |
887 | Bluebird | Diesel | 0 | 55 | 3743 | 8 | 93672 | 11704 |
464 | Bluebird | Gasoline | 1 | 55 | 2540 | 3 | 34530 | 11698 |
43 | Bluebird | Gasoline | 1 | 55 | 8263 | 9 | 102969 | 11615 |
704 | Bluebird | Diesel | 0 | 55 | 4218 | 8 | 83424 | 11610 |
814 | Bluebird | Diesel | 0 | 55 | 2028 | 4 | 40824 | 11576 |
39 | Bluebird | Gasoline | 1 | 55 | 5821 | 6 | 69444 | 11533 |
699 | Bluebird | Gasoline | 1 | 55 | 9069 | 9 | 98307 | 11518 |
75 | Bluebird | Diesel | 0 | 55 | 3011 | 6 | 71970 | 11462 |
982 | Bluebird | Diesel | 0 | 55 | 505 | 1 | 10276 | 11359 |
321 | Bluebird | Diesel | 0 | 42 | 2732 | 6 | 70122 | 11358 |
884 | Bluebird | Diesel | 0 | 55 | 4364 | 9 | 92457 | 11231 |
57 | Bluebird | Diesel | 0 | 55 | 3190 | 7 | 79240 | 11222 |
731 | Bluebird | Diesel | 0 | 42 | 3213 | 6 | 68526 | 11168 |
135 | Bluebird | Diesel | 0 | 55 | 3560 | 7 | 76426 | 11127 |
692 | Bluebird | Diesel | 0 | 55 | 3770 | 8 | 93248 | 11048 |
200 | Bluebird | Diesel | 0 | 55 | 5168 | 10 | 103700 | 11018 |
540 | Bluebird | Gasoline | 1 | 55 | 3656 | 4 | 45284 | 10945 |
660 | Bluebird | Gasoline | 1 | 55 | 6213 | 6 | 64434 | 10911 |
482 | Bluebird | Gasoline | 1 | 55 | 10575 | 10 | 116534 | 10802 |
984 | Bluebird | Diesel | 0 | 55 | 3809 | 8 | 87664 | 10760 |
977 | Bluebird | Diesel | 0 | 55 | 3769 | 7 | 79422 | 10759 |
326 | Bluebird | Diesel | 0 | 55 | 4563 | 9 | 107343 | 10724 |
554 | Bluebird | Diesel | 0 | 42 | 1826 | 4 | 44604 | 10662 |
695 | Bluebird | Diesel | 0 | 55 | 1061 | 2 | 23152 | 10633 |
861 | Bluebird | Gasoline | 1 | 55 | 9669 | 10 | 106040 | 10551 |
883 | Bluebird | Gasoline | 1 | 55 | 1881 | 2 | 20742 | 10344 |
954 | Bluebird | Diesel | 0 | 42 | 5284 | 10 | 101000 | 10235 |
768 | Bluebird | Diesel | 0 | 42 | 3173 | 7 | 71778 | 10227 |
490 | Bluebird | Gasoline | 1 | 55 | 10133 | 10 | 106240 | 10210 |
725 | Bluebird | Diesel | 0 | 55 | 2356 | 5 | 57065 | 10209 |
507 | Bluebird | Diesel | 0 | 55 | 3690 | 7 | 72849 | 10095 |
40 | Bluebird | Gasoline | 1 | 55 | 9573 | 10 | 118470 | 10081 |
918 | Bluebird | Diesel | 0 | 55 | 2470 | 5 | 53620 | 10075 |
387 | Bluebird | Gasoline | 1 | 55 | 6863 | 8 | 89960 | 10055 |
418 | Bluebird | Diesel | 0 | 55 | 4513 | 9 | 104715 | 10000 |
10 | Keiser | Gasoline | 1 | 14 | 4646 | 5 | 54375 | 11973 |
751 | Keiser | Diesel | 0 | 14 | 1078 | 2 | 22444 | 11948 |
759 | Keiser | Diesel | 0 | 55 | 3952 | 8 | 87872 | 11883 |
365 | Keiser | Diesel | 0 | 55 | 3065 | 6 | 63384 | 11778 |
162 | Keiser | Gasoline | 1 | 55 | 3143 | 3 | 31266 | 11758 |
370 | Keiser | Gasoline | 1 | 55 | 7766 | 8 | 86528 | 11707 |
948 | Keiser | Diesel | 0 | 42 | 4342 | 9 | 97956 | 11691 |
678 | Keiser | Diesel | 0 | 55 | 3361 | 7 | 75229 | 11668 |
481 | Keiser | Gasoline | 1 | 6 | 3097 | 3 | 34362 | 11662 |
693 | Keiser | Gasoline | 1 | 55 | 9193 | 9 | 101889 | 11461 |
989 | Keiser | Diesel | 0 | 55 | 4795 | 9 | 106605 | 11418 |
724 | Keiser | Diesel | 0 | 42 | 3754 | 8 | 91968 | 11344 |
732 | Keiser | Diesel | 0 | 42 | 4640 | 9 | 101196 | 11342 |
880 | Keiser | Gasoline | 1 | 55 | 8410 | 9 | 97065 | 11336 |
61 | Keiser | Diesel | 0 | 55 | 4139 | 9 | 103536 | 11148 |
754 | Keiser | Diesel | 0 | 14 | 7380 | 14 | 146860 | 11003 |
353 | Keiser | Gasoline | 1 | 55 | 4279 | 4 | 45744 | 10902 |
705 | Keiser | Diesel | 0 | 42 | 2152 | 4 | 47596 | 10755 |
767 | Keiser | Diesel | 0 | 55 | 2985 | 6 | 71538 | 10726 |
120 | Keiser | Diesel | 0 | 42 | 4723 | 10 | 110320 | 10674 |
9 | Keiser | Gasoline | 1 | 55 | 3527 | 4 | 46848 | 10591 |
603 | Keiser | Diesel | 0 | 14 | 2116 | 4 | 44384 | 10518 |
427 | Keiser | Gasoline | 1 | 55 | 6927 | 7 | 73423 | 10355 |
45 | Keiser | Diesel | 0 | 55 | 3124 | 6 | 60102 | 10167 |
38 | Keiser | Gasoline | 1 | 14 | 5976 | 6 | 61662 | 10140 |
396 | Thompson | Diesel | 0 | 14 | 1072 | 2 | 21858 | 11969 |
193 | Thompson | Diesel | 0 | 14 | 5922 | 11 | 128711 | 11248 |
833 | Thompson | Diesel | 0 | 14 | 3920 | 8 | 90968 | 11112 |
671 | Thompson | Gasoline | 1 | 14 | 6733 | 8 | 89792 | 11100 |
398 | Thompson | Diesel | 0 | 6 | 4752 | 9 | 95922 | 10802 |
156 | Thompson | Diesel | 0 | 14 | 6212 | 12 | 140460 | 10473 |
168 | Thompson | Gasoline | 1 | 14 | 7004 | 7 | 83006 | 10315 |
314 | Thompson | Diesel | 0 | 6 | 5408 | 11 | 128117 | 10128 |
In: Math