A bag contains 10 blue marbles, 15 red marbles and 20 green marbles. Marbles are then chosen at random.
a) Find the probability of getting a red and then a green marble.
b) Find the probability of getting a red or a green marble.
In: Math
Is the magnitude of an earthquake related to the depth below the surface at which the quake occurs? Let x be the magnitude of an earthquake (on the Richter scale), and let y be the depth (in kilometers )of the earthquake below the surface at the epicenter. The following is based on information taken from the national earthquake information service of the U.S. Geographical Survey. Additional data may be found by visiting the website for the service.
x 2.9 4.2 3.3 4.5 2.6 3.2 3.4
y 5.0 10.0 11.2 10.0 7.9 3.9 5.5
test on correlation using 0.05 significance
In: Math
A set of solar batteries is used in a research satellite. The satellite can run on only one battery, but it runs best if more than one battery is used. The variance σ2 of lifetimes of these batteries affects the useful lifetime of the satellite before it goes dead. If the variance is too small, all the batteries will tend to die at once. Why? If the variance is too large, the batteries are simply not dependable. Why? Engineers have determined that a variance of σ2 = 23 months (squared) is most desirable for these batteries. A random sample of 30 batteries gave a sample variance of 14.4 months (squared). Using a 0.05 level of significance, test the claim that σ2 = 23 against the claim that σ2 is different from 23.
(a) What is the level of significance?
State the null and alternate hypotheses.
Ho: σ2 = 23; H1: σ2 > 23Ho: σ2 = 23; H1: σ2 < 23 Ho: σ2 > 23; H1: σ2 = 23Ho: σ2 = 23; H1: σ2 ≠ 23
(b) Find the value of the chi-square statistic for the sample.
(Round your answer to two decimal places.)
What are the degrees of freedom?
What assumptions are you making about the original
distribution?
We assume a normal population distribution.We assume a uniform population distribution. We assume a exponential population distribution.We assume a binomial population distribution.
(c) Find or estimate the P-value of the sample test
statistic.
P-value > 0.1000.050 < P-value < 0.100 0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.005
(d) Based on your answers in parts (a) to (c), will you reject or
fail to reject the null hypothesis?
Since the P-value > α, we fail to reject the null hypothesis.Since the P-value > α, we reject the null hypothesis. Since the P-value ≤ α, we reject the null hypothesis.Since the P-value ≤ α, we fail to reject the null hypothesis.
(e) Interpret your conclusion in the context of the
application.
At the 5% level of significance, there is insufficient evidence to conclude that the variance of battery life is different from 23.At the 5% level of significance, there is sufficient evidence to conclude that the variance of battery life is different from 23.
(f) Find a 90% confidence interval for the population variance.
(Round your answers to two decimal places.)
| lower limit | |
| upper limit |
(g) Find a 90% confidence interval for the population standard
deviation. (Round your answers to two decimal places.)
| lower limit | months |
| upper limit | months |
In: Math
Suppose a random sample of size 40 is selected from a population with = 11. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate).
In: Math
When a survey asked subjects whether they would be willing to accept cuts in their standard of living to protect the environment, 354 of 1180 subjects said yes. a. Find the point estimate of the proportion of the population who would answer yes. b. Find the margin of error for a 95% confidence interval. c. Construct the 95% confidence interval for the population proportion. What do the numbers in this interval represent? d. State and check the assumptions needed for the interval in (c) to be valid.
a. Find the point estimate of the proportion of the population who would answer yes. ModifyingAbove p with caretequals (Round to five decimal places as needed.)
b. Find the margin of error for a 95% confidence interval. (Round to five decimal places as needed.)
c. Construct the 95% confidence interval for the population proportion. (Round to five decimal places as needed.)
In: Math
Please answer using R code!
install.packages("wooldridge")
require("wooldridge")
d1 <- data("attend")
View(attend)
Q) Draw as scatter plot of stndfnl against priGPA. Customize your plot, such as give it a title, x-axis and y-axis labels, and you may put nice color to make it pretty. Run a simple regression of stndfnl on priGPA and save regression model as reg1. Are these variables related in the direction you expected? Interpret your estimated slope and intercept coefficient? Now run a multiple regression of stndfnl on priGPA and dummy variable frosh and soph. Interpret the coefficient of soph.
In: Math
Now that you have your data set for your final study mostly analyzed, you thought the data analysis was over, right? Not so fast. I want you to run one more analysis, and this is going to be a tough one. Rather than a 2 X 2 ANOVA, I want you to run a 2 X 2 X 2 ANOVA. That is, I want you to include participant gender as a third independent variable. The good news here is that the analysis is almost identical to the 2 X 2 ANOVAs you already did for Paper IV. With a 2 X 2 X 2 ANOVA, though, simply pull gender over as another “fixed factor” in your design and then run the univariate ANOVA. In your discussion, tell me what (if anything) was significant in the analysis. Think about this as an A X B X C design. There are three different independent variables, all with two levels, so there should be three main effects (one for A, one for B, and one for C). There should be three 2 X 2 interactions (AB, AC, and BC). There should be one possible three way interaction (ABC). All I need you to tell me is which (if any) main effects are significant, which (if any) two way interactions are significant), and if the three way interaction is significant. I don’t need to see the statistics, means, standard deviations, or simple effects tests: just tell me which tests are significant! Then try to interpret it for me by looking at the means. Did differences seem to emerge for the DVs? Work with your group on this interpretation.
In: Math
In country A, the vast majority (90%) of companies in the chemical industry are ISO 14001 certified. The ISO 14001 is an international standard for environmental management systems. An environmental group wished to estimate the percentage of country B's chemical companies that are ISO 14001 certified. Of the 550 chemical companies sampled, 374 are certified.
a) What proportion of the sample reported being certified?
b) Create a 95% confidence interval for the proportion of country B's chemical companies with ISO 14001 certification. (Be sure to check conditions.) Compare to the country A proportion.
In: Math
The USA Today reports that the average expenditure on Valentine's Day is $100.89. Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of 48 male consumers was $135.67, and the average expenditure in a sample survey of 38 female consumers was $68.64. Based on past surveys, the standard deviation for male consumers is assumed to be $38, and the standard deviation for female consumers is assumed to be $18.
In: Math
Budget Sales
14.08 27.96
16.17 22.92
12.01 21.52
18.74 25.62
19.57 29.04
16.89 22.47
16.88 25.92
19.39 25.91
24.76 32.70
22.03 28.97
20.89 34.21
24.05 30.46
15.90 24.45
19.20 27.98
20.58 29.62
22.70 35.73
17.84 23.77
18.51 25.83
21.10 27.78
23.19 27.97
20.42 25.49
22.31 25.74
18.77 28.49
16.09 25.80
22.93 29.12
19.83 27.80
21.83 34.94
15.80 27.02
22.16 26.37
19.00 28.31
21.63 32.08
23.42 31.32
23.34 32.97
27.82 28.40
23.88 34.17
17.90 27.31
18.28 26.46
19.59 26.24
14.92 23.40
22.07 29.31
20.02 24.87
19.19 30.70
19.91 30.53
19.29 30.65
17.83 24.05
21.51 26.75
23.59 31.26
24.13 30.42
21.81 27.75
19.04 24.85
27.71 34.14
27.20 32.17
20.43 30.64
19.02 28.51
15.32 28.74
20.29 27.05
17.90 28.63
15.27 21.10
19.15 27.36
21.03 32.19
19.30 29.53
21.65 25.68
14.80 28.04
19.12 33.21
12.67 22.44
23.06 31.38
17.06 29.05
18.89 30.19
21.47 31.57
14.95 25.84
24.36 29.65
25.68 36.30
14.82 21.97
12.46 22.65
16.37 21.15
21.01 30.69
18.61 25.82
21.59 31.95
21.04 23.59
21.15 30.05
13.25 26.47
12.92 23.51
17.76 25.20
16.24 29.74
17.39 28.49
17.55 25.41
17.94 25.78
22.74 32.39
16.80 26.44
26.77 31.28
13.83 20.11
17.30 25.23
17.94 24.15
19.51 29.63
24.95 35.08
25.99 31.96
27.69 35.37
21.91 30.46
23.28 31.73
14.24 21.61
8.05 19.14
25.20 28.55
16.20 29.84
20.98 25.29
23.55 30.96
21.12 28.87
20.49 25.87
20.36 32.00
18.77 31.22
18.12 24.53
24.00 28.34
23.41 29.13
21.68 28.44
18.44 28.07
26.65 30.23
19.48 26.73
22.61 25.83
17.29 22.75
18.38 30.61
17.36 23.83
Using SPSS
a. [ 10 pts ] Create a scatter plot of budget vs sales.
b. [ 10 pts ] Calculate the correlation coefficient of budget and sales.
c. [ 15 pts ] Based on the results and the plot, is this data correlated? How do you know? Note that you do not need to interpret the p-value.
In: Math
Two teaching methods and their effects on science test scores are being reviewed. A random sample of 19 students, taught in traditional lab sessions, had a mean test score of 77 with a standard deviation of 3.6 . A random sample of 12 students, taught using interactive simulation software, had a mean test score of 86.7 with a standard deviation of 6.5 . Do these results support the claim that the mean science test score is lower for students taught in traditional lab sessions than it is for students taught using interactive simulation software? Let μ1 be the mean test score for the students taught in traditional lab sessions and μ2 be the mean test score for students taught using interactive simulation software. Use a significance level of α=0.05 for the test. Assume that the population variances are equal and that the two populations are normally distributed.
In: Math
In: Math
Dr. Krauze wants to see how cell phone use impacts reaction
time. To test this, Dr. Krauze conducted a study where participants
are randomly assigned to one of two conditions while driving: a
cell phone or no cell phone. Participants were then instructed to
complete a driving simulator course where reaction times (in
milliseconds) were recorded by how quickly they hit the breaks in
response to a dog running in the middle of the road during the
course. Below are the data. What can Dr. Krauze conclude with an α
= 0.01?
cell phone |
no cell phone |
|---|---|
| 235 250 239 243 232 |
232 238 227 228 227 |
If appropriate, compute the CI. If not appropriate, input "na"
for both spaces below.
[ , ]
e) Compute the corresponding effect size(s) and
indicate magnitude(s).
If not appropriate, input and/or select "na" below.
d = ; ---Select--- na trivial effect
small effect medium effect large effect
r2 = ; ---Select--- na
trivial effect small effect medium effect large effect
f) Make an interpretation based on the
results.
Cell phone use results in significantly slower reaction time than no cell phone use.Cell phone use results in significantly faster reaction time than no cell phone use. There is no significant reaction time difference between cell phone use or no cell phone use.
In: Math
Question: A survey was conducted to attempt to determine how many hours the typical worker works during one year in the US. A survey of 33 workers found the mean number of hours worked in a year to be 1784 hours with a standard deviation of 65 hours.
a. Predict the actual mean number of hours worked by a worker in the US. State your answer using appropiate statistical terminology.
b. Explain what this answer means to someone who has never taken statistics, that is avoid statistical jargon and use common language. Use complete sentences.
*note: please give a step by step explanation for explaining what you did and why
In: Math
Imagine an automobile company looking for additives that might increase gas mileage. As a pilot study, they send 30 cars fueled with a new additive on a road trip from Boston to Los Angeles. Without the additive, those cars are known to average 25.0mpg with a standard deviation of 2.4 mpg. Suppose it turns out that the thirty cars averaged 26.3 mpg with the additive. What should the company conclude? Is the additive effective? Let α=0.01.
a)Use three methods: the p-value, the critical value approach and the confidence interval method.
b) Describe what a type I error would be. Describe what a type II error would be.
In: Math