An urn contains 5 blue marbles and 4 yellow marbles. One marble is removed, its color noted, and not replaced. A second marble is removed and its color is noted.
(a) What is the probability that both marbles are blue? yellow?
(b) What is the probability that exactly one marble is blue?
A tree diagram has a root that splits into 2 branches labeled blue and yellow. Each primary branch splits into 2 secondary branches, labeled blue and yellow.yellowblueblueblueyellowyellow
In: Math
4. What is the empirical probability of a loss? [Topic 2]
Date OLIM Int.
15/6/2014 2.36
22/6/2014 2.46
29/6/2014 2.52
6/7/2014 2.46
13/7/2014 2.44
20/7/2014 2.54
27/7/2014 2.46
3/8/2014 2.42
10/8/2014 2.54
17/8/2014 2.53
24/8/2014 2.65
31/8/2014 2.64
7/9/2014 2.56
14/9/2014 2.54
21/9/2014 2.4
28/9/2014 2.3
5/10/2014 2.2
12/10/2014 2.08
19/10/2014 2.06
26/10/2014 2.13
2/11/2014 2.11
9/11/2014 2.25
16/11/2014 2.24
23/11/2014 2.16
30/11/2014 2.09
7/12/2014 2.04
14/12/2014 2.11
21/12/2014 2.09
28/12/2014 2.04
4/1/2015 2.01
11/1/2015 1.96
18/1/2015 2
25/1/2015 1.975
1/2/2015 2.03
8/2/2015 2
15/2/2015 2
22/2/2015 2
1/3/2015 2
8/3/2015 2.01
15/3/2015 1.98
22/3/2015 1.99
29/3/2015 2
5/4/2015 2.03
12/4/2015 2.05
19/4/2015 2
26/4/2015 2.02
3/5/2015 2
10/5/2015 1.98
17/5/2015 1.985
24/5/2015 1.985
31/5/2015 1.88
7/6/2015 1.885
14/6/2015 1.865
21/6/2015 1.865
28/6/2015 1.885
5/7/2015 1.825
12/7/2015 1.79
19/7/2015 1.78
26/7/2015 1.84
2/8/2015 1.8
9/8/2015 1.8
16/8/2015 1.755
23/8/2015 2.07
30/8/2015 1.98
6/9/2015 1.975
13/9/2015 2.04
20/9/2015 1.995
27/9/2015 2
4/10/2015 2
11/10/2015 2
18/10/2015 1.98
25/10/2015 2
1/11/2015 1.99
8/11/2015 1.915
15/11/2015 1.845
22/11/2015 1.82
29/11/2015 1.805
6/12/2015 1.77
13/12/2015 1.81
20/12/2015 1.835
27/12/2015 1.82
3/1/2016 1.695
10/1/2016 1.665
17/1/2016 1.63
24/1/2016 1.62
31/1/2016 1.61
7/2/2016 1.58
14/2/2016 1.585
21/2/2016 1.61
28/2/2016 1.755
6/3/2016 1.74
13/3/2016 1.745
20/3/2016 1.74
27/3/2016 1.69
3/4/2016 1.655
10/4/2016 1.72
17/4/2016 1.725
24/4/2016 1.65
1/5/2016 1.595
8/5/2016 1.6
15/5/2016 1.705
22/5/2016 1.815
29/5/2016 1.835
5/6/2016 1.86
12/6/2016 1.815
19/6/2016 1.855
26/6/2016 1.88
3/7/2016 1.91
10/7/2016 1.885
17/7/2016 1.88
24/7/2016 1.91
31/7/2016 1.83
7/8/2016 1.85
14/8/2016 1.96
21/8/2016 2.06
28/8/2016 2.07
4/9/2016 2.09
11/9/2016 2.03
18/9/2016 2.04
25/9/2016 2.06
2/10/2016 2.05
9/10/2016 2.07
16/10/2016 2.06
23/10/2016 2.1
30/10/2016 2.08
6/11/2016 2.1
13/11/2016 1.95
20/11/2016 1.96
27/11/2016 2.02
4/12/2016 2.07
11/12/2016 2.13
18/12/2016 2
25/12/2016 1.97
1/1/2017 2
8/1/2017 2.06
15/1/2017 1.995
22/1/2017 2
29/1/2017 2.01
5/2/2017 2.02
12/2/2017 2.1
19/2/2017 2.06
26/2/2017 2
5/3/2017 1.975
12/3/2017 1.93
19/3/2017 1.86
26/3/2017 1.92
2/4/2017 1.955
9/4/2017 1.91
16/4/2017 1.91
23/4/2017 1.91
30/4/2017 1.9
7/5/2017 1.96
14/5/2017 1.995
21/5/2017 2.07
28/5/2017 2.02
4/6/2017 2.03
11/6/2017 2
18/6/2017 1.96
25/6/2017 1.95
2/7/2017 1.915
9/7/2017 1.94
16/7/2017 1.945
23/7/2017 1.93
30/7/2017 1.96
6/8/2017 1.95
13/8/2017 2.02
20/8/2017 2.1
27/8/2017 2.06
3/9/2017 2.02
10/9/2017 2.01
17/9/2017 2.01
24/9/2017 2.02
1/10/2017 2.14
8/10/2017 2.22
15/10/2017 2.29
22/10/2017 2.35
29/10/2017 2.36
5/11/2017 2.33
12/11/2017 2.19
19/11/2017 2.2
26/11/2017 2.25
3/12/2017 2.19
10/12/2017 2.16
17/12/2017 2.07
24/12/2017 2.03
31/12/2017 2.04
7/1/2018 2.09
14/1/2018 2.11
21/1/2018 2.19
28/1/2018 2.22
4/2/2018 2.08
11/2/2018 2.17
18/2/2018 2.26
25/2/2018 2.23
4/3/2018 2.4
11/3/2018 2.34
18/3/2018 2.37
25/3/2018 2.34
1/4/2018 2.34
8/4/2018 2.35
15/4/2018 2.29
22/4/2018 2.28
29/4/2018 2.18
6/5/2018 2.3
13/5/2018 2.29
20/5/2018 2.28
27/5/2018 2.19
3/6/2018 2.21
10/6/2018 2.17
In: Math
A problem experiment is conducted in which the sample space of the experiment is S= {1,2,3,4,5,6,7,8,9,10,11,12}, event F={7,8}, and event G={9,10,11,12}. Assume that each outcome is equally likely. List the outcomes in F and G. Find P(F or G) by counting the number of outcomes in F or G. Determine P(F or G) using the general addition rule.
In: Math
Hormone replacement therapy (HRT) is thought to increase the risk of breast cancer. The accompanying data on
x = percent of women using HRT and
y = breast cancer incidence (cases per 100,000 women)
for a region in Germany for 5 years appeared in the paper "Decline in Breast Cancer Incidence after Decrease in Utilization of Hormone Replacement Therapy." The authors of the paper used a simple linear regression model to describe the relationship between HRT use and breast cancer incidence.
| HRT Use | Breast Cancer Incidence |
|---|---|
| 46.30 | 103.30 |
| 40.60 | 105.00 |
| 39.50 | 100.00 |
| 36.60 | 93.80 |
| 30.00 | 83.50 |
(a)
What is the equation of the estimated regression line? (Round your answers to three decimal places.)
ŷ = __+(___x)
(b)
What is the estimated average change in breast cancer incidence (in cases per 100,000 women) associated with a 1 percentage point increase in HRT use? (Round your answer to three decimal places.)
cases per 100,000 women
(c)
What would you predict the breast cancer incidence (in cases per 100,000 women) to be in a year when HRT use was 34%? (Round your answer to three decimal places.)
cases per 100,000 women
(d)
Should you use this regression model to predict breast cancer incidence for a year when HRT use was 13%? Explain.
(e)
Calculate the value of
r2.
(Round your answer to three decimal places.)Interpret the value of
r2.
(f)
Calculate the value of
se.
(Round your answer to three decimal places.)Interpret the value of
In: Math
|
The undergraduate grade point averages (UGPA) of students taking an admissions test in a recent year can be approximated by a normal distribution, as shown in the figure. (a) What is the minimum UGPA that would still place a student in the top55% of UGPAs?(b) Between what two values does the middle5050% of the UGPAs lie? |
3.3842.76Grade point
average
mu equals 3.38μ=3.38 sigma equals 0.19σ=0.19 x |
In: Math
A simple random sample of 33 men from a normally distributed population results in a standard deviation of 8.2 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.10 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute. Complete parts (a) through (d) below.
a. Identify the null and alternative hypotheses.
b. Compute the test statistic; χ2 = ___ (Round to three decimal places as needed.)
c. Find the P-value; P-value = ____ (Round to four decimal places as needed.)
d. State the conclusion. (choose one from each ( x, y) set)
In: Math
In her book Red Ink Behaviors, Jean Hollands reports on the assessment of leading Silicon Valley companies regarding a manager's lost time due to inappropriate behavior of employees. Consider the following independent random variables. The first variable x1 measures manager's hours per week lost due to hot tempers, flaming e-mails, and general unproductive tensions. x1: 1 3 6 2 2 4 10 The variable x2 measures manager's hours per week lost due to disputes regarding technical workers' superior attitudes that their colleagues are "dumb and dispensable". x2: 8 3 2 7 9 4 10 3 (i) Use a calculator with sample mean and sample standard deviation keys to calculate x1, s1, x2, and s2. (Round your answers to two decimal places.) x1 = s1 = x2 = s2 = (ii) Does the information indicate that the population mean time lost due to hot tempers is different (either way) from population mean time lost due to disputes arising from technical workers' superior attitudes? Use α = 0.05. Assume that the two lost-time population distributions are mound-shaped and symmetric. (a) What is the level of significance? State the null and alternate hypotheses. H0: μ1 = μ2; H1: μ1 ≠ μ2 H0: μ1 = μ2; H1: μ1 < μ2 H0: μ1 = μ2; H1: μ1 > μ2 H0: μ1 ≠ μ2; H1: μ1 = μ2 (b) What sampling distribution will you use? What assumptions are you making? The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. The standard normal. We assume that both population distributions are approximately normal with known standard deviations. The Student's t. We assume that both population distributions are approximately normal with known standard deviations. The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. What is the value of the sample test statistic? (Test the difference μ1 − μ2. Do not use rounded values. Round your final answer to three decimal places.) (c) Find (or estimate) the P-value. P-value > 0.500 0.250 < P-value < 0.500 0.100 < P-value < 0.250 0.050 < P-value < 0.100 0.010 < P-value < 0.050 P-value < 0.010 Sketch the sampling distribution and show the area corresponding to the P-value. Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α? At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. (e) Interpret your conclusion in the context of the application. Fail to reject the null hypothesis, there is sufficient evidence that there is a difference in mean time lost due to hot tempers and technical workers' attitudes. Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean time lost due to hot tempers and technical workers' attitudes. Reject the null hypothesis, there is sufficient evidence that there is a difference in mean time lost due to hot tempers and technical workers' attitudes. Reject the null hypothesis, there is insufficient evidence that there is a difference in mean time lost due to hot tempers and technical workers' attitudes.
In: Math
A random sample of n1 = 10 regions in New England gave the following violent crime rates (per million population). x1: New England Crime Rate 3.5 3.7 4.2 3.9 3.3 4.1 1.8 4.8 2.9 3.1 Another random sample of n2 = 12 regions in the Rocky Mountain states gave the following violent crime rates (per million population). x2: Rocky Mountain Crime Rate 3.5 4.3 4.5 5.1 3.3 4.8 3.5 2.4 3.1 3.5 5.2 2.8 Assume that the crime rate distribution is approximately normal in both regions. (i) Use a calculator to calculate x1, s1, x2, and s2. (Round your answers to two decimal places.) x1 = s1 = x2 = s2 = (ii) Do the data indicate that the violent crime rate in the Rocky Mountain region is higher than in New England? Use α = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. H0: μ1 = μ2; H1: μ1 < μ2 H0: μ1 = μ2; H1: μ1 ≠ μ2 H0: μ1 < μ2; H1: μ1 = μ2 H0: μ1 = μ2; H1: μ1 > μ2 (b) What sampling distribution will you use? What assumptions are you making? The Student's t. We assume that both population distributions are approximately normal with known standard deviations. The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. The standard normal. We assume that both population distributions are approximately normal with known standard deviations. The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. What is the value of the sample test statistic? (Test the difference μ1 − μ2. Round your answer to three decimal places.) (c) Find (or estimate) the P-value. P-value > 0.250 0.125 < P-value < 0.250 0.050 < P-value < 0.125 0.025 < P-value < 0.050 0.005 < P-value < 0.025 P-value < 0.005 Sketch the sampling distribution and show the area corresponding to the P-value. Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α? At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. (e) Interpret your conclusion in the context of the application. Reject the null hypothesis, there is sufficient evidence that violent crime in the Rocky Mountain region is higher than in New England. Fail to reject the null hypothesis, there is insufficient evidence that violent crime in the Rocky Mountain region is higher than in New England. Reject the null hypothesis, there is insufficient evidence that violent crime in the Rocky Mountain region is higher than in New England. Fail to reject the null hypothesis, there is sufficient evidence that violent crime in the Rocky Mountain region is higher than in New England.
In: Math
Please outline each step used along the way to solve the problem using excel only with cell numbers and formulas used. Thank you.
Whenever an Alliance Air customer flies on a prepurchased seat, Alliance Air obtains $100 in profits. However, if Alliance Air has more customers seeking a seat then they have prepurchased, Alliance Air is forced to book that passenger on a seat purchased that day. In such a situation, Alliance Air has a profit of -$170 due to the high cost of same-day flights. If not all of their prepurchased seats are taken, then Alliance Air makes a profit of -$20 by selling the seats at a discount to passengers outside of their customer base. Based on their data, Alliance Air knows that number of customers seeking a flight on any day follows a Poisson distribution with mean 40.
Using this information, complete the following tasks/questions:
| Alliance Air Service | ||||||||
| Yellow Cell is Input Cell | ||||||||
| Prepurchased Seat Sale | $ 100 | Avg Profit | Min Profit | Max Profit | % above 2250 | |||
| Same Day Flight | $ (170) | |||||||
| Discounted Flight Sale | $ (20) | |||||||
| Average Demand | 40 | |||||||
| Pre-Purchased Flights | 37 | |||||||
| Same Day Flights to purchase | ||||||||
| Discounted Flights Sold | ||||||||
| Daily Profit |
In: Math
In the population, the average IQ is 100 with a standard deviation of 15. A team of scientists wants to test a new medication to see if it has either a positive or negative effect on intelligence, or no effect at all. A sample of 30 participants who have taken the medication has a mean of 105. It is assumed that the data are drawn from a normally distributed population. Did the medication affect intelligence, using α = 0.05?
(a) State hypotheses appropriate to the research question.
(b) Describe what test would you use and state the reasons for your choice.
(c) Draw a conclusion in the context of the problem using the p-value.
(d) Construct a 95% CI for µ. Conclude in the context of the problem.
(e) Compute the power if the true population mean is 110.
In: Math
home / study / math / statistics and probability / statistics and probability questions and answers / suppose that we fit model (1) to the n observations (y1, x11, x21), …, (yn, x1n, x2n). yi ... Your question has been answered Let us know if you got a helpful answer. Rate this answer Question: Suppose that we fit Model (1) to the n observations (y1, x11, x21), …, (yn, x1n, x2n). yi = β0 + ... Suppose that we fit Model (1) to the n observations (y1, x11, x21), …, (yn, x1n, x2n). yi = β0 + β1x1i + β2x2i + εi , i = 1, …., n, (1) where ε’s are identically and independently distributed as a normal random variable with mean zero and variance σ2, i = 1, …, n , and all the x’s are fixed. a) Suppose that Model (1) is the true model. Show that at any observation yi , the point estimator of the mean response and its residual are two statistically independent normal random variables. b) Suppose the true model is Model (1), but we fit the data to the following Model (2) (that is, ignore the variable x2). yi = β 0 + β 1x1i + εi , i = 1, …., n. Assume that average of x1 =0, average of x2=0. The sum of x1i and x2i equals 0. Derive the least-squares estimator of β1 obtained from fitting Model (2). Is this least-squares estimator biased for β1 under Model (1)?
In: Math
Quality Associates, Inc., a consulting firm, advises its clients about sampling and statistical procedures that can be used to control their manufacturing processes. In one particular application, a client gave Quality Associates a sample of 800 observations taken while that client’s process was operating satisfactorily. The sample standard deviation for these data was 0.21; hence, with so much data, the population standard deviation was assumed to be 0.21. Quality Associates then suggested that random samples of size 30 be taken periodically to monitor the process on an ongoing basis. By analyzing the new samples, the client could quickly learn whether the process was operating satisfactorily. When the process was not operating satisfactorily, corrective action could be taken to eliminate the problem. The design specification indicated that the mean for the process should be 12. The hypothesis test suggested by Quality Associates is as follows: ± H H :1 2 :1 2 0 a m m 5 Corrective action will be taken any time H0 is rejected. The samples listed in the following table were collected at hourly intervals during the first day of operation of the new statistical process control procedure. These data are available in the file Quality. Sample 1 Sample 2 Sample 3 Sample 4 11.55 11.62 11.91 12.02 11.62 11.69 11.36 12.02 11.52 11.59 11.75 12.05 11.75 11.82 11.95 12.18 11.90 11.97 12.14 12.11 11.64 11.71 11.72 12.07 11.64 11.71 11.72 12.07 11.80 11.87 11.61 12.05 12.03 12.10 11.85 11.64 11.94 12.01 12.16 12.39 11.92 11.99 11.91 11.65 12.13 12.20 12.12 12.11 12.09 12.16 11.61 11.90 11.93 12.00 12.21 12.22 12.21 12.28 11.56 11.88 12.32 12.39 11.95 12.03 11.93 12.00 12.01 12.35 11.85 11.92 12.06 12.09 11.76 11.83 11.76 11.77 12.16 12.23 11.82 12.20 11.77 11.84 12.12 11.79 12.00 12.07 11.60 12.30 12.04 12.11 11.95 12.27 11.98 12.05 11.96 12.29 12.30 12.37 12.22 12.47 12.18 12.25 11.75 12.03 11.97 12.04 11.96 12.17 12.17 12.24 11.95 11.94 11.85 11.92 11.89 11.97 12.30 12.37 11.88 12.23 12.15 12.22 11.93 12.25 1. Conduct a hypothesis test for each sample at the 0.01 level of significance and determine what action, if any, should be taken. Provide the test statistic and p value for each test. 2. Compute the standard deviation for each of the four samples. Does the conjecture of 0.21 for the population standard deviation appear reasonable? 3. Compute limits for the sample mean x around 12 m 5 such that, as long as a new sample mean is within those limits, the process will be considered to be operating satisfactorily. If x exceeds the upper limit or if x is below the lower limit, corrective action will be taken. These limits are referred to as upper and lower control limits for quality-control purposes. 4. Discuss the implications of changing the level of significance to a larger value. What mistake or error could increase if the level of significance is increased? Can you show it in excel of how you get the answers, Thanks
In: Math
What is the purpose of using correlation as well as the interpretation of the correlation coefficient? In your video response, please describe at least 2 examples of an extremely low relationship among variables and an extremely high relationship among variables. Finally, discuss the two most common statistical techniques for determining relationships of variables.
In: Math
A political pollster is conducting an analysis of sample results in order to make predictions on election night. Assuming a two-candidate election, if a specific candidate receives at least 55% of the vote in the sample, that candidate will be forecast as the winner of the election. You select a random sample of 100 voters. Complete parts (a) through (c) below.
a. What is the probability that a candidate will be forecast as the winner when the population percentage of her vote is 50.1%? The probability is nothing that a candidate will be forecast as the winner when the population percentage of her vote is 50.1%. (Round to four decimal places as needed.)
b.
| What is the probability that a candidate will be forecast as
the winner when the population percentage of her vote is
55%? |
c.
| What is the probability that a candidate will be forecast as
the winner when the population percentage of her vote is
49% (and she will actually lose the election)? |
d.
| Suppose that the sample size was increased to
400. Repeat process (a) through (c), using this new sample size. Comment on the difference. |
In: Math
In a random sample of 13 residents of the state of Washington, the mean waste recycled per person per day was 1.6 pounds with a standard deviation of 0.43 pounds. Determine the 98% confidence interval for the mean waste recycled per person per day for the population of Washington.
In: Math