Use for Questions 1-7: Hector will roll two fair, six-sided dice at the same time. Let A = the event that at least one die lands with the number 3 facing up. Let B = the event that the sum of the two dice is less than 5.
1. What is the correct set notation for the event that “at least one die lands with 3 facing up and the sum of the two dice is less than 5”?
2. Calculate the probability that at least one die lands with 3 facing up and the sum of the two dice is less than 5.
3. What is the correct set notation for the event that “at least one die lands with 3 facing up if the sum of the two dice is less than 5”?
4. Calculate the probability that at least one die lands with 3 facing up if the sum of the two dice is less than 5.
5. What is the correct set notation for the event that “the sum of the two dice is not less than 5 if at least one die lands with 3 facing up”?
6. Calculate the probability that the sum of the two dice is not less than 5 if at least one die lands with 3 facing up.
7. Are A and B independent? Explain your reasoning
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A sample of 50 night-school students' ages is obtained in order to estimate the mean age of night-school students. x = 24.3 years. The population variance is 16.
(b) Find the 95% confidence interval for μ. (Give your
answer correct to two decimal places.)
Lower Limit
Upper Limit
(c) Find the 99% confidence interval for μ. (Give your answer correct to two decimal places.)
Lower Limit
Upper Limit
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Solve the problem.
21) The total home-game attendance for major-league baseball is the sum of all attendees for all stadiums during the entire season. The home attendance (in millions) for a number of years is shown in the table below.
21)
Year
Home Attendance (millions)
1978
40.6
1979
43.5
1980
43.0
1981
26.6
1982
44.6
1983
46.3
1984
48.7
1985
49.0
1986
50.5
1987
51.8
1988
53.2
a) Make a scatterplot showing the trend in home attendance. Describe what you see.
b) Determine the correlation, and comment on its significance.
c) Find the equation of the line of regression. Interpret the slope of the equation.
d) Use your model to predict the home attendance for 1998. How much confidence do you have in this prediction? Explain.
e) Use the internet or other resource to find reasons for any outliers you observe in the
scatterplot.
In: Math
In: Math
In 1997, the average household expenditure for energy was $1,338, according to data obtained from the U.S. Department of Energy. An economist claims that energy usage today is different from its 1997 level. In a random sample of 36 households, the economist found the mean expenditure, adjusted for inflation, for energy in 2004 to be $1,423. with a sample standard deviation s = 360.
At a 95% level of confidence (α = .05), we wish to test the economists claim.
1. State the Null Hypothesis and Alternate Hypothesis for this experiment.
a. |
Ho: p = $1,338 Ha: p not = $1,423 |
|
b. |
Ho: µ <= $1,338 Ha: µ > $1,338 |
|
c. |
Ho: µ = $1,423 Ha: µ not = $1,423 |
|
d. |
Ho: µ = $1,338 Ha: µ not = $1,338 |
2.What is the p-value and decision of this research?
a. |
p-value = .165; Do Not Reject Ho. |
|
b. |
p-value = .165; Reject Ho. |
|
c. |
p-value = .0825; Do Not Reject Ho. |
|
d. |
P-value = .0825; Reject Ho. |
3.State the conclusion.
a. |
With 95% Confidence, there is sufficient evidence to show that energy usage today is different from its 1997 level. |
|
b. |
With 95% Confidence, there is insufficient evidence to show that energy usage today is different from its 1997 level. |
|
c. |
With 95% Confidence, there is sufficient evidence to show that energy usage today is greater than its 1997 level. |
|
d. |
With 95% Confidence, there is insufficient evidence to show that energy usage today is greater than its 1997 level. |
4.State the Type I error for this Hypothesis Test and the corresponding probability of a Type I error occurring in this experiment.
a. |
Conclude energy usage is not different, but it really is. Probability = .05 |
|
b. |
Conclude energy usage is not different, but it really is. Probability = .95 |
|
c. |
Concluded energy usage is different, but it really isn't. Probability = .95 |
|
d. |
Conclude energy usage is different, but it really isn't. Probability = .05 |
5.In order to decrease the probability of a Type I error, we would do the following before conducting this experiment:
a. |
Increase the Confidence Level of the Hypothesis Test, thereby decreasing alpha. |
|
b. |
Decrease the Confidence Level of the Hypothesis Test, thereby decreasing alpha. |
|
c. |
Increase the sample size from 36. |
|
d. |
Decrease the sample size from 36. |
In: Math
Below are means, standard deviations, and sample sizes of three different data sets. Estimate the 90% confidence interval for dataset A, 95% for data set B, and 99% for set C.
Set A: mean=6300, standard deviation= 300, n=200
Set B: mean=65, standard deviation= 15, n=75
Set C: mean=93, standard deviation= 37, n=200
In: Math
Kroger runs Buy One Get One (BOGO) promotions every year to promote charcoal for Memorial Day. Their data indicates that 76 customers per day per store purchase this deal every spring and the standard deviation historically is 12 customers. Assume that the population is normally distributed. What is the probability that for a random sample of 15 days, at least 70 customers per day will buy charcoal with the BOGO?
1) 0.6915
2) 0.9772
3) 0.0262
4)0.9738
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The IQs of students at Wilson Elementary School were measured recently and found to be normally distributed with a mean of 110 and a standard deviation of 13. What is the probability that a student selected at random will have the following IQs? (Round your answers to four decimal places.)
(a) 140 or higher
(b) 115 or higher
(c) between 110 and 115
(d) 100 or less
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Suppose the installation time in hours for a software on a laptop has probability density function f(x) = (4/3) (1 − x3 ), 0 ≤ x ≤ 1.
(a) Find the probability that the software takes between 0.3 and 0.5 hours to be installed on your laptop.
(b) Let X1, . . . , X30 be the installation times of the software on 30 different laptops. Assume the installation times are independent. Find the probability that the average installation time is between 0.3 and 0.5 hours. Cite the theorem you use.
(c) Instead of taking a sample of 30 laptops as in the previous question, you take a sample of 60 laptops. Find the probability that the average installation time is between 0.3 and 0.5 hours. Cite the theorem you use.
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Over the past 6 years, Elk County Telephone has paid the dividends shown in the following table. he firm's dividend per share in
2020 is expected to be $1.27
2019 $1.22
2018 $1.17
2017 $1.12
2016 $1.08
2015 $1.04
2014 $1.00
a. If you can earn 11% on similar-risk investments, what is the most you would be willing to pay per share in 2019, just after the $1.22 dividend?
b. If you can earn only 8% on similar-risk investments, what is the most you would be willing to pay per share?
c. Compare your findings in parts a and b, what is the impact of changing risk on share value?
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10.12 A bank with a branch located in a commercial district of a city has the business objective of developing an improved process for serving customers during the noon-to-1 P.M. lunch period. Management decides to first study the waiting time in the current process. The waiting time is defined as the number of minutes that elapses from when the customer enters the line until he or she reaches the teller window. Data are collected from a random sample of 15 customers and stored in Bank1. These data are:
4.21 | 5.55 | 3.02 | 5.13 | 4.77 | 2.34 | 3.54 | 3.20 |
4.50 | 6.10 | 0.38 | 5.12 | 6.46 | 6.19 | 3.79 |
Suppose that another branch, located in a residential area, is also concerned with improving the process of serving customers in the noon-to-1 p.m. lunch period. Data are collected from a random sample of 15 customers and stored in Bank2. These data are:
9.66 | 5.90 | 8.02 | 5.79 | 8.73 | 3.82 | 8.01 | 8.35 |
10.49 | 6.68 | 5.64 | 4.08 | 6.17 | 9.91 | 5.47 |
a. Assuming that the population variances from both banks are equal, is there evidence of a difference in the mean waiting time between the two branches? (Use α=0.05.α=0.05. alpha equals , 0.05.)
b. Determine the p-value in (a) and interpret its meaning.
c. In addition to equal variances, what other assumption is necessary in (a)?
d. Construct and interpret a 95% confidence interval estimate of the difference between the population means in the two branches.
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A population of values has a normal distribution with μ = 194 μ = 194 and σ = 13.4 σ = 13.4 . You intend to draw a random sample of size n = 127 n = 127 . Find the probability that a single randomly selected value is greater than 197.3. P(X > 197.3) = Find the probability that a sample of size n = 127 n = 127 is randomly selected with a mean greater than 197.3. P(M > 197.3) = Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
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For each of the following examples of tests of hypothesis about µ, show the rejection and nonrejection regions on the t-distribution curve. (a) A two-tailed test with α = 0.01 and n = 15 (b) A left-tailed test with α = 0.005 and n = 25 (c) A right-tailed test with α = 0.025 and n = 22
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Demonstrate the relationship between two variables. You will be required to use the least squares approach as well as use software (SPSS preferred) to perform analyses that will yield the coefficient of correlation, the coefficient of determination, and a simple linear regression analysis
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The average height of professional basketball players is around 6 feet 7 inches, and the standard deviation is 3.89 inches. Assuming Normal distribution of heights within this group
(a) What percent of professional basketball players are taller than 7 feet?
(b) If your favorite player is within the tallest 20% of all players, what can his height be?
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