The contents of bottles of beer are Normally distributed with a mean of 300 ml and a standard deviation of 5 ml.
What is the probability that the average contents of a six-pack will be between 293 ml and 307 ml?
In: Math
1. Murphy’s Law, a pub in downtown Rochester, claims its patrons average 25 years of age. A random sample of 40 bar patrons is taken and their mean age is found to be 26.6 years with a standard deviation of 4.5 years. Do we have enough evidence to conclude at the level of significance α = 0.025 that, on average, patrons at Murphy’s Law are older than 25?
Determine the test statistic.
Determine the range of P-values.
Write your decision and explain how you reached it.
Write the conclusion that addresses the original claim.
Determine the type of error you could have made and explain why. (Type I or Type II
error)
2. The coffee machine at your company has been acting weirdly these past few days. You were assured that the machine would pour 7 ounces of coffee every time you press the button. You believe that this is not true anymore and want to call the technician. Before you do so, you gather a sample of 15 coffees and find out that the mean amount of coffee in each cup is 6.8 ounces with a standard deviation of 1 ounce. Is there sufficient evidence to show that the population mean is different than 7 ounces? Perform a test at the 0.05 level of significance. Assume normality.
Determine the test statistic.
Determine the range of P-values.
Write your decision and explain how you reached it.
Write the conclusion that addresses the original claim.
Determine the type of error you could have made and explain why. (Type I or Type II
error)
In: Math
A well-designed questionnaire should meet the research objectives. Give examples of preparatory work that one should conduct to ensure that these objectives are met.
In: Math
The age distribution of the Canadian population and the age distribution of a random sample of 455 residents in the Indian community of a village are shown below.
Age (years) | Percent of Canadian Population | Observed Number in the Village |
Under 5 | 7.2% | 47 |
5 to 14 | 13.6% | 72 |
15 to 64 | 67.1% | 295 |
65 and older | 12.1% | 41 |
Use a 5% level of significance to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village.
(a) What is the level of significance?
State the null and alternate hypotheses.
H0: The distributions are different.
H1: The distributions are
different.H0: The distributions are the
same.
H1: The distributions are the
same. H0: The
distributions are different.
H1: The distributions are the
same.H0: The distributions are the same.
H1: The distributions are different.
(b) Find the value of the chi-square statistic for the sample.
(Round your answer to three decimal places.)
Are all the expected frequencies greater than 5?
YesNo
What sampling distribution will you use?
uniformStudent's t binomialnormalchi-square
What are the degrees of freedom?
(c) 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 that the population fits the
specified distribution of categories?
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, the evidence is insufficient to conclude that the village population does not fit the general Canadian population.At the 5% level of significance, the evidence is sufficient to conclude that the village population does not fit the general Canadian population.
In: Math
2. We are interested in analyzing data related to the Olympics from one decade. We are looking at individuals and if they participated in the summer or winter Olympics and whether or not they won a medal. Use S to denote summer and M to denote if a medal was won. The probability that someone participated in the summer Olympics is 72%. The probability that they won a medal is 13%. The probability that they won a medal and it was in the summer Olympics is 10%. ( please show steps)
a. What percentage of people participated in the summer Olympics or won a medal?
b. What percentage of people participated in the winter Olympics?
c. Given someone won a medal, what is the probability that they participated in the summer Olympics?
d. What percentage of people did NOT participate in the summer games NOR won a medal?
e. Are M and S mutually exclusive events? Why or why not? f. Are M and S independent events? Explain, using probabilities.
g. If we know someone participated in the summer Olympics, what is the probability that they also won a medal?
In: Math
Shipment | Time to Deliver (Days) |
1 | 7.0 |
2 | 12.0 |
3 | 4.0 |
4 | 2.0 |
5 | 6.0 |
6 | 4.0 |
7 | 2.0 |
8 | 4.0 |
9 | 4.0 |
10 | 5.0 |
11 | 11.0 |
12 | 9.0 |
13 | 7.0 |
14 | 2.0 |
15 | 2.0 |
16 | 4.0 |
17 | 9.0 |
18 | 5.0 |
19 | 9.0 |
20 | 3.0 |
21 | 6.0 |
22 | 2.0 |
23 | 6.0 |
24 | 5.0 |
25 | 6.0 |
26 | 4.0 |
27 | 5.0 |
28 | 3.0 |
29 | 4.0 |
30 | 6.0 |
31 | 9.0 |
32 | 2.0 |
33 | 5.0 |
34 | 6.0 |
35 | 7.0 |
36 | 2.0 |
37 | 6.0 |
38 | 9.0 |
39 | 5.0 |
40 | 10.0 |
41 | 5.0 |
42 | 6.0 |
43 | 10.0 |
44 | 3.0 |
45 | 12.0 |
46 | 9.0 |
47 | 6.0 |
48 | 4.0 |
49 | 3.0 |
50 | 7.0 |
51 | 2.0 |
52 | 7.0 |
53 | 3.0 |
54 | 2.0 |
55 | 7.0 |
56 | 3.0 |
57 | 5.0 |
58 | 7.0 |
59 | 4.0 |
60 | 6.0 |
61 | 4.0 |
62 | 4.0 |
63 | 7.0 |
64 | 8.0 |
65 | 4.0 |
66 | 7.0 |
67 | 9.0 |
68 | 6.0 |
69 | 7.0 |
70 | 11.0 |
71 | 9.0 |
72 | 4.0 |
73 | 8.0 |
74 | 10.0 |
75 | 6.0 |
76 | 7.0 |
77 | 4.0 |
78 | 5.0 |
79 | 8.0 |
80 | 8.0 |
81 | 5.0 |
82 | 9.0 |
83 | 7.0 |
84 | 6.0 |
85 | 14.0 |
86 | 9.0 |
87 | 3.0 |
88 | 4.0 |
A) Find the upper limit for the mean at the 90% confidence level.
B) Find the lower limit for the mean at the 90% confidence level.
C) Find the width of the confidence interval at the 90% confidence level.
D) Find the score from the appropriate probability table (standard normal distribution, t distribution, chi-square) to construct a 99% confidence interval.
If you use Excel, please list what Excel functions would allow me to get this answers for future reference
In: Math
Question 1:
Eight measurements were made on the inside diameter of forged piston rings used in an automobile engine. The data (in millimeters) are 74.001, 74.003, 74.015, 74.000, 74.005, 74.002, 74.005, and 74.004.
Question 2:
The April 22, 1991 issue of Aviation Week and Space Technology reports that during Operation Desert Storm, U.S. Airforce F-117A pilots flew 1270 combat sorties for a total of 6905 hours. What is the mean duration of an F-117A mission during this operation? Why is the parameter you have calculated a population mean?
In: Math
14.- A sociologist asserts that only 5% of all seniors in high
school, capable of performing work at the university level,
actually attend university. Find the probabilities that among 180
students capable of performing work at university level:
a) exactly 10 attend college using the binomial
b) Using the normal distribution
c) at least 10 go to university using binomial T.I or excel
d) Using the normal distribution
e) when many eight go to university using binomial or excel
f) Using the normal distribution
In: Math
The mean of a population is 77 and the standard deviation is 12. The shape of the population is unknown. Determine the probability of each of the following occurring from this population. a. A random sample of size 35 yielding a sample mean of 81 or more
b. A random sample of size 150 yielding a sample mean of between 76 and 80
c. A random sample of size 221 yielding a sample mean of less than 77.2
(Round all the values of z to 2 decimal places and final answers to 4 decimal places.)
In: Math
A laboratory tested 12 chicken eggs and found that the mean amount of cholesterol was 183 milligrams with s=12.7. Construct a 95% confidence interval for the true mean cholesterol content of all such eggs and demonstrate two methods for finding margin of error.
In: Math
A random sample of 121 observations produced a sample proportion of 0.4. An approximate 95% confidence interval for the population proportion p is between
In: Math
Use the population of ages {56, 49, 58, 46} of the four U.S. presidents (Lincoln, Garfield, McKinley, Kennedy) when they were assassinated in office. Assume that random samples of size n = 2 are selected with replacement.
1. List the 16 different samples. For example, the samples for age 56 would be
56, 56
56, 49
56, 58
56, 46.
2. After listing all 16 samples, find the mean of each sample, then construct a table representing the sampling distribution of the sample mean. In the table, combine values of the sample mean that are the same.
3. Compare the mean of the population {56, 49, 58, 46} to the mean of the sampling distribution of the sample mean.
4. Do the sample means target the value of the population mean? In general, do sample means make good estimators of population means? Why or why not?
In: Math
1) The PDF of a Gaussian random variable is given by fx(x).
fx(x)= (1/(3*sqrt(2pi) )*e^((x-4)^2)/18
determine
a.) P(X > 4) b). P(X > 0). c). P(X < -2).
2) The joint PDF of random variables X and Y is given by
fxy(x,y)=Ke^-(x+y), x>0 , y>0
Determine
a. The constant k.
b. The marginal PDF fX(x).
c. The marginal PDF fY(y).
d. The conditional PDF fX|Y(x|y). Note
fX|Y(x|y) =
fxy(x,y)/fY(y)
e. Are X and Y independent.
In: Math
Three resistors with resistances R1, R2, R3 are connected in parallel across a battery with voltage V. By Ohm’s law, the current (amps) is
I = V* [ (1/R1) + (1/R2) + (1/R3) ]
Assume that R1, R2, R3, and V are independent random variables
where R1 ~ Normal (m = 10 ohms, s = 1.5 ohm)
R2 ~ Normal (m = 15 ohms, s = 1.5 ohm)
R3 ~ Normal (m =20 ohms, s = 1.0 ohms)
V ~ Normal (m = 120 volts, s = 2.0 volts
(a) Use Monte Carlo Simulation (10,000 random draws from each input random variable) to estimate the mean and standard deviation of the output variable current. (b) Assess whether the output variable current is normally distributed. (c) Assess whether the inverse of current squared (1/ I2 ) is normally distributed. (d) Estimate the probability that the current is less than 25 amps assuming that the inverse of current squared is normally distributed. (e) Compare your answer to (d) with your simulation results – how many of the 10,000 random results for current are below 25 amps via the Stat > Tables > Tally command?
In: Math
A survey of 2645 consumers by DDB Needham Worldwide of Chicago for public relations agency Porter/Novelli showed that how a company handles a crisis when at fault is one of the top influences in consumer buying decisions,with 73% claiming it is an influence. Quality of product was the number one influence, with 96% of consumers stating that quality influences their buying decisions. How a company handles complaints was number two, with 85% of consumers reporting it as an influence in their buying decisions. Suppose a random sample of 1,100 consumers is taken and each is asked which of these three factors influence their buying decisions.
*a. What is the probability that more than 820
consumers claim that how a company handles a crisis when at fault
is an influence in their buying decisions?
**b. What is the probability that fewer than 1,030
consumers claim that quality of product is an influence in their
buying decisions?
*c. What is the probability that between 82% and
83% of consumers claim that how a company handles complaints is an
influence in their buying decisions?
*(Round the values of z to 2 decimal places. Round
the intermediate values to 4 decimal places. Round your answer to 4
decimal places.)
**(Round the values of z to 2 decimal places. Round the
intermediate values to 4 decimal places. Round your answer to 5
decimal places.)
In: Math