In a study where the capability of a gauge was measured by the weight of paper, the following measurements were obtained: 3.481 3.448 3.485 3.475 3.472 3.477 3.472 3.464 3.508 3.170 4.123 3.470 2.893 3.473 4.201 3.474 4.301 3.021 3.231 3.405
Part I Using R do the following(SHOW R CODE): 1. Draw an appropriately titled histogram. Interpret the graph. 2. Draw an appropriately titled boxplot. Interpret the graph. 3. Compute the five-number summary. 4. Find the interquartile range. 5. Find the mean 6. Find the standard deviation. 7. What would be the appropriate measures of center and dispersion?
Part 2 Assuming the above sample data is coming from a normal population, construct a 95% confidence interval for the population mean.
In: Math
For X ~ BIN(20, 0.6), find the following probabilities (PLEASE SHOW CLEAR WORK):
P(X = 14) =
P(X > 15) =
P(X < 9) =
In: Math
According to the British United Provident Association, a major health care provider in the U.K., snoring can be an indication of sleep apnea which can cause chronic illness if left untreated. In the United States, the National Sleep foundation reports that 36.8% of the 995 adults they surveyed snored. Of the respondents, 81.5% were over the age of 30, and 32% were both over the age of 30 and snorers.
A. What is the probability of snoring?
B. What percent of the respondent were 30 or younger and did not snore?
In: Math
You may need to use the appropriate technology to answer this question.
Home values tend to increase over time under normal conditions, but the recession of 2008 and 2009 has reportedly caused the sales price of existing homes to fall nationwide.† You would like to see if the data support this conclusion. The file HomePrices contains data on 30 existing home sales in 2006 and 40 existing home sales in 2009.
| 213,100 | 226,200 | 239,100 |
| 214,300 | 161,700 | 181,200 |
| 228,600 | 222,100 | 228,900 |
| 235,800 | 219,400 | 238,800 |
| 301,800 | 264,200 | 320,200 |
| 315,000 | 118,900 | 172,400 |
| 137,500 | 212,800 | 175,400 |
| 311,400 | 296,900 | 292,500 |
| 287,700 | 246,500 | 195,600 |
| 155,300 | 152,400 | 211,200 |
| 155,400 | 189,800 | 200,800 | 280,400 |
| 213,200 | 181,100 | 117,400 | 130,000 |
| 170,000 | 149,600 | 146,200 | 54,400 |
| 213,800 | 186,000 | 182,100 | 180,000 |
| 215,700 | 164,200 | 95,300 | 239,500 |
| 207,200 | 188,200 | 169,400 | 185,600 |
| 177,000 | 178,000 | 161,200 | 249,200 |
| 146,400 | 99,800 | 246,700 | 173,500 |
| 138,100 | 112,200 | 137,500 | 147,900 |
| 179,000 | 116,200 | 197,500 | 164,200 |
(a)
Provide a point estimate of the difference (in dollars) between the population mean prices for the two years. (Use year 2006 − year 2009. Round your answer to the nearest dollar.)
$
(b)
Develop a 99% confidence interval estimate of the difference (in dollars) between the resale prices of houses in 2006 and 2009. (Use year 2006 − year 2009. Round your answers to the nearest dollar.)
$ to $
(c)
Would you feel justified in concluding that resale prices of existing homes have declined from 2006 to 2009? Why or why not?
To answer this question, we need to conduct a hypothesis test.
State the null and alternative hypotheses. (Let μ1 = mean home price in 2006 and let μ2 = mean home price in 2009.)
H0:μ1 − μ2 > 0
Ha:μ1 − μ2 ≤ 0
H0:μ1 − μ2 ≤ 0
Ha:μ1 − μ2 > 0
H0:μ1 − μ2 ≠ 0
Ha:μ1 − μ2 = 0
H0:μ1 − μ2 = 0
Ha:μ1 − μ2 ≠ 0
H0:μ1 − μ2 ≤ 0
Ha:μ1 − μ2 = 0
Find the value of the test statistic. (Round your answer to three decimal places.)
Find the p-value. (Round your answer to four decimal places.)
p-value =
State your conclusion. (Use α = 0.01)
Do not reject H0. We can conclude that existing home prices have declined between 2006 and 2009.
Do not reject H0. We can not conclude that existing home prices have declined between 2006 and 2009.
Reject H0. We can conclude that existing home prices have declined between 2006 and 2009
.Reject H0. We can not conclude that existing home prices have declined between 2006 and 2009.
In: Math
Here are summary statistics for randomly selected weights of newborn girls: nequals220, x overbarequals30.3 hg, sequals6.3 hg. Construct a confidence interval estimate of the mean. Use a 99% confidence level. Are these results very different from the confidence interval 29.0 hgless thanmuless than31.8 hg with only 18 sample values, x overbarequals30.4 hg, and sequals2.1 hg? What is the confidence interval for the population mean mu? nothing hgless thanmuless than nothing hg (Round to one decimal place as needed.)
In: Math
What are distinctions between big data, applied math, (finance/ economics) and statistics?
In: Math
Consider the following table of data that was generated from randomly surveying 100 people and recording how much change (from coins) was in their pockets:
|
0.33 |
0.01 |
0.69 |
0.04 |
0.46 |
|
0.16 |
1.67 |
0.12 |
0.03 |
0.17 |
|
0.09 |
0.17 |
0.57 |
0.04 |
0.29 |
|
0.85 |
0.46 |
1.17 |
0.02 |
0.12 |
|
0.74 |
1.72 |
0.28 |
0.12 |
1.37 |
|
0.61 |
0.06 |
1.46 |
0.42 |
0.03 |
|
0.39 |
0.10 |
0.02 |
0.20 |
1.08 |
|
1.27 |
0.30 |
1.13 |
0.06 |
0.27 |
|
3.76 |
0.43 |
0.04 |
0.37 |
0.09 |
|
0.09 |
0.22 |
1.06 |
0.09 |
0.01 |
|
0.17 |
1.23 |
0.12 |
1.51 |
0.13 |
|
0.18 |
0.50 |
0.73 |
0.03 |
0.63 |
|
0.05 |
0.36 |
0.11 |
0.74 |
0.12 |
|
0.90 |
0.91 |
0.12 |
0.38 |
0.02 |
|
0.17 |
0.20 |
0.40 |
0.47 |
0.36 |
|
0.99 |
0.35 |
1.27 |
1.64 |
1.67 |
|
0.74 |
0.04 |
0.62 |
0.08 |
0.09 |
|
0.15 |
0.01 |
0.05 |
1.03 |
0.15 |
|
0.09 |
0.49 |
0.89 |
0.18 |
0.10 |
|
0.15 |
1.27 |
1.23 |
0.34 |
0.42 |
1. Construct a histogram of the empirical data. Use ten "bins".Hint: It may be helpful to construct ten "bins" over the interval [0,4]
2. Construct a histogram of the empirical data. Use 20 bins.
3. Describe the shape of each graph.
In: Math
The Consumer Reports National Research Center conducted a telephone survey of 2,000 adults to learn about the major economic concerns for the future. The survey results showed that 1,740 of the respondents think the future health of Social Security is a major economic concern.
If computing the confidence intervals manually, make sure to use at least three decimal digits for the critical values.
a. What is the point estimate of the population
proportion of adults who think the future health of Social Security
is a major economic concern?
b. At 90% confidence, what is the margin of
error (to 4 decimals)?
c. Develop a 90% confidence interval for the population proportion of adults who think the future health of Social Security is a major economic concern (to 3 decimals).
( , ) , ( , )
d. Develop a 95% confidence interval for this population proportion (to 3 decimals).
( , ) , ( , )
Video
The range for a set of data is estimated to be 24.
e. What is the planning value for the population standard deviation?
f. At 95% confidence, how large a sample would provide a margin of error of 3?
g. At 95% confidence, how large a sample would provide a margin of error of 2?
In: Math
Assume that f is differentiable at a.
Compute limn→∞n∑i=1k[f(a+in)−f(a)]
Deduce the limit limn→∞n∑i=1k[(n+i)mnm−1−1]
In: Math
The number of female customers arriving to a coffee shop follow a Poisson process with a mean rate of 3 per hour. The number of male customers arriving to the same coffee shop also follow a Poisson process with a mean rate of 6 per hour and their arrival is independent of the arrivals of female customers.
a) What is the probability that the next customer will arrive within 5 minutes?
b) What is the probability that exactly thee customers will arrive in the next 5 minutes?
c) What is the probability of exactly two male and exactly one female customer will arrive in the next 5 minutes?
d). Parts b) and c) ask for the probability of exactly three arrivals in the next 5 minutes. Are they identical? Explain why?
e) What is the probability of exactly five customers will arrive between 6 and 7 hours from now?
In: Math
Suppose a legislator is deciding whether they should put in the effort to draft a bill. The legislator only wants to do this if they are convinced that a majority of their consituents support the bill. The legislator runs a poll of 1,000 constituents, and will be convinced that a majority of their constituents support the bill if the lower bound of the 95% confidence interval for the probability that a constituent supports the bill is greater than 0.50. 550 out of the 1,000 constituents polled indicate support for the bill. Will the legislator put in the effort to draft the bill? (Possible answers are yes or no).
In: Math
1. An employment information service claims the mean annual pay for full-time workers without a high school diploma is less than $19,100. The annual pay for a random sample of 8 full-time non-high school graduates is listed below. Salaries for people without high school diplomas are normally distributed. Based on this information, you decide to
18,165 16,012 18,803 19,864
17,328 21,445 19,237 18,316
2. A company that makes cola drinks states that the mean caffeine content per one 12-ounce bottle of cola is 35 milligrams. You believe that the mean caffeine content is not 35 milligrams. You decide to test this claim. During your tests, you find that a random sample of thirty 12-ounce bottles of cola has a mean caffeine content of 38.2 milligrams with a standard deviation of 7.5 milligrams. Based on this information, you decide to
In: Math
Studies have shown that the frequency with which shoppers browse Internet retailers is related to the frequency with which they actually purchase products and/or services online. The following data show respondents age and answer to the question “How many minutes do you browse online retailers per week?”
| Age (X) | Time (Y) |
| 34 | 123,556.00 |
| 17 | 92,425.00 |
| 42 | 250,908.00 |
| 35 | 204,540.00 |
| 19 | 77,897.00 |
| 43 | 197,012.00 |
| 51 | 195,126.00 |
| 50 | 177,100.00 |
| 22 | 83,230.00 |
| 58 | 140,012.00 |
| 48 | 265,296.00 |
| 35 | 189,420.00 |
| 39 | 235,872.00 |
| 39 | 230,724.00 |
| 59 | 238,655.00 |
| 40 | 138,560.00 |
| 60 | 259,680.00 |
| 22 | 93,208.00 |
| 33 | 91,212.00 |
| 36 | 153,216.00 |
| 28 | 77,308.00 |
| 22 | 56,496.00 |
| 28 | 106,652.00 |
| 44 | 242,748.00 |
| 54 | 195,858.00 |
| 30 | 178,560.00 |
| 28 | 190,876.00 |
| 16 | 98,528.00 |
| 52 | 169,572.00 |
| 22 | 79,420.00 |
| 28 | 167,928.00 |
| 35 | 215,705.00 |
| 50 | 146,350.00 |
1. Use Data > Data Analysis > Correlation to compute the correlation check the Labels checkbox. Show work in excel.
2. Use the excel function =CORREL to compute the correlation. If answer for #1 and 2 do not agree, there is an error. Show work in excel.
In: Math
A random sample of 30 stocks was selected from each of the three major U.S. exchanges and their performance over the previous year was noted. The median performance for all 90 stocks was noted and the following table constructed, Exchange Median New York 18 American 17 NASDAQ 10 Was there a significant difference in the performance of stocks on the three exchanges during the previous year?
In: Math
In a recent year the average movie ticket cost $10.50, In a random sample of 50 movie tickets from various areas
What is the probability that the mean cost exceeds $8.50, given that the population standard deviation is $1.50?
In: Math