In a sample of 169 trees, we found that a pear tree grow to average height of 32 feet and a sample standard deviation of 5 feet. The distribution is approximately normal. Find the 95% confidence interval for the mean population.
In: Math
For a sample of eight bears, researchers measured the distances around the bears' chests and weighed the bears. Minitab was used to find that the value of the linear correlation coefficient is r=0.931 Using alphaα=0.05, determine if there is a linear correlation between chest size and weight. What proportion of the variation in weight can be explained by the linear relationship between weight and chest size?
a. Is there a linear correlation between chest size and weight?
A.Yes, because the absolute value of r exceeds the critical value of 0.707
B.No, because the absolute value of r exceeds the critical value of 0.707.
C.Yes, because r falls between the critical values of −0.707 and 0.707.
D. The answer cannot be determined from the given information.
b. What proportion of the variation in weight can be explained by the linear relationship between weight and chest size?
In: Math
A company wants to build a plant but is considering the size. The table below shows their payoffs under different states of demand.
| Demand | ||
| Low (p=0.45) | High (p=0.55) | |
| Small Plant | 500000 | 500000 |
| Medium Plant | 200000 | 800000 |
| Large Plant | -200000 | 1000000 |
They can hire a consultant who can conduct a survey to evaluate demand. The consultant will report to the company whether demand is strong or weak. The probabilities are 0.60 and 0.40 for strong and weak survey results respectively. The conditional probabilities for demand given survey results are as follow:
P(Low/Strong) = 0.35; P(High/Strong) = 0.65;
P(Low/Weak) = 0.70; P(High/Weak) = 0.30;
a) Draw the decision tree for this problem including with and without a survey.
b) What is the best decision without a survey?
c) What is the decision strategy when survey is conducted?
d) What is the EVPI?
e) What is the EVII
In: Math
A random variable X has density function f(x) = 4x ( 1 + x2)-3 for x > 0.
Determine the mode of X.
In: Math
A survey of 1060people who took trips revealed that 94 of them included a visit to a theme park. Based on those survey results, a management consultant claims that less than 11 % of trips include a theme park visit. Test this claim using the ?=0.01significance level.
(a) The test statistic is ___
(b) The P-value is ___
(c) The conclusion is
A. There is sufficient evidence to support the
claim that less than 11 % of trips include a theme park
visit.
B. There is not sufficient evidence to support the
claim that less than 11 % of trips include a theme park visit.
Independent random samples, each containing 90 observations,
were selected from two populations. The samples from populations 1
and 2 produced 36 and 26 successes, respectively.
Test ?0:(?1−?2)=0against ??:(?1−?2)>0 Use ?=0.1
(a) The test statistic is ___
(b) The P-value is ___
(c) The final conclusion is
A. There is not sufficient evidence to reject the
null hypothesis that (?1−?2)=0
B. We can reject the null hypothesis that
(?1−?2)=0 and conclude that (?1−?2)>0
In: Math
A random sample of 1500 residential telephones in Phoenix found
that 385 of the numbers were unlisted. A random sample in the same
year of 1200 telephones in Scottsdale found that 311 were
unlisted.
Round your answers to four decimal places (e.g. 98.7654).
(a) Calculate a 95% two-sided confidence interval on the difference
in the proportions of unlisted numbers between the two
cities.
Enter your answer; 95% confidence interval, lower bound ≤p1-p2≤
Enter your answer; 95% confidence interval, upper bound
(b) Is there a significant difference between the two proportions
at α = 0.05? Choose your answer in accordance to the item
b) of the question statement
No.Yes.
(c) Calculate a 90% two-sided confidence interval on the difference
in the proportions of unlisted numbers between the two
cities.
Enter your answer; 90% confidence interval, lower bound ≤p1-p2≤
Enter your answer; 90% confidence interval, upper bound
In: Math
A local bank needs information concerning the account balance of its customers. A random sample of 15 accounts was checked. The mean balance was $686.75 with a standard deviation of $256.20.
A. Construct a 98% confidence interval for the population mean, assuming account balances are normally distributed.
B. Based on your previous answer, would a population mean of $500 be unusual? What about a mean of $800?
In: Math
The personnel office at a large electronics firm regularly schedules job interviews and maintains records of the interviews. From the past records, they have found that the length of a first interview is normally distributed, with mean μ = 37 minutes and standard deviation σ = 6 minutes. (Round your answers to four decimal places.)
(a) What is the probability that a first interview will last 40
minutes or longer?
(b) Two first interviews are usually scheduled per day. What is the
probability that the average length of time for the two interviews
will be 40 minutes or longer?
In: Math
Access the hourly wage data on the below Excel Data File (Hourly Wage). An economist wants to test if the average hourly wage is less than $28. Assume that the population standard deviation is $8.
b-1. Find the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
| Hourly Wage | Education | Experience | Age | Gender |
|---|---|---|---|---|
| 39.00 | 11 | 2 | 40 | 1 |
| 21.02 | 4 | 1 | 39 | 0 |
| 42.36 | 4 | 2 | 38 | 0 |
| 20.17 | 5 | 9 | 53 | 1 |
| 22.57 | 6 | 15 | 59 | 1 |
| 43.43 | 6 | 12 | 36 | 1 |
| 17.87 | 9 | 5 | 45 | 0 |
| 24.62 | 4 | 12 | 37 | 0 |
| 28.36 | 5 | 14 | 37 | 1 |
| 10.25 | 11 | 3 | 43 | 1 |
| 27.14 | 8 | 5 | 32 | 0 |
| 10.35 | 9 | 18 | 40 | 1 |
| 27.09 | 7 | 1 | 49 | 1 |
| 21.34 | 4 | 10 | 43 | 0 |
| 19.71 | 1 | 9 | 31 | 0 |
| 32.41 | 9 | 22 | 45 | 0 |
| 22.80 | 11 | 3 | 31 | 1 |
| 26.07 | 4 | 14 | 55 | 0 |
| 42.14 | 6 | 5 | 30 | 1 |
| 21.42 | 9 | 3 | 28 | 0 |
| 21.52 | 6 | 15 | 60 | 1 |
| 34.00 | 4 | 13 | 32 | 0 |
| 38.85 | 4 | 9 | 58 | 1 |
| 29.06 | 5 | 4 | 28 | 0 |
| 12.60 | 6 | 5 | 40 | 1 |
| 27.64 | 6 | 2 | 37 | 0 |
| 32.28 | 4 | 18 | 52 | 1 |
| 33.46 | 6 | 4 | 44 | 0 |
| 18.05 | 6 | 4 | 57 | 0 |
| 28.56 | 9 | 3 | 30 | 1 |
| 13.41 | 5 | 8 | 43 | 0 |
| 43.54 | 7 | 6 | 31 | 1 |
| 33.23 | 4 | 3 | 33 | 0 |
| 27.34 | 6 | 23 | 51 | 1 |
| 18.41 | 4 | 15 | 37 | 0 |
| 31.82 | 4 | 9 | 45 | 0 |
| 31.30 | 6 | 3 | 55 | 0 |
In: Math
Researchers at a food company are interested in how a new ketchup made from green tomatoes (and green in color) will compare to their traditional red ketchup. They are worried that the green color will adversely affect the tastiness scores. They randomly assign subjects to either the green or red ketchup condition. Subjects indicate the tastiness of the sauce on a 20-point scale. Tastiness scores tend to be skewed. The scores follow:
Green Ketchup
14
15
16
18
16
16
19
Red Ketchup
16
16
19
20
17
17
18
a. What statistical test should be used to analyze these data?
b. Identify H0 and Ha for this study.
c. Conduct the appropriate analysis.
d. Should H0 be rejected? What should the researcher
conclude?
In: Math
Problem 2.22 (modified from Montgomery, 9th edition) The mean shelf life of a carbonated drink should exceed 120 days. Ten bottles are randomly selected and tested, and the results below are obtained: shelf life (days) = {108, 124, 124, 106, 115, 138, 163, 159, 134, 139} a) Clearly state the hypothesis to be tested, first in English and then in mathematical expressions for H0 and H1. b) Test the hypothesis at significance level 0.01. Report both the p-value and a 99% confidence interval to support your conclusion. Be sure to clearly state your conclusion in plain English and within the context of the problem.
In: Math
A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean μ = 88 and standard deviation σ = 28. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.)
(a) x is more than 60
(b) x is less than 110
(c) x is between 60 and 110
(d) x is greater than 125 (borderline diabetes starts at
125)
In: Math
The population proportion is .65 . What is the probability that a sample proportion will be within + or - .02 of the population proportion for each of the following sample sizes? Round your answers to 4 decimal places. Use z-table. a. n=100 b. n=200 c. n=500 d. n=1000 e. What is the advantage of a larger sample size? With a larger sample, there is a probability will be within + or - .02 of the population proportion .
In: Math
Consider a random sample of 200 one-way commute distances (in miles) from Radcliffe College to a student’s primary place of residence. The sample mean is 10.33 miles and the sample standard deviation is 3.77 miles. What percent of students sampled live between 0.81 and 19.85 miles from Radcliffe College? Suppose a student lived 25 miles from Radcliffe College. Would this commute distance be considered an outlier?
In: Math
Discuss the differences between Attributes Control Charts and Variables Control Charts and how you believe one can benefit a company/organization over the other, and why/why not.
(Note: Pleaee, the answer has to be typed, not hand written nor a picture.)
Thank you.
In: Math