1. Assume that a sample is used to estimate a population
proportion p. Find the 90% confidence interval for a
sample of size 112 with 28% successes. Enter your answer as a
tri-linear inequality using decimals (not percents) accurate to
three decimal places.
2. You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 88%. You would like to be 98% confident that your estimate is within 3% of the true population proportion. How large of a sample size is required? n= ________
3. You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ=43.7σ=43.7. You would like to be 90% confident that your estimate is within 3 of the true population mean. How large of a sample size is required? n= _____
In: Math
An investor holding a certain portfolio consisting of two stocks invests 20% in Stock A and 80% in Stock B. The expected return from Stock A is 4% and that from Stock B is 12%. The standard deviations are 8% and 10% for Stocks A and B respectively. Compute the expected return of the portfolio. b) Compute the standard deviation of the portfolio assuming the correlation between the two stocks is 0.75. c) Compute the standard deviation of the portfolio assuming the correlation between the two stocks is 1. d) Compare your answers in (b) and (c). What do you observe and why?
In: Math
From public records, individuals were identified as having been charged with drunken driving not less than 6 months or more than 12 months from the starting date of the study. Two random samples from this group were studied. In the first sample of 29 individuals, the respondents were asked in a face-to-face interview if they had been charged with drunken driving in the last 12 months. Of these 29 people interviewed face to face, 11 answered the question accurately. The second random sample consisted of 43 people who had been charged with drunken driving. During a telephone interview, 28 of these responded accurately to the question asking if they had been charged with drunken driving during the past 12 months. Assume the samples are representative of all people recently charged with drunken driving. Please show all steps in getting the answer.
(a) Categorize the problem below according to parameter being estimated, proportion p, mean μ, difference of means μ1 – μ2, or difference of proportions p1 – p2. Then solve the problem.
μ
μ1 – μ2
p
p1 – p2
(b) Let p1 represent the population proportion of all people with recent charges of drunken driving who respond accurately to a face-to-face interview asking if they have been charged with drunken driving during the past 12 months. Let p2 represent the population proportion of all people who respond accurately to the question when it is asked in a telephone interview. Find a 95% confidence interval for p1 – p2. (Use 3 decimal places.)
lower limit
upper limit
(c) Does the interval found in part (a) contain numbers that are all positive? all negative? mixed? Comment on the meaning of the confidence interval in the context of this problem. At the 95% level, do you detect any differences in the proportion of accurate responses to the question from face-to- face interviews as compared with the proportion of accurate responses from telephone interviews?
Because the interval contains only positive numbers, we can say that there is a higher proportion of accurate responses in face-to-face interviews.
Because the interval contains both positive and negative numbers, we can not say that there is a higher proportion of accurate responses in face-to-face interviews.
We can not make any conclusions using this confidence interval.
Because the interval contains only negative numbers, we can say that there is a higher proportion of accurate responses in telephone interviews.
In: Math
(1) A researcher wants to test H0: x1 = x2 versus the two-sided alternative Ha: x1 ≠ x2.
(a) This alternative hypothesis indicates a one-sided hypothesis instead of a two-sided hypothesis.
(b) The alternative hypothesis Ha should indicate that x1 ≥ x2 .
(c)The null hypothesis (but not the alternative hypothesis) should involve μ1 and μ2 (population means) rather than x1 and x2 (sample means).
(d) Hypotheses should involve μ1 and μ2 (population means) rather than x1 and x2 (sample means).
(e) The null hypothesis H0 should indicate that the two means are not equal.
(2) A study recorded the IQ scores of 50 college freshmen. The scores of the 24 males in the study were compared with the scores of all 50 freshmen using the two-sample methods of this section.
(a)The samples are too large to be used for hypothesis testing.
(b)The samples are not independent; we would need to compare the 24 males to the 26 females.
(c) The samples are too small to be used for hypothesis testing.
(d)The sample sizes are too different to be used for hypothesis testing; we would need to have more males in the sample.
(e)A two-sample method is not appropriate in this situation.
(3)A two-sample t statistic gave a P-value of 0.93. From this we can reject the null hypothesis with 90% confidence.
(a)We can reject the null hypothesis, but with less than 90% confidence.
(b) We need the P-value to be small to reject H0.
(c) We can reject the null hypothesis, but with more than 90% confidence.
(d) We need the P-value to be negative to reject H0.
(e)A P-value of this size is impossible.
(4)A researcher is interested in testing the one-sided alternative Ha: μ1 < μ2. The significance test gave t = 2.25. Since the P-value for the two-sided alternative is 0.04, he concluded that his P-value was 0.02.
(a) The alternative hypothesis should state that Ha: μ1 ≠ μ2.
(b) A one-sided alternative should never be used.
(c) The alternative hypothesis should state that Ha: μ1 ≤ μ2.
(d) Assuming the researcher computed the t statistic using x1 − x2,a positive value of t does not support Ha.
(e)A t statistic of this size should have a much larger P-value associated with it.
In: Math
Solve this word problem using step by step procedure: The math department at a local university has customarily advised students to purchase Calculator A. The manufacturer has recently released a new model, Calculator B, which is reputed to be more user-friendly. The faculty decided to determine if there is a difference in the time required to perform a certain common statistical calculation. Twelve students chosen at random are given drills with both calculators so that they are familiar with the operation of each type. Then the time they take to complete the test calculation on each device is measured in seconds (which calculator they are to use first is determined by some random procedure to control for any additional learning during the first calculations). To be clear, each student worked through a particular type of statistics problem with one calculator and then did a similar problem on the other calculator. For each student, the amount of time in seconds that they spent on the problem with each calculator was recorded. Is Calculator B likely to be a more effective device than Calculator A?
| Student | CalculatorA | Calculator B |
| 1 | 23 | 19 |
| 2 | 18 | 18 |
| 3 | 29 | 24 |
| 4 | 22 | 23 |
| 5 | 33 | 31 |
| 6 | 20 | 22 |
| 7 | 17 | 16 |
| 8 | 25 | 23 |
| 9 | 27 | 24 |
| 10 | 30 | 26 |
| 11 | 25 | 24 |
| 12 | 27 | 28 |
b) Please use step by step guidelines so I can follow in this excel problem: In the sheet entitled “Part 2 Question 7”, you will find the death rate (per 1,000 resident population) for random samples of counties in Alaska and Texas. Is the average death rate among Alaska counties likely to be lower than that among Texas counties?
| Alaska | Texas |
| 1.4 | 7.2 |
| 4.2 | 5.8 |
| 7.3 | 10.5 |
| 4.8 | 6.6 |
| 3.2 | 6.9 |
| 3.4 | 9.5 |
| 5.1 | 8.6 |
| 5.4 | 5.9 |
| 6.7 | 9.1 |
| 3.3 | 5.4 |
| 1.9 | 8.8 |
| 8.3 | 6.1 |
| 3.1 | 9.5 |
| 6 | 9.6 |
| 4.5 | 7.8 |
| 2.5 | 10.2 |
| 5.6 | |
| 8.6 |
In: Math
The head start program provides a wide range of services to
low-income children up to the age of 5 years and their families.
Its goals are to provide services to improve social and learning
skills and to improve health and nutrition status so that the
participants can begin school on an equal footing with their more
advantaged peers. The distribution of ages for participating
children is as follows 12% five-year-olds, 47% four-year-olds, 33%
three-year-olds, and 8% under three years. When the program was
assessed in a particular region, it was found that of the 215
randomly selected participants, 17 were 5 years old, 101 were 4
years old, 60 were 3 years old, 37 were under 3 years old. Perform
a test to see if there sufficient evidence at αα = 0.10 that the
region's proportions differ from the national proportions.
The correct hypotheses are:
The test value is (round to 3 decimal places)
The p-value is (round to 3 decimal places)
According to the Bureau of Transportation Statistics, on-time performance by airlines is described as follows:
| Action | % of time |
| On Time | 71 |
| National Aviation System Delay | 8 |
| Aircraft arriving late | 8 |
| Other (weather and other conditions) | 13 |
When a study was conducted it was found that of the 250 randomly
selected flights, 180 were on time, 18 were a National Aviation
System Delay, 20 arriving late , 32 were due to weather. Perform a
test to see if there is sufficient evidence at αα = 0.05 to see if
these differ from the governments statistics.
The correct hypotheses are:
The test value is (round to 3 decimal places)
The p-value is (round to 3 decimal places)
The head start program provides a wide range of services to
low-income children up to the age of 5 years and their families.
Its goals are to provide services to improve social and learning
skills and to improve health and nutrition status so that the
participants can begin school on an equal footing with their more
advantaged peers. The distribution of ages for participating
children is as follows 10% five-year-olds, 50% four-year-olds, 28%
three-year-olds, and 12% under three years. When the program was
assessed in a particular region, it was found that of the 202
randomly selected participants, 20 were 5 years old, 99 were 4
years old, 46 were 3 years old, 37 were under 3 years old. Perform
a test to see if there sufficient evidence at αα = 0.01 that the
region's proportions differ from the national proportions.
The correct hypotheses are:
The test value is (round to 3 decimal places)
The p-value is (round to 3 decimal places)
According to the Bureau of Transportation Statistics, on-time performance by airlines is described as follows:
| Action | % of time |
| On Time | 68 |
| National Aviation System Delay | 7 |
| Aircraft arriving late | 8 |
| Other (weather and other conditions) | 17 |
When a study was conducted it was found that of the 230 randomly
selected flights, 159 were on time, 21 were a National Aviation
System Delay, 21 arriving late , 29 were due to weather. Perform a
test to see if there is sufficient evidence at αα = 0.01 to see if
these differ from the governments statistics.
The correct hypotheses are:
The test value is (round to 3 decimal places)
The p-value is (round to 3 decimal places)
In: Math
A graduate picks 25 exams at random from a total of 194 exams. Those 25 exams have a mean of 78.2% ± 17.1% (mean ± 1 standard deviation). You may assume that these 25 exam scores are approximately normally distributed.
a) Estimate the population mean exam score and its confidence interval for the 95% confidence level.
b) Estimate the population exam score standard deviation and its confidence interval for the 95% confidence level.
c) Estimate how many students failed the exam if the passing grade is 60%.
d) Estimate how many students scored above 90% on the exam.
e) The graduate draws another set of exams of 25 exams, and these exam scores are not normally distributed: they are skewed towards a high score. What would you tell the graduate so that s/he can estimate the population mean using methods we learned in class?
In: Math
For the given reports, are the given values of the correlation coefficient reasonable?
1. A) A correlation of r = +0.7 between gender and height.
i) Reasonable ii) Unreasonable
1. B) A correlation of r = +1.0 between outdoor temperature and sales of ice cream.
i) Reasonable ii) Unreasonable
1. C) A correlation of r = 0 between shoe size and IQ scores in a study of adults.
i) Reasonable ii) Unreasonable
1. D) A correlation of r = +0.7 between distance from the equator for North American cities and average January temperature.
i) Reasonable ii) Unreasonable
1. E) A correlation of r = -0.8 between outside temperature and sales of hot chocolate.
i) Reasonable ii) Unreasonable
In: Math
In: Math
|
A type of new car is offered for sale with 4 option packages. A
customer can buy any number of these, from none to all 4. A
manager proposes the null hypothesis that customers pick packages
at random, implying the number of packages bought by a customer
should be binomial with n equals=4.
(a) Find the binomial parameter p needed to calculate the expected counts. (b) Find the estimated probability that a customer picks one option. (c) Find the degrees of freedom for chiχsquared2. (d) Find the value of chiχsquared2 for testing Upper H0 (e) Find the p-value for testing Upper H0
|
In: Math
In a preschool class of n, exactly n1 children are needed for activity 1, n2 for activity 2, and n3 for activity 3. Luckily n = n1 + n2 + n3. The teachers want to know in how many distinct ways the children can be assigned into these activities. (Two assignments are distinct if at least one student is in a different activity in each.) (a) They figure they could start by lining up the children arbitrarily. How many different line-ups are possible? (b) They then take the first n1 for activity 1, the next n2 for activity 2, and the rest for activity 3. How many different line-ups will create the exact same assignment of children to activities? (c) Use your answers from (a) and (b) to deduce the total number of distinct assignments.
In: Math
Problem 16-13 (Algorithmic)
The wedding date for a couple is quickly approaching, and the wedding planner must provide the caterer an estimate of how many people will attend the reception so that the appropriate quantity of food is prepared for the buffet. The following table contains information on the number of RSVP guests for the 145 invitations. Unfortunately, the number of guests does not always correspond to the number of RSVPed guests.
Based on her experience, the wedding planner knows it is extremely rare for guests to attend a wedding if they notified that they will not be attending. Therefore, the wedding planner will assume that no one from these 50 invitations will attend. The wedding planner estimates that the each of the 25 guests planning to come solo has a 75% chance of attending alone, a 20% chance of not attending, and a 5% chance of bringing a companion. For each of the 60 RSVPs who plan to bring a companion, there is a 90% chance that she or he will attend with a companion, a 5% chance of attending solo, and a 5% chance of not attending at all. For the 10 people who have not responded, the wedding planner assumes that there is an 80% chance that each will not attend, a 15% chance each will attend alone, and a 5% chance each will attend with a companion.
| RSVped Guests | Number of invitations |
| 0 | 50 |
| 1 | 25 |
| 2 | 60 |
| No response | 10 |
In: Math
What is the best measure of center (mean, median, or mode) for each topic? And why?
Country
Infant mortality
Health expenditure
Obesity rate
Average income
Life expectancy
Diabetes rate
Leading cause of death
In: Math
Problem 16-01
The management of Brinkley Corporation is interested in using simulation to estimate the profit per unit for a new product. The selling price for the product will be $45 per unit. Probability distributions for the purchase cost, the labor cost, and the transportation cost are estimated as follows:
| Procurement Cost ($) |
Probability |
Labor Cost ($) |
Probability |
Transportation Cost ($) |
Probability |
| 10 | 0.25 | 20 | 0.10 | 3 | 0.75 |
| 11 | 0.45 | 22 | 0.25 | 5 | 0.25 |
| 12 | 0.30 | 24 | 0.35 | ||
| 25 | 0.30 |
In: Math
The sample mean is 19.0, the sample standard deviation is 6.6,
and n = 41. Establish a 90% confidence interval for the population
mean. (by default two tailed test, α is reliability
factor)
In: Math