A simple random sample of 100 postal employees is used to test if the average time postal employees have worked for the postal service has changed from the value of 7.5 years, as recorded 20 years ago. The sample of the current employees gave a mean service time of 7.9 years with a standard deviation of s = 2 years. Assume the distribution of the time the employees work in service jobs is approximately normal.
What are you to test?
Is the standard deviation equal to 2.
Is the mean equal to 2.
Is the variance equal to 20.
How long has 100 employees worked for the post-office.
Has the average employment changed from 7.5.
In: Statistics and Probability
Thank you!
For this question, you will flip fair coin to take some samples and analyze them. First, take any fair coinand flip it 12 times. Count the number of heads out of the 12 flips. This is your first sample. Do this 4 more timesand count the number of heads out of the 12 flips in each sample. Thus, you should have 5 samples of 12 flipseach. The important number is the number of heads in each sample (this can be any whole number between 0 and12). Then answer the following questions:
(A) If you had a very large number of samples, what value(s) should the mean and median have? Why?
(B) In general, what proportion of samples of fair coin flips (when N is sufficiently large that a rejection region of the binomial distribution exists) should result in rejecting the null hypothesis (a = .05, two-tailed)?
In: Statistics and Probability
Determine whether the distributions below are probability distributions. If not, what characteristic of the distribution is the reason? Bulleye Hit Darts X P(X = x) 0 0.64 1 0.26 2 0.18 3 0.04 4 -0.12
Bullseye's Hit in Darts X P(X = x) 0 0.69 1 0.16 2 0.12 3 0.08 4 0.03
Bullseye's Hit in Darts X P(X = x) 0 0.57 1 0.26 2 0.11 3 0.04 4 0.02
Bullseye's Hit in Darts X P(X = x) 0 0.53 1 0.24 2 0.11 3 0.04 4 0.02
In: Statistics and Probability
| Before Course | After Course |
| 144 | 139 |
| 144 | 145 |
| 145 | 146 |
| 141 | 149 |
| 145 | 139 |
| 141 | 147 |
| 142 | 143 |
| 143 | 166 |
| 142 | 151 |
| 145 | 144 |
| 140 | 140 |
| 145 | 144 |
| 140 | 136 |
| 141 | 140 |
| 140 | 137 |
| 142 | 149 |
| 140 | 147 |
| 140 | 167 |
| 145 | 146 |
| 144 | 145 |
| 145 | 145 |
| 144 | 137 |
| 144 | 150 |
| 140 | 144 |
| You need to create two histograms: one for the pre-LSAT scores and another for the post-LSAT scores. | ||||||||
| Please provide your interpretation of the results. For example, you might want to compare | ||||||||
| the two histograms and point out the similarties and differences. You may want to share some | ||||||||
| relevant descriptive statistics about the two groups of data. | ||||||||
In: Statistics and Probability
A sample survey of 36 randomly selected households shows that the median household income of the eastern NC residents is $51,000, with a standard deviation of $1075. Test the (null) hypothesis that the actual (real) median household income is $52,752 at 0.05% confidence level.
In: Statistics and Probability
| BOXPLOTS AND WHISKERS | ||||||||
| Scenario: | ||||||||
| You work for the Medical Center's retail division. This division is responsible for managing the | ||||||||
| sales and rentals of products from the gift shops, cafes, cafetrias, and medical equipment | ||||||||
| rentals. You've been asked by the Director to undertake initiatives to boost sales at the gift | ||||||||
| shops. You've worked with the Marketing Department to produce a couple of posters to | ||||||||
| strategically place throughout the system. You're expected to create a boxplot & whiskers | ||||||||
| diagram for each scenario (sales without posters & sales with posters). | ||||||||
| Gift Shops | Sales w/o Posters | Sales w/Posters | ||||||
| 218 | 215 | 240 | ||||||
| 224 | 180 | 220 | ||||||
| 236 | 150 | 190 | ||||||
| 252 | 180 | 175 | ||||||
| 270 | 201 | 220 | ||||||
| 282 | 207 | 215 | ||||||
| 292 | 195 | 219 | ||||||
| 304 | 180 | 295 | ||||||
| Please provide your interpretation of the results. For example, you might want to compare the two | ||||||||
| diagrams and point out the similarties and differences. You may want to share some relevant descriptive | ||||||||
| statistics about the two groups of data. | ||||||||
In: Statistics and Probability
In a study of binge drinking among undergraduates at Ohio
University, a researcher was interested in gender differences as
related to binge drinking and to drinking-related arrests. She
wanted to know two things: (a) Is there a significant relationship
between gender and binge drinking (as defined by 5 or more drinks
at one sitting), and (b) Is there a significant relationship
between gender and drinking-related arrests? A random sample of
males and females were asked about their experiences with binge
drinking and with drinking-related arrests. Test for a relationship
in the following data:
Binge
Drinking?
YES NO
Male 36 21
Female 26 45
What is the calculated chi-squared value
In: Statistics and Probability
Five students were tested before and after taking a class to
improve their study habits. They were given articles to read which
contained a known number of facts in each story. After reading the
stories, the students listed as many facts as they could recall.
The following data were recorded. This a multiple choice
question!
Before After
10
15
12
14
14
17
16
17
12
20
The degrees of freedom for this sample are
[ Select ]
["8", "5", "6", "4", "2.132", "2.776",
"2.306", "1.860", "-3.106", "3.106", "-3.062", "3.602", "reject",
"fail to reject", "may affect study habits", "does not affect study
habits"]
The two tailed critical value at an alpha level of .05
is
[
Select ]
["8", "5", "6", "4",
"2.132", "2.776", "2.306", "1.860", "-3.106", "3.106", "-3.062",
"3.602", "reject", "fail to reject", "may affect study habits",
"does not affect study habits"]
The obtained value of the statistic calculated for this sample
is
[
Select ]
["8", "5", "6", "4",
"2.132", "2.776", "2.306", "1.860", "-3.106", "3.106", "-3.062",
"3.602", "reject", "fail to reject", "may affect study habits",
"does not affect study habits"]
My decision is to
[ Select ]
["8",
"5", "6", "4", "2.132", "2.776", "2.306", "1.860", "-3.106",
"3.106", "-3.062", "3.602", "reject", "fail to reject", "may affect
study habits", "does not affect study habits"]
the null hypothesis
Based on this data I conclude that the
course
[ Select ]
["8",
"5", "6", "4", "2.132", "2.776", "2.306", "1.860", "-3.106",
"3.106", "-3.062", "3.602", "reject", "fail to reject", "may affect
study habits", "does not affect study habits"]
In: Statistics and Probability
| BOXPLOT & WHISKERS | |||||||||||||
| Student ID | Score pre training | Score post training | Scenario: | ||||||||||
| 102 | 50 | 75 | You work for the Medical Center's Corporate Education Department. You developed a new | ||||||||||
| 442 | 60 | 75 | leadership program as part of the Center's succession plan. You had your first cohort of | ||||||||||
| 325 | 65 | 85 | managers successfully complete the training program. Each participant completed pre- | ||||||||||
| 154 | 75 | 90 | assessment before starting the classroom instruction and a post-assessment following the | ||||||||||
| 114 | 80 | 95 | completion of the program. You are expected to prepare a BOXPLOT & WHISKER diagram for | ||||||||||
| 178 | 40 | 75 | each group of data (score before training & score post training). | ||||||||||
| 165 | 60 | 80 | |||||||||||
| 520 | 90 | 90 | Please provide your interpretation of the results. For example, you might want to compare | ||||||||||
| 220 | 80 | 85 | the two diagrams and point out the similarties and differences. You may want to share some | ||||||||||
| 335 | 60 | 85 | relevant descriptive statistics about the two groups of data. | ||||||||||
In: Statistics and Probability
In preparing for the upcoming holiday season, Fresh Toy Company (FTC) designed a new doll called The Dougie that teaches children how to dance. The fixed cost to produce the doll is $100,000. The variable cost, which includes material, labor, and shipping costs, is $34 per doll. During the holiday selling season, FTC will sell the dolls for $42 each. If FTC overproduces the dolls, the excess dolls will be sold in January through a distributor who has agreed to pay FTC $10 per doll. Demand for new toys during the holiday selling season is uncertain. The normal probability distribution with an average of 60,000 dolls and a standard deviation of 15,000 is assumed to be a good description of the demand. FTC has tentatively decided to produce 60,000 units (the same as average demand), but it wants to conduct an analysis regarding this production quantity before finalizing the decision.
| (a) | Create a what-if spreadsheet model using formulas that relate the values of production quantity, demand, sales, revenue from sales, amount of surplus, revenue from sales of surplus, total cost, and net profit. What is the profit when demand is equal to its average (60,000 units)? | ||||||||||||||||||||||||||||||
| $ | |||||||||||||||||||||||||||||||
| (b) | Modeling demand as a normal random variable with a mean of 60,000 and a standard deviation of 15,000, simulate the sales of The Dougie doll using a production quantity of 60,000 units. What is the estimate of the average profit associated with the production quantity of 60,000 dolls? Round your answer in whole dollar. | ||||||||||||||||||||||||||||||
| $ | |||||||||||||||||||||||||||||||
| How does this compare to the profit corresponding to the average demand (as computed in part a)? | |||||||||||||||||||||||||||||||
| The input in the box below will not be graded, but may be reviewed and considered by your instructor. | |||||||||||||||||||||||||||||||
| (c) | Before making a final decision on the production quantity, management wants an analysis of a more aggressive 70,000-unit production quantity and a more conservative 50,000-unit production quantity. Run your simulation with these two production quantities. What is the average profit associated with each? Round your answer in whole dollar. | ||||||||||||||||||||||||||||||
| When ordering 50,000 units, the
average profit is approximately $ When ordering 70,000 units, the average profit is approximately $ |
|||||||||||||||||||||||||||||||
| (d) | Besides average profit, what other factors should FTC consider in determining a production quantity? Compare the four production quantities (40,000; 50,000; 60,000; and 70,000) using all these factors. What trade-offs occur? | ||||||||||||||||||||||||||||||
| If required, round Probability of a Loss to three decimal places and Probability of a Shortage to two decimal places. Round your answer in whole dollar. | |||||||||||||||||||||||||||||||
|
|||||||||||||||||||||||||||||||
| What is your recommendation? | |||||||||||||||||||||||||||||||
| The input in the box below will not be graded, but may be reviewed and considered by your instructor. |
In: Statistics and Probability
*Please answer the following question using R code*
3. A bank wants to get new customers for their credit card. They try two different approaches in their marketing campaign. The first promises a "cash back" reward, and the second promises low interest rates. A sample of 500 people is mailed the first brochure; of these, 125 get the credit card. A separate sample of 500 people is mailed the second brochure; 150 get the credit card. Are the two campaigns equally attractive to customers? Compute a 95% confidence interval for the difference in the two proportions. Answer the question of interest by interpreting your result.
In: Statistics and Probability
Question 1) A certain genetic trait affects, independently, 30%
of progeny.
Part A. If 5 progeny are selected at random what is the probability
that exactly 3 have the genetic trait?
Part B. If 50 progeny are selected at random...
Part Bi. ...What is the approximate probability that exactly 15
have the genetic trait?
Part Bii. Use R to determine the actual answer to Part Bi.
Part C. If 50 progeny are selected at random...
Part Ci. ...What is the approximate probability that less than 15
have the genetic trait?
Part Cii. Use R to determine the actual answer to Part Ci.
Part Ciii. Time to make a mistake on purpose. In part Ci you had to
make a continuity correction. Try answering the same question but
without that continuity correction. How does your answer compare to
the actual answer?
In: Statistics and Probability
60. A recent debate about where in the United States skiers believe the skiing is best prompted the following survey. Test to see if the best ski area is independent of the level of the skier. U.S. Ski Area Beginner Intermediate Advanced Tahoe 20 30 40 Utah 10 30 60 Colorado 10 40 50 .
In: Statistics and Probability
On September 11, 2002, a particular state lottery's daily number came up 9 - 1 - 1. Assume that no more than one digit is used to represent the first nine months.
a) What is the probability that the winning three numbers match the date on any given day?
b) What is the probability that a whole year passes without this happening?
c) What is the probability that the date and winning lottery number match at least once during any year?
d) If 27 states have a three-digit lottery, what is the probability that at least one of them will come up 3 - 1 - 0 on March 10?
In: Statistics and Probability
For a certain candy, 15% of the pieces are yellow, 10% are red, 15% are blue, 20% are green, and the rest are brown. a) If you pick a piece at random, what is the probability that it
is brown?
it is yellow or blue?
it is not green?
it is striped?
b) Assume you have an infinite supply of these candy pieces from which to draw. If you pick three pieces in a row, what is the probability that they
are all brown?
the third one is the first one that is red?
none are yellow?
at least one is green?
In: Statistics and Probability