A geneticist interested in human populations has been studying the growth patterns in American males since 1900. A monograph | ||
written in 1902 states that the mean height of adult American males is 67.0 inches with a standard deviation of 3.5 inches. Wishing | ||
to see if these values have changed over the 20th century, the geneticist measured a random sample of 28 adult American males | ||
and found that the sample mean was 69.4 inches and the sample standard deviation was 4.0 inches. | ||
Considering the 1902 data to be a
population, do the more recent data suggest that the height of
American males has significantly changed? |
||
Put your answers in column B | ||
H_{o}: | ||
H_{a}: | ||
test-statistic*: | ||
df: | ||
Exact P value for the test-statistic: | ||
Conclusion relative to the hypothesis: | ||
(Don't forget your parenthetical | ts= ,df= ,P= | |
support statement) | ||
*test-statistic refers to the statistical test value for whatever statistical test is done to answer the question. | ||
What is the Statistical Power of this test?: | % |
In: Math
A genetic experiment involving peas yielded one sample of offspring consisting of 416 green peas and 144 yellow peas. Use a 0.05 significance level to test the claim that under the same circumstances, 23% of offspring peas will be yellow. Identify the null hypothesis, alternative hypothesis, test statistic, P value, conclusion about the null hypothesis, and the final conclusion that addresses the The original claim. Use the P value method and the normal distribution as an approximation to the binomial distribution.
In: Math
1. One of the most important measures of the quality of service provided by any firm is the speed with which it responds to customer complaints. Comcast, a U.S. global telecommunications conglomerate, wants to greatly improve its customer satisfaction. Comcast states the desired mean call time involving customer complaints is 12 minutes (including wait time). Assume the standard deviation is known to be 0.15 minutes. A sample of 70 customer calls yields a mean time of 12.14 minutes. This sample will be used to obtain a 99% confidence interval for the mean time of a customer complaint call. Round final answers to two decimal places. Solutions only.
(A) The critical value to use in obtaining the confidence interval is.
(B) The confidence interval goes from to.
(C) True, False, or Uncertain: The confidence interval indicates that Comcast is not meeting its goal.
(D) True, False, or Uncertain: The confidence interval is valid only if the length of calls are normally distributed
(E) Suppose the manager had decided to estimate the mean call time to within 0.03 minutes with 99% confidence. Then the sample size would be?
In: Math
Ada Nixon, a student, has just begun a 30-question, multiple-choice exam. For each question, there is exactly one correct answer out of four possible choices. Unfortunately, Ada hasn't prepared well for this exam and has decided to randomly select an answer choice for each question.
(a) (4 points) For a given question, what is the probability Ada picks the correct answer, assuming each answer choice is equally likely to be selected?
(b) Assume the number of questions Ada answers correctly is Binomially distributed.
i. (4 points) What is the average number of questions Ada will answer correctly? Show your work and round your nal answer to 1 decimal place.
ii. (3 points) If Ada answers at least 16 questions correctly, she will receive a passing grade. What is the probability that Ada receives a passing grade? Show your work, including any calculator functions you use, and round your nal answer to 3 decimal places.
(c) (3 points) Suppose Ada comes across a question for which she knows two of the answer choices are certainly wrong, which means the correct answer must be one of the two remaining choices. Assuming Ada will answer every other question using the same random selection procedure as before, will the number of questions she answers correctly remain binomially distributed? State Yes or No and explain why
In: Math
A random sample is drawn from a normally distributed population with mean μ = 19 and standard deviation σ = 1.8. [You may find it useful to reference the z table.]
a. Are the sampling distribution of the sample mean with n = 27 and n = 54 normally distributed?
Yes, both the sample means will have a normal distribution.
No, both the sample means will not have a normal distribution.
No, only the sample mean with n = 27 will have a normal distribution.
No, only the sample mean with n = 54 will have a normal distribution.
b. Calculate the probabilities that the sample mean is less than 19.9 for both sample sizes. (Round intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)
In: Math
A fun size bag of M&Ms has 4 blue, 3 orange, 3 red, 2 green, 2 yellow, and 1 brown M&Ms. What is the probability of randomly selecting 5 M&Ms where 3 are blue and 2 are orange?
In: Math
Flair Furniture Company produces inexpensive tables and chairs. The production process for each is similar in that both require a certain number of labor hours in the carpentry department and a certain number of labor hours in the painting department. Each table takes 3 hours of carpentry work, an hour and a half of assembly and 2 hours of finishing work. Each chair requires 4 hours of carpentry, and hour and 15 minutes of assembly and 1 hour of painting. During the current month, 2,400 hours of carpentry time, 800 hours of assembly time and 1,000 hours of painting time are available. Each table sold results in a profit contribution of $7, and each chair sold yields a profit contribution of $5.
a. Set up a Solver model for determine the number of tables and chairs to produce that will maximize total profit contribution. Run Solver and generate the Answer Report and Sensitivity Report.
b. Identify the binding and nonbinding constraints and explain what it means.
c. Construct the sensitivity range for the objective function coefficients. Give an interpretation for each range.
d. Construct the sensitivity range for the right hand side coefficient of constraints. Give an interpretation for each range and the corresponding shadow price of all the constraints.
e. Suppose that 100 hours of additional labor can be added. In which department would you add these hours? Explain why. How much additional profit can be generated by this addition?
In: Math
3) A tax auditor has a pile of federal tax returns and she has been directed to randomly select 20 of these returns for a special audit. Describe how systematic sampling could be used. 4) A recent radio station asked listeners to go to their website and vote for their favorite singing star. A responder would be randomly chosen and would receive two tickets to the performance of their choice. What type of sampling is used for the vote? 5) A community college is selected at random from all US community colleges and the GPAs and ages of all students from that college are examined. a) What type of sampling was done? b) What is the population of interest for this study? c) If the average GPA is computed for this sample would it be considered a statistic or a parameter? d) Suppose instead the researchers wanted to implement a Simple Random Sample of community college students, how might they do this? 6) Explain the difference between cluster sampling and stratified sampling.
In: Math
the music on a music player can be stored digitally in several formats. a popular format for a digital music player is aiffshort for Audio Interchange File Format. Another format is known as AAC, short for Advanced Audio Coding. Files on a digital music player can be in either of these formats or both. The 25 songs in this data set use a mixture of these two formats. Complete parts (a) through (d) below. Create a dummy variable using the arc format as the baseline category to represent the format of the song in the data file and then fit the regression model for how much space is needed to store a song based on the length of a song. write down the regression model including the estimates of the intercepts
In: Math
Sheila's measured glucose level one hour after a sugary drink varies according to the Normal distribution with μμ = 130 mg/dl and σσ = 15 mg/dl. What is the level L such that there is probability only 0.15 that the mean glucose level of 4 test results falls above L?
L=
A study of the career paths of hotel general managers sent questionnaires to an SRS of 210 hotels belonging to major U.S. hotel chains. There were 88 responses. The average time these 88 general managers had spent with their current company was 12.7 years. (Take it as known that the standard deviation of time with the company for all general managers is 3.6 years.)
(a) Find the margin of error for an 85% confidence interval to estimate the mean time a general manager had spent with their current company: years
(b) Find the margin of error for a 99% confidence interval to estimate the mean time a general manager had spent with their current company: years
(c) In general, increasing the confidence level the margin of error (width) of the confidence interval. (Enter: ''DECREASES'', ''DOES NOT CHANGE'' or ''INCREASES'', without the quotes.)
In: Math
Use SPSS for this Application Exercise:
A staff psychologist at a police precinct believes that the new
week-long training courses worsens on the job sensitivity of police
officers. The psychologist designs a study where some policemen
randomly get and complete the course. A month later the
psychologist records the number of domestic disputes the police
officers successfully resolved from their police reports. What can
the psychologist conclude with α = 0.05. The success data
are below.
no course |
course |
---|---|
11.2 12.5 10.6 12.7 8.3 15.6 12.1 |
14.8 16.3 14.3 17.4 11.2 16.5 15.4 |
a) What is the appropriate test statistic?
---Select--- na z-test One-Sample t-test Independent-Samples t-test
Related-Samples t-test
b)
Condition 1:
---Select--- job sensitivity no course completing the course police
precinct domestic disputes
Condition 2:
---Select--- job sensitivity no course completing the course police
precinct domestic disputes
c) Compute the appropriate test statistic(s) to
make a decision about H_{0}.
(Hint: Make sure to write down the null and alternative hypotheses
to help solve the problem.)
p-value = ; Decision: ---Select---
Reject H0 Fail to reject H0
d) Using the SPSS results,
compute the corresponding effect size(s) and indicate
magnitude(s).
If not appropriate, input and/or select "na" below.
d = ; ---Select--- na trivial
effect small effect medium effect large effect
r^{2} = ; ---Select--- na
trivial effect small effect medium effect large effect
e) Make an interpretation based on the
results.
Participants that received training had significantly less resolved domestic disputes than those that did not receive training.
Participants that received training had significantly more resolved domestic disputes than those that did not receive training.
Participants that received training did not differ significantly on resolved domestic disputes than those that did not receive training.
In: Math
In: Math
4. What is the difference between the null and alternative hypotheses? What does alpha
represent? (4 pts)
The proportion of professional baseball players who take steroids has been assumed to be twenty percent by the team owner council. The Commissioner of Baseball has instituted a new campaign to reduce the proportion of players who take steroids. The Commissioner would now like to test whether their campaign has worked. (α = 0.05)
State the null and alternative hypotheses that the Commissioner would test. Use
symbols in the hypotheses. State alpha and define the parameter. (7 pts)
Ho: p = 0.2 (.)
Ha: p < 0.2 (.)
Time Magazine states that the nationwide drop out rate for high school seniors is ten percent. You conduct a test to see if the drop out rate for high school seniors is actually more than ten percent. ( α = 0.01)
State the null and alternative hypotheses for this test. Use symbols in the hypotheses.
State alpha and define the parameter. (7 pts)
The Maryland Department of Health claims that the proportion of heroin users in Maryland that have been infected by HIV is four percent. Suppose a researcher wants to show that this claim is not true. ( α = 0.1)
State the null and alternative hypotheses to dispute the Maryland Department of
Health’s claim. Use symbols in the hypotheses. State alpha and define the parameter.
(7 pts)
Ho:
Ha:
In: Math
1) (from Samuels and Witmer, 2003) If you walk toward a squirrel that is on the ground, it will eventually run to the nearest tree for safety. A researcher wondered whether he could get closer to the squirrel than the squirrel was to the nearest tree before the squirrel would start to run. Thus, for each studied squirrel he recorded the distance from person-to-squirrel and the distance from squirrel-to-tree, at the moment when the squirrel started to run. The measurements are in the txt file on the web. Conduct statistical test to determine if there is a difference between person-to-squirrel and squirrel-to-tree distances (use α=0.05). For the test do the following:
a) Explain whether you will do a test for independent samples or a test for paired samples.
b) Explain whether you will do a 1-tailed or a 2-tailed test.
c) What is the assumption for this statistical test? Is it met?
Show 2 different indicators that you used for checking assumptions (you can do this part in either SAS or R and show only the outputs from either SAS or R). Comment on what each indicator tells you about the assumption.
d) Conduct the test you decided on in
parts a) and b) by hand. Show:
Null hypothesis:
Research Hypothesis:
Value of Test Statistic:
Critical Value:
Conclusion:
e) Use SAS and R to conduct the test you decided on in parts a) and b)
What is the p-value for your test?
Explain how you used p-value to reach conclusion.
squirrelID TypeOfDistance y
1 fromPerson 81
2 fromPerson 178
3 fromPerson 202
4 fromPerson 325
5 fromPerson 238
6 fromPerson 120
7 fromPerson 240
8 fromPerson 326
9 fromPerson 60
10 fromPerson 119
11 fromPerson 189
12 fromPerson 79
13 fromPerson 180
14 fromPerson 200
15 fromPerson 330
16 fromPerson 240
17 fromPerson 132
18 fromPerson 242
19 fromPerson 328
20 fromPerson 55
21 fromPerson 121
1 fromTree 137
2 fromTree 34
3 fromTree 51
4 fromTree 150
5 fromTree 54
6 fromTree 236
7 fromTree 45
8 fromTree 293
9 fromTree 277
10 fromTree 83
11 fromTree 81
12 fromTree 47
13 fromTree 233
14 fromTree 42
15 fromTree 31
16 fromTree 290
17 fromTree 51
18 fromTree 48
19 fromTree 80
20 fromTree 274
21 fromTree 134
In: Math
. Identify the independent variable, dependent variable and direction of the hypotheses.
a) The higher the income, the less likely a person will vote Republican.
b) The more often a student attends class, the higher the student’s score on the final exam.
c) The smaller the automobile’s engine, the higher the automobile’s gas mileage.
d) If an undergraduate student visits an advisor for course scheduling, the more likely the
student will graduate within four years.
e) The more spinach a person consumes, the lower the person’s total cholesterol.
In: Math