Statistics_4

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Pergunta 1
1 em 1 pontos
	
	
	
	The Medical College Admission Test (MCAT) is an examination for prospective medical students.Suppose that based on data collected from a random sample of 100 MCAT takers, the 95% confidence interval for μ, the mean MCAT score, was calculated to be (497, 503).
Skill:
Calculate interpret the confidence interval for the population mean , and recognize the effect of level of confidence and sample size on the precision of the interval estimation.
"multiple choice" question: select the correct answer. If we were to use the same data to calculate a 90% confidence interval for μ, the mean MCAT score, which of the following could be this interval?
	
	
	
	
		Resposta Selecionada:
	 
(498, 502)
	Resposta Correta:
	 
(498, 502)
	Feedback da resposta:
	This is correct. The 90% confidence interval calculated using the same data has to be both narrower and, like the 95% confidence interval, centered at the same sample mean (500).
	
	
	
Pergunta 2
1 em 1 pontos
	
	
	
	t was found that 25% of community college students in the state of California do not complete their Intro Stats class (i.e., either withdraw mid-course or fail). In an effort to reduce the non-completion rate, a new hybrid course format (on-line materials + face-to-face instructions) was designed to replace the traditional course. To test its effectiveness, a random sample of 300 California community college students who took the Intro Stats course in the new format was chosen and it was found that 66 of them (22%) did not complete the course.Do these data provide enough evidence to conclude that when the course is taught in the new format the non-completion rate is reduced? Let p be the proportion of all community college students in the state of California who took Intro Stats in the new format and did not complete the course.
Skill: Carry out the hypothesis test for the population proportion and draw conclusions in context
"multiple choice" question: select the correct answer. Which of the following are the correct null and alternative hypotheses in this case? 
	
	
	
	
		Resposta Selecionada:
	 
H0: p=0.25  ;   Ha: p≠0.25
	Resposta Correta:
	 
H0: p=0.25  ;   Ha: p≠0.25
	Feedback da resposta:
	This is correct.
	
	
	
Pergunta 3
1 em 1 pontos
	
	
	
	Skill: Determine the likelihood of making type I and type II errors, and explain how to reduce them, in context.
"multiple choice" question: select the correct answer. What can be done in order to reduce the risk of Type II error?
	
	
	
	
		Resposta Selecionada:
	 
Increase the sample size.
	Resposta Correta:
	 
Increase the sample size.
	Feedback da resposta:
	This is correct.
	
	
	
Pergunta 4
0 em 1 pontos
	
	
	
	Skill: Carry out the hypothesis test for the population proportion and draw conclusions in context. "multiple choice" question: select the correct answer.
Recall that in order to assess whether the new Intro Stats course format reduces the non-completion rate, a random sample of 300 California community college students who took the course in the new format was chosen and it was found that 66 of them (22%) did not complete the course.Which of the following would have provided stronger evidence that the new course format reduces the non-completion? In other words, which of the following would have resulted in a smaller p-value for this test?
	
	
	
	
		Resposta Selecionada:
	 
A random sample of 200 students was chosen and 44 of them (22%) did not complete the course.
	Resposta Correta:
	 
Both (B) and (C) are correct
	
	
	
Pergunta 5
1 em 1 pontos
	
	
	
	Wineries use machines that automatically fill the bottles. The amount of wine that the machine dispenses will naturally vary slightly from bottle to bottle. To determine whether the machine is working properly, bottles are occasionally sampled and the volume of wine is measured. A winery in California randomly sampled 5 bottles and found that the average volume in these bottles was 747.6 milliliters (ml). If the machine is working properly, bottles should contain 752 ml of wine, on average. Using the data they collected, the winery would like to test whether μ, the mean volume dispensed by the machine differs from this value (752 ml). Suppose that the volume of wine dispensed by the machine is known to have a normal distribution with standard deviation σ=4.3 ml.
Skill: Carry out the hypothesis test for the population mean and draw conclusions in context
"multiple choice" question: select the correct answer. Which of the following is the correct test-statistic in this case?
	
	
	
	
		Resposta Selecionada:
	 
z=747.6−7524.35√/
	Resposta Correta:
	 
z=747.6−7524.35√/
	Feedback da resposta:
	This is correct.
	
	
	
Pergunta 6
1 em 1 pontos
	
	
	
	A large insurance company wanted to estimate μ, the mean claim size (in $) on an auto insurance policy. A random sample of 225 claims was chosen and it was found that the average claim size was $2875. From past experience the population standard deviation is assumed to be $1350.
Determine point estimates in simple cases, and make the connection between the sampling distribution of a statistic, and its properties as a point estimator.
"multiple choice" question: select the correct answer. Which of the following is the point estimate for μ?
	
	
	
	
		Resposta Selecionada:
	 
$2875
	Resposta Correta:
	 
$2875
	Feedback da resposta:
	This is correct. The point estimate for the population mean is the sample mean.
	
	
	
Pergunta 7
1 em 1 pontos
	
	
	
	Skill: Perform inference for the linear relationship between two quantitative variables
"multiple choice" question: select the correct answer. The following output is available:
Based on the output, which of the following is the appropriate conclusion?
	
	
	
	
		Resposta Selecionada:
	 
The data provide strong evidence that IQ and DI are linearly related.
	Resposta Correta:
	 
The data provide strong evidence that IQ and DI are linearly related.
	Feedback da resposta:
	This is correct.
	
	
	
Pergunta 8
0 em 1 pontos
	
	
	
	Skill: Carry out the two-sample t-test for comparing two population means when appropriate and draw meaningful conclusions.
"multiple choice" question: select the correct answer. 
The data analysis also found that the 95% confidence interval for μ1 − μ2  is (1.1, 6.1).Which of the following is the correct interpretation of this interval? 
	
	
	
	
		Resposta Selecionada:
	 
There is 95% chance that if a child is taught by Method 2, his/her performance score will be between 1.1 and 6.1. 
	Resposta Correta:
	 
We are 95% confident that the mean performance score of all children taught by Method 1 is between 1.1 and 6.1 points higher than the mean performance score of all children taught by Method 2.
	
	
	
Pergunta 9
1 em 1 pontos
	
	
	
	In 1989, a major earthquake struck the San Francisco Bay area. The earthquake caused major damage, and would be expected to have emotional post-traumatic stress effects on the residents. Any psychological measure taken in the days or weeks just before the quake would have provided a good baseline for subsequent comparison.Two Stanford researchers happened to measure the depression level of 25 college students from the San Francisco Bay area two weeks before the quake. They then measured depression for the same group of 25 students again 10 days after the earthquake to track the students’ adjustment to the traumatic event. The depression scale that the researchers used is such that the higher the score the more depressed the individual is. Do the data provide evidence that students in the San Francisco Bay area became more depressed following the earthquake?
Let [Math Processing Error] be the mean difference in depression score (Before earthquake– After earthquake) of all students in the San Francisco Bay area.
Skill: Carry out the paired t-test when appropriate and draw meaningful conclusions
"multiple choice" question: select the correct answer. Which of the following are the appropriate null and alternative hypotheses?
	
	
	
	
		Resposta Selecionada:
	 
H0: μd = 0
Ha: μd < 0
	Resposta Correta:
	 
H0: μd = 0
Ha: μd < 0
	Feedback da resposta:
	This is correct. If students became more depressed after the earthquake, we expect the differences (depression before – depression after) to be, on average, negative.
	
	
	
Pergunta 10
1 em 1 pontos
	
	
	
	The Medical College Admission Test (MCAT) is an examination for prospective medical students.Suppose that based on data collected from a random sample of 100 MCAT takers, the 95% confidence interval for μ, the mean MCAT score, was calculated to be (497, 503).
Skill:
Calculate interpret the confidence interval for the population mean , and recognize the effect of level of confidence and sample size on the precision of the interval estimation.
"multiple choice" question: select the correct answer.
Which of the following is the correct interpretation of this confidence interval?
	
	
	
	
		Resposta Selecionada:
	 
We are 95% confident that the mean MCAT score is covered by the interval (497, 503).
	Resposta Correta:
	 
We are 95% confident that the mean MCAT score is covered by the interval (497, 503).
	Feedback da resposta:
	This is correct.