ESTATÍSTICA 4

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ESTATÍSTICA 4
Pergunta 1
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.
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 the insurance company wanted to estimate μ with 99% confidence interval with a margin of error of 180, how large a sample of claims would they have needed?
	
	
	
	
		Resposta Selecionada:
	 
374
	Resposta Correta:
	 
374
	Feedback da resposta:
	This is correct. n=[2.576⋅1350]2180=373.2624⇒n=374
	
	
	
Pergunta 2
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.
A pharmaceutical company would like to asses the effectiveness of a new pain reliever and test the following:H0: The drug is not effectiveHa: The drug is effectiveThe company runs an experiment and the data do not provide enough evidence to conclude that the drug is effective. What type of error is possible in this situation?
	
	
	
	
		Resposta Selecionada:
	 
 Type II
	Resposta Correta:
	 
 Type II
	Feedback da resposta:
	This is correct. It is possible that even though based on the data the researchers cannot conclude that the drug is effective, in reality the drug actually is effective. In other words, there is a risk that the researchers fail to reject the null hypothesis by mistake. This is type II error.
	
	
	
Pergunta 3
0 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: pˆ=0.22  ;   Ha: pˆ<0.22
	Resposta Correta:
	 
H0: p=0.25  ;   Ha: p≠0.25
	
	
	
Pergunta 4
0 em 1 pontos
	
	
	
	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 true regarding the t-distribution.
	
	
	
	
		Resposta Selecionada:
	 
The larger n, the closer the t distribution with n-1 degrees is to the standard normal distribution
	Resposta Correta:
	 
All of the above are correct.
	
	
	
Pergunta 5
0 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=747.6−7524.3
	Resposta Correta:
	 
z=747.6−7524.35√/
	
	
	
Pergunta 6
1 em 1 pontos
	
	
	
	Skill: Carry out the hypothesis test for the population mean and draw conclusions in context
"Fill in the blank" question: select the correct answer.
Consider the following two scenarios involving hypothesis testing the population mean, and complete the sentences that follow.
I. The mean IQ score of adults is known to be 100. In order to test whether the mean IQ of lawyers is higher than 100, a random sample of 10 lawyers was chosen and their IQ measured and recorded. It was found that for the 10 sampled lawyers the average IQ score was 101.4 with a standard deviation of 14.5. It is known that IQ scores follow a normal distribution.
II. The mean IQ score of adults is known to be 100. In order to test whether the mean IQ of lawyers is higher than 100, a random sample of 10 lawyers was chosen and their IQ measured and recorded. It was found that for the 10 sampled lawyers the average IQ score was 101.4. It is known that IQ scores follow a normal distribution with standard deviation of 15.
Complete the following sentences: In scenario I, the , and therefore the should be used.In scenario II, the , and therefore the should be used.
	
	
	
	
		Resposta Selecionada:
	 
standard deviation is calculated from the sample
	Resposta Correta:
	 
standard deviation is calculated from the sample
	Feedback da resposta:
	This is correct.
	
	
	
Pergunta 7
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 8
1 em 1 pontos
	
	
	
	Skill: Carry out the ANOVA procedure or comparing more than two population means.
"multiple choice" question: select the correct answer. Consistent with the group numbering, let μ1, μ2, and μ3 the mean SAT-Math score of all students who study on their own, work with a tutor, and complete a prep-course, respectively.
Which of the following are the appropriate null and alternative hypotheses?
	
	
	
	
		Resposta Selecionada:
	 
H0: μ1 = μ2 = μ3
Ha: Not all the μ’s are equal 
	Resposta Correta:
	 
H0: μ1 = μ2 = μ3
Ha: Not all the μ’s are equal 
	Feedback da resposta:
	This is correct.
	
	
	
Pergunta 9
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 themean performance score of all children taught by Method 2.
	
	
	
Pergunta 10
0 em 1 pontos
	
	
	
	It 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.
The p-value is this case is above 10%. Which of the following is the appropriate conclusion at the 5% significance level?
	
	
	
	
		Resposta Selecionada:
	 
The data provide evidence to reject H0 and conclude that the new course format does not reduce the non-completion rate.
	Resposta Correta:
	 
We cannot reject H0. The data do not provide enough evidence to conclude that the new course format reduces the non-completion rate.