statistic 04

Prévia do material em texto

· Pergunta 1
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 are the correct null and alternative hypotheses in this case?
	
	
	
	
		Resposta Selecionada:
	 
H0: μ=752  ;  Ha: μ≠752
	Resposta Correta:
	 
H0: μ=752  ;  Ha: μ≠752
	Feedback da resposta:
	This is correct.
	
	
	
· Pergunta 2
1 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.
In 2015 60% of all U.S. adults supported same-sex marriage. We would like to test whether the proportion of all U.S. adults who support same-sex marriage has increased since then. In a recent poll, 20 U.S. adults were randomly chosen and 13 of them (65%) supported same-sex marriage.Can we safely use the z-test for p in this case?
Which of the following is correct?
	
	
	
	
		Resposta Selecionada:
	 
It is not safe to use the z-test for p in this case since 20*(1-.60) is not large enough.
	Resposta Correta:
	 
It is not safe to use the z-test for p in this case since 20*(1-.60) is not large enough.
	Feedback da resposta:
	This is correct. It is not safe to use the z-test for p in this case since n(1-p0)=20(1-.60)=8 is not at least 10.
	
	
	
· Pergunta 3
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. The p-value of the test is 0.022. 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 mean volume dispensed is the required 752ml.
	Resposta Correta:
	 
The data provide evidence to reject H0 and conclude that the mean volume dispensed is not the required 752ml.
	
	
	
· Pergunta 4
1 em 1 pontos
	
	
	
	Skill: Carry out the ANOVA procedure or comparing more than two population means.
"multiple choice" question: select the correct answer. Consider the following situation when comparing three populations’ means:
and testing:
H0: μ1 = μ2 = μ3
Ha: Not all the μ’s are equal
Consider now the following two scenarios of what the three samples might look like. Note that both scenarios have the same three sample means:
Scenario 1: 
Scenario 2: 
In which of the two scenarios is the ANOVA F-test statistic larger (providing more evidence to reject H0)? 
	
	
	
	
		Resposta Selecionada:
	 
Scenario 2, since the variability within groups (i.e., the variability in the samples) is much smaller than the variability within groups in Scenario 1.
	Resposta Correta:
	 
Scenario 2, since the variability within groups (i.e., the variability in the samples) is much smaller than the variability within groups in Scenario 1.
	Feedback da resposta:
	This is correct. The F-test statistic in Scenario 2 will be larger since the variability within groups (which is in the denominator of the F-test statistic) is much smaller.
	
	
	
· Pergunta 5
1 em 1 pontos
	
	
	
	Skill: Carry out the ANOVA procedure or comparing more than two population means.
"multiple choice" question: select the correct answer. The following output provides summary statistics (sample size, mean, and standard deviation) of the the three study-strategy samples:
Based on this information, does the data meet the ANOVA condition of equal population standard deviations?
	
	
	
	
		Resposta Selecionada:
	 
Yes, since
	Resposta Correta:
	 
Yes, since
	Feedback da resposta:
	This is correct.
	
	
	
· Pergunta 6
0 em 1 pontos
	
	
	
	Skill: Carry out the ANOVA procedure or comparing more than two population means.
"multiple choice" question: select the correct answer. Results of the analysis that was run on the SAT-Math data:
Which of the following is an appropriate conclusion based on the output?
	
	
	
	
		Resposta Selecionada:
	 
We can reject H0and conclude that the data provides strong evidence that performance on the SAT-math is related to the study strategy in the following way: the mean SAT-math score of students who use a prep-course is larger than the mean SAT-math score of students who used a tutor, which in turn is larger than the mean SAT-math score of students who studied on their own.
	Resposta Correta:
	 
Both (A) and (B) are are appropriate conclusions.
	
	
	
· Pergunta 7
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 8
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 9
1 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:
	 
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.
	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.
	Feedback da resposta:
	This is correct.
	
	
	
· Pergunta 10
1 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. 
When the two-sample t-test is carried out, the researchers find that the test statistic is t = 2.83 and P-value = 0.003 P-value = 0.003 tells us that it would be quite unlikely to get results like that observed in our study (or more extreme) assuming that:
	
	
	
	
		Resposta Selecionada:
	 
There is no difference in effectiveness between the two methods.
	Resposta Correta:
	 
There is no difference in effectiveness between the two methods.
	Feedback da resposta:
	This is correct. The P-value is calculated assuming that the null hypothesis is true, which in this case is that there is no difference in effectiveness between the two methods.