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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?

R:$2875

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 certain type of lightbulb is advertised to have mean lifetime of 750 hours.A consumer advocacy group would like to check this claims and test:H0: The mean lifetime is the advertised 750 hoursHa: The mean lifetime is less than the advertised 750 hours.The advocacy group chooses at random 40 lightbulbs and records their lifetimes. Based on the data the group concludes that the mean lifetime is less than 750 hours and accuses the manufacturer of the lightbulbs in false advertising. What type of error is possible in this situation?

R:Type I

A recent Gallup poll concerning abortion reported that 30% (.30) of the sampled U.S. adults said that abortion should be legal in all cases. The report added that the margin of error at the 95% confidence level was 4% (.04).

Skill: Calculate interpret the confidence interval for the population proportion p, 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 the margin of error in this case?

R: We are 95% confident that the proportion of all U.S. adults who feel that abortion should be legal in all cases is no more than .04 away from .30.

Skill: Recognize the different steps of hypothesis testing and its logic. In particular, determine the hypotheses, interpret the p-value and draw conclusions.

"multiple choice" question: select the correct answer. Which of the following is true in hypothesis testing?

R:The smaller the p-value, the more evidence the data provide against the null hypothesis and in favor of the alternative hypothesis.

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.

Skills:

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.

Calculate interpret the confidence interval for the population proportion p, 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 will produce a narrower confidence interval than the one in Question #2?

R:None of the above. The width of the confidence interval does not depend on the sample size

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?

R:The data provide strong evidence that IQ and DI are linearly related.

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.

R:standard deviation is calculated from the sample

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)?

R: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.

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).

Skills:

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. Calculate interpret the confidence interval for the population proportion p, 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.

What is the margin of error of this confidence interval?

R:5%

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?

R:We cannot reject H0. The data provide enough evidence to conclude that the new course format reduces the non-completion rate.

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 I error?

R:Choose a smaller significance level (for example, 0.01 instead of 0.05)

Fine 'motor control' of the hands and fingers is an important milestone for little children. Such motor control skills are often taught in pre-school, but the outcome might differ depending on the teaching method.One particular study was conducted to compare the effectiveness of two teaching methods for teaching a specific motor skill. The subjects, 70 pre-school children, were each randomly assigned to be taught by either Method 1 or Method 2. The outcome (the response) is a performance measure of the motor skill (higher is better) as measured by an outside expert who did not know which teaching method each child was assigned to.

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. Method 1 is a newer method and according to its developers, is more effective than Method 2. Does the data provide enough evidence to support the developers' claim?

Let µ1 and µ2 be the mean motor skill performance measure of all children taught by method 1 and method 2, respectively.Which of the following are the appropriate hypotheses in this case?

R:H0: μ1 − μ2 = 0

Ha: μ1 − μ2 > 0

Skill: Carry out the paired t-test when appropriate and draw meaningful conclusions

"multiple choice" question: select the correct answer. The researchers analyze the data and obtain the following output:

Which of the following is an appropriate conclusion based on the output?

R:The data provided sufficient evidence to reject H0. Thus, the researcher can conclude that the depression scores of students in the San Francisco and Bay area are, on average, higher following the earthquake.

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?

R:374

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?

R:Yes, since

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:

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 true regarding the sample proportion ρˆ, as a point estimator for the population proportion p?

R:All of the above are true.

Skill: Recognize the different steps of hypothesis testing and its logic. In particular, determine the hypotheses, interpret the p-value and draw conclusions.

"multiple choice" question: select the correct answer. Suppose that the p-value of a test is 0.035. Which of the following is correct regarding the conclusions we can draw?

R:We cannot reject the null hypothesis at both at a significance level of 0.01 and at a significance level of 0.05ERRADA

We can reject the null hypothesis at a significance level of 0.01 but cannot reject the null hypothesis at a significance level of 0.05

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?

R:We are 95% confident that the mean MCAT score is covered by the interval (497, 503).

The question whether birth order affects juvenile delinquency was examined in a large study using a high school population. A random sample of 1,060 boys attending public school were given a questionnaire that measured delinquent behavior and then classified each boy as either 'Yes' or 'No'. Each boy also indicated his birth order: the oldest, in between, or the youngest. The results are summarized in the following two-way table:

R:the sample size is larger than 30.ERRADA

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. 70 pre-school children, were each randomly assigned to be taught by either Method 1 or Method 2. The outcome (the response) is a performance measure of the motor skill (higher is better) as measured by an outside expert who did not know which teaching method each child was assigned to. Here are the summary statistics of performance measure data:

Which of the following justifies why we can safely use the two-sample t-test in this case?

R:Both samples sizes are larger than 30.ERRADA

The two samples are independent (since each of the children was randomized to one of the two methods) and both samples sizes are larger than 30.

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.

The larger n, the closer the t distribution with n-1 degrees is to the standard normal distribution

R:All of the above are correct.

Skill: Carry out the ANOVA procedure or comparing more than two population means.

"multiple choice" question: select the correct answer. The analysis was run on the data and the following output was obtained:

Which of the following is the correct interpretation of the P-value in the context of this study?

R:The probability of getting data like that observed in the study (or more extreme) if performance on the SAT-Math is not related to the the study strategy.

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?

R:TYPE 2

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.

Skills: Carry out the hypothesis test for the population proportion and draw conclusions in context. Carry out the hypothesis test for the population mean and draw conclusions in context

"multiple choice" question: select the correct answer.

The p-value in this case is the probability of getting data like that observed or more extreme (i.e., getting an observed non-completion rate of 22% or lower) assuming that:

R:the new course format did reduce the non-completion rateERRADA

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?

R: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.

The question whether birth order affects juvenile delinquency was examined in a large study using a high school population. A random sample of 1,060 boys attending public school were given a questionnaire that measured delinquent behavior and then classified each boy as either 'Yes' or 'No'. Each boy also indicated his birth order: the oldest, in between, or the youngest. The results are summarized in the following two-way table:

To test whether the data provides significant evidence for a relationship between birth order and delinquent behavior, we will use the Chi-square test for independence.

Skill: Carry out the chi-square test for the independence of two categorical variables and draw meaningful conclusions.

"multiple choice" question: select the correct answer. Two-way table that summarizes the results of the study:

R:19.8

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. Recall that the P-value of the test for assessing whether

Method 1 is more effective than Method 2 for teaching children a motor skill was P-value = 0.003. Which of the following is the appropriate conclusion? (Use significance level of 0.05).

R:Since P−value=0.003<0.05, we conclude that the results of the study provide sufficient evidence that Method 1 is more effective than method 2.

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?

R:We can reject H0 and conclude that the data provides strong evidence that performance on the SAT-math is related to the study strategy.ERRADA

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?

R:We cannot reject H0. The data provide evidence to conclude that the mean volume dispensed is not the required 752ml.ERRADA

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?

R:(498, 502)

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?

R:H0: μd = 0

Ha: μd > 0

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:

R:There is no difference in effectiveness between the two methods.

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?

R:Choose a larger significance level (for example, 0.1 instead of 0.05).