Inferential Statistics Week 3 Quiz Answer

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Week 3 Quiz

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Question 1)

Which of the following is false about bootstrapping?

A bootstrap confidence interval constructed based on a biased sample will still yield an unbiased estimate for the population parameter of interest.

The endpoints of a 95% bootstrap confidence interval are the cutoff values for the top and bottom 2.5% of the bootstrap distribution.

Bootstrap distributions that are extremely skewed or have isolated clumps of values may yield unreliable confidence intervals.

Bootstrap distributions are constructed by sampling with replacement from the original sample, while sampling distributions are constructed by sampling with replacement from the population

Question 2)

Suppose we wanted to compare the rates of return for two stocks: the technology company Intel and the U.S. airline Southwest Airlines. To compare the rates of return, we take a random sample of 50 days of Intel's stock returns and another random sample of 50 days for Southwest's stock returns (not necessarily the same days). These data should not be treated as paired. Why would these data not be considered paired data?

When random sampling is involved, data can't be treated as paired.

50 observations is not enough to be able to consider the data as paired.

The data can't be considered paired data because the days for which we have Intel data may be different from the days for which we have Southwest Airlines data.

The data can't be considered paired data because the two companies are in different industries.

Question 3)

The distribution of duration of unemployment for all 18-24 year-old Americans is nearly normal with mean 12.7 weeks and standard deviation 0.3 weeks. Suppose we randomly sample 20 people from this population, ask them about the duration of their unemployment in number of weeks), and record the sample mean. We repeat this 5,000 times, and build a a distribution of sample means. What is the name of this distribution?

bootstrap distribution

sample distribution

randomization distribution

population distribution

sampling distribution

Question 4)

A study examining the relationship between weight of school children (4th to 6th graders) found a 95% confidence interval for the difference between the average number of school days missed by overweight and normal weight children (Loverweight - Mnormal) to be 1.3 to 2.8 days. Which of the following is true based on this confidence interval?

We are 95% confident that overweight children on average miss 1.3 to 2.8 days fewer than children with normal weight.

At 5% significance level, the data do not provide convincing evidence of a difference between the average number of missed days by overweight and normal weight children.

We are 95% confident that overweight children on average miss 1.3 to 2.8 days more than children with normal weight.

At 10% significance level, the data do not provide convincing evidence of a difference between the average number of missed days by overweight and normal weight children.

Question 5)

When doing inference on a single mean, which of the following is the correct justification for using the t-distribution rather than the normal distribution?

Because the standard error estimate may not be accurate,

Because the t-distribution is not symmetric.

O All of the above. O None of the above.

Question 6)

How does the shape of the t-distribution change as the sample size increases?

It becomes flatter

It becomes more normal looking

It becomes wider

It becomes skewed

Question 7)

Air quality measurements were collected in a random sample of 25 country capitals in 2013, and then again in the same cities in 2014. We would like to use these data to compare average air quality between the two years. Which of the following tests is the most appropriate?

independent samples t-test with one-sided alternative hypothesis

paired t-test with two-sided alternative hypothesis

independent samples t-test with two-sided alternative hypothesis

paired t-test with one-sided alternative hypothesis

Question 8)

Suppose that a one-tailt test is being applied to find out if the population mean is less than 100. The level of significance is 0.05 and 25 observations were sampled. The null hypothesis would be rejected for t scores in which of the following regions? Choose the best answer.

T>1.32

T<1.96

T<-1.71

T>1.71

T<-1.32

Question 9)

We would like to test if students who are in the social sciences, natural sciences, arts & humanities, and other fields spend the same amount of time studying for this course. What type of test should we use?

t-test for two dependent groups

z-test

t-test for two independent groups

F-test (ANOVA)

Question 10)

Which of the following is not a condition required for comparing means across multiple groups using ANOVA?

The observations should be independent within and across groups.

There should be at least 10 successes and 10 failures.

The variability across the groups should be about equal.

The data within each group should be nearly normal.

Question 11)

Based on the ANOVA output below, what is the value of the F-statistic? Choose the closest answer.

10.71

14.45

1.87

27.00

0.54

Question 12)

A study compared five different methods for teaching descriptive statistics. The five methods were traditional lecture and discussion, programmed textbook instruction, programmed text with lectures computer instruction, and computer instruction with lectures. 45 students were randomly assigned, 9 to each method. After completing the course, students took a 1-hour exam. We are interested in finding out if the average test scores are different for the different teaching methods.

The p-value of the test is 0.0168. What is the conclusion of the test?

All five group means are equal to each other.

At least two group means are significantly different from each other.

At most two group means are significantly different from each other.

All five group means are significantly different from each other.

Only two group means are significantly different from each other.

Question 13)

Researchers studying people's sense of smell devised a measure of smelling ability. A higher score on this scale means the subject can smell better. A random sample of 36 people (18 male and 18 female) were involved in the study. The average score for the males was 10 with a standard deviation of 3.4 and the average score for the females was 11 with a standard deviation of 2.7. Which of the following is the correct standard error for the test evaluating whether the males and females have differing smelling abilities, on average? Choose the closest answer.

1.023

0.724

0.801

1.047

3.504

Question 14)

A study compared five different methods for teaching descriptive statistics. The five methods were traditional lecture and discussion, programmed textbook instruction, programmed text with lectures, computer instruction, and computer instruction with lectures. 45 students were randomly assigned, 9 to each method. After completing the course, students took a 1-hour exam. We are interested in finding out if the average test scores are different for the different teaching methods.

If the original significance level for the ANOVA was 0.05, what should be the adjusted significance level for the pairwise tests to compare all pairs of means to each other?