Describing Data
A student scored in the 82nd percentile on a test. This is the correct interpretation of that percentile.
What is the student scored higher than or equal to 82% of test takers?
A principal assigns every student a number and uses a random number generator to choose 50 students for a survey. This type of sample gives every group of 50 students an equal chance of being selected.
What is a simple random sample (SRS)?
At a school, 60% of students take math, 35% take art, and 20% take both. This is the probability that a randomly selected student takes math or art.
What is 75% or 0.75?
This part of a confidence interval represents the maximum likely distance between the sample statistic and the population parameter.
What is the margin of error?
A company claims its website visitors arrive by browser type in proportions 0.50, 0.30, 0.15, and 0.05. In a sample of 400 visitors, the expected count for the rarest category is this.
What is 20?
A test has a mean of 72 and a standard deviation of 8. A student scores 90. This is the student’s z-score.
What is 2.25?
Researchers record the amount of sleep students get and compare it to their test scores. This type of study is being conducted.
What is an observational study?
A survey finds that 40% of students play a sport, 30% play an instrument, and 12% do both. Since 0.4(0.3)=0.12, this describes the relationship between the two events.
What are independent events?
This theorem states that when you take sufficiently large random samples from any population, the averages (means) of those samples will be approximately normally distributed, regardless of the original population's shape.
What is the Central Limit Theorem?
A single random sample of adults is classified by education level and opinion on a policy. This is the chi-square test that should be used to determine association between education level and opinion on a policy.
What is a chi-square test of independence?
A data set has one extremely large outlier. These two summary statistics will be most affected by the outlier.
What are the mean and standard deviation?
A researcher believes that gender may affect response to a new study strategy. Students are first separated by gender, and then within each gender group, students are randomly assigned to either the new strategy or the standard strategy. This experimental design technique is being used.
What is blocking?
A basketball player makes 72% of his free throws. He takes 10 free throws. This is the probability that he makes exactly 8.
What is 25.5% or .255?
A researcher decreases the confidence level from 99% to 90% while keeping sample size constant. This is the effect on the width of the confidence interval.
What is the interval becomes narrower?
A least-squares regression model predicting test scores from hours studied the night before has the value r2 = 0.58. This is the correct interpretation of this value in context.
What is 58% of the variation in test scores is explained by the linear relationship with hours studied?
In a normal distribution, this percent of data falls between 2 standard deviations below the mean and 1 standard deviation above the mean.
What is 81.9% or 0.819?
A researcher randomly selects 20 schools, then randomly selects 30 students within each selected school. This is the correct name for the design.
What is a multistage sample?
A game costs $4 to play. You roll a fair six-sided die. If you roll a 6, you win $20. If you roll anything else, you win $0. This is your expected profit.
What is -$0.67?
A researcher compares mean test scores between American and Canadian high school students using independent random samples of size 30 from each country. The sample means are 78 and 72, with standard deviations 10 and 12. This is the approximate p-value found when determining if there is a statistically significant difference between the countries' test-takers using a t-distribution.
What is 0.04?
From a least-squares regression model, a student calculates the average residual as +1.5. This is why the student's calculation is incorrect.
What is the average of the residuals must equal 0 in a least-squares regression model?
A data set has a mean of 100 and standard deviation of 15. A value of 130 is added to every observation, and then each result is divided by 5. These are the new mean, standard deviation, and z-score of an original value of 145 after the transformation.
What are a mean of 46, standard deviation of 3, and a z-score of 3?
A survey has no bias in its design, but the sample proportion differs from the true population proportion simply because a sample was used. This is the name of the reason for that difference.
What is sampling variability?
At a school, 52% of students are female. Of females, 64% participate in at least one club. Of males, 45% participate in at least one club. Given that a randomly selected student participates in at least one club, this is the probability that the student is female.
What is 60.6% or 0.606?
n a randomized experiment, 83 of 212 subjects assigned to Treatment A recovered within one week, while 112 of 245 subjects assigned to Treatment B recovered within one week. The researcher believes that the proportion of subjects recovered within one week will be the same for either treatment. This is the conclusion the researcher should draw at the 0.05 significance level, with the respective p-value.
What is a p-value of .158 and the decision to not reject the null hypothesis?
This English statistician developed the Chi-Square test in 1900.
Who is Karl Pearson?