Adam tabulated the values for the average speeds on each day of his road trip as 60.5, 63.2, 54.7, 51.6, 72.3,
70.7, 67.2, and 65.4 mph. He wishes to
... [Show More] construct a 98% confidence interval.
What value of t* should Adam use to construct the confidence interval? Answer choices are rounded to the thousandths place.
2.517
2.896
4.489
2.998
RATIONALE
Recall that we have n = 8, so the df = n-1 = 7. So if we go to the
row where df = 7 and then 0.01 for the tail probability, this gives us a value of 2.998. Recall that a 98%
confidence interval would have 2% for the tails, so 1% for each tail.
We can also use the last row and find the corresponding confidence level.
CONCEPT
How to Find a Critical T Value
2
Which of the following statements is true?For the Central Limit Theorem to be true, you must have a large
sample, the underlying population must be normally distributed, and
the standard deviation should not be finite.
Even with a very large sample size, the Central Limit Theorem
states that the sample means of repeated samples of a population
cannot be normally distributed.
For a large enough sample size, the Central Limit Theorem states
that the sample medians of repeated samples of a population are
normally distributed.
For a large enough sample size, the Central Limit Theorem states
that the sample means of repeated samples of a population are
normally distributed.
RATIONALE
The Central Limit Theorem gives us information about the properties' sampling distributions of statistics to have
given that the sample size is large enough. It tells us the sampling distribution's mean should be equal to the
true population mean.
CONCEPT
Shape of a Sampling Distribution
3
Regan wants to study how reading on a computer affects comprehension among elementary school students.
Regan thinks that girls and boys might differ and he also suspects that grade level will affect the results. He
decides to create a male and a female group for each grade. Within each group, he randomly assigns half of the
students to read an article on paper and half of the students to read the article on a computer.
Which type of experimental design does this situation illustrate?
Double-Blind
Randomized Block
Matched-Pair
Completely Randomized
RATIONALE
Since students are put into gender and grade blocks and are then assigned treatment or control randomly this is
called a randomized block design.
CONCEPT
Randomized Block Design
4
For the data plotted in the scatterplot, the r 2 value was calculated to be 0.9846.Which of the following sets of statements is true?
98.5% of the variation in age is explained by a nonlinear relationship
with yearly income.
The correlation coefficient, r, is 0.969.
98.5% of the variation in yearly income is explained by a linear
relationship with age.
The correlation coefficient, r, is 0.992
98.5% of the variation in yearly income is explained by a nonlinear
relationship with age.
The correlation coefficient, r, is 0.992.
98.5% of the variation in age is explained by a linear relationship
with yearly income.
The correlation coefficient, r, is 0.969.
RATIONALE
The coefficient of determination measures the percent of variation in the outcome, y, explained by the
regression. So a value of 0.9846 tells us the regression with age, x, can explain about 98.5% of the variation in
income, y.
We can also note that r = .
CONCEPT
Coefficient of Determination/r^25
On a candy production line, 3% of bags are overfilled. An employee randomly selects 100 bags and finds that 5%
are overfilled. A second employees takes another random sample of 250 bags and finds that 2% are overfilled.
Which of the following explains why there is a difference between the two percentages?
The sample sizes were both too small, which is why they both
obtained figures different than 3%
The samples were not random samples.
Random error; the numbers were different due to variability inherent
in sampling.
Both samples suffered from non-response bias.
RATIONALE
When sampling, there is always some variability that occurs. So,
although the sample values are different from each other and the 3% true value, since they were randomly
chosen, the differences are simply due to the variability that comes from sampling and not due to some
systematic bias. As the sample size would increase we would expect the variability to get smaller.
CONCEPT
Random and Systematic Errors
6
Sharon, an 8th grader, found the following values for weekly allowances in dollars of seven of her friends: 5, 7, 10,
8, 6, 12, and 15.
If Sharon wanted to construct a one-sample t-statistic, what would the value for the degrees of freedom be?
3
6
7
8
RATIONALE
The degrees of freedom for a 1 sample t-test are df=n-1 where n is the sample size. In this case, n=7, then df =
n-1 = 7-1 = 6.
CONCEPT
T-Tests
7
In which of these cases should the mean be used?
When the data is left-skewed
When the data has extreme values
When the data is right-skewed
When the data is symmetricRATIONALE
Since the mean uses the actual values in the data, it is most affected by outliers and skewness. So, we only
want to use the mean when the data is symmetric as a measure of centrality. When the data is skewed, the
median is a better measure.
CONCEPT
Measures of Center
8
Henri has calculated a z-test statistic of -2.73.
What is the p-value of the test statistic? Answer choices are rounded to the thousandths place. [Show Less]