Unit 3
A florist wanted to investigate whether a new powder added to the water of cut flowers helps to keep the flowers fresh longer than just water alone. For a shipment of roses that was delivered to the store, the florist flipped a coin before placing each rose in its own individual container with water. If the coin landed heads up, the rose was placed in water with the new powder; otherwise, the rose was placed in water alone. Which of the following is the best description of the method used by the florist?
A: A census, because all roses are assigned to a container
B: An experiment with a completely randomized design
C: An experiment with a blocked design, with blocking by type of water
D: An experiment with a matched-pairs design
E: An observational study
B: An experiment with a completely randomized design
What are the three measures of center?
Mean, median, mode
A: n = 1,000 and p close to 0
B: n = 1,000 and p close to 1
C: n = 1,000 and p close to 1/2
D: n = 100 and p close to 0
E: n = 100 and p close to 1/2
E: n = 100 and p close to 1/2
Define Proportion
describes the share or fraction of a specific characteristic within a whole
A scientist wants to test a hypothesis that a population mean is greater than 85. He gathers a
sample of 40 measurements and the sample mean was 86.8 and the standard deviation was 8.2. What is the
value of the test statistic for a one sample t test for population means?
(A) -0.22
(B) 0.22
(C) -1.39
(D) 1.39
(E) None of the above match the test statistic
(D) 1.39
The director of a fitness center wants to examine the effects of two exercise classes (spinning and aerobics) on body fat percentage. A six-week spinning class and a six-week aerobics class are offered at the same time and on the same days, so that a person can enroll in only one of them. A new class of each is about to begin, and each class has 25 people in it. Ten people are randomly selected from each class. Each person's body fat percentage is measured at the beginning and again at the end of the six-week class. Using the change in body fat percentage as the response variable and conducting a test at the a = 0.01 level, the director determines that there is a significant difference between the treatment means. Which of the following is a confounding variable in the study?
A: The director's choice of spinning and aerobics classes as the types for use in the study.
B: The random sample of 10 people from each class.
C: The participants' choice of which class to take.
D: The use of body fat percentage as the measure of effectiveness of the treatment.
E: The fact that both classes were conducted three times each week at the same time of day and for the same amount of time each day.
C: The participants' choice of which class to take.
What are the summary statistics that are not resistant to outliers?
Mean, Range, Standard deviation
There were 5,317 previously owned homes sold in a western city in the year 2000. The distribution of the sales prices of these homes was strongly right-skewed, with a mean of $206,274 and a standard deviation of $37,881. If all possible simple random samples of size 100 are drawn from this population and the mean is computed for each of these samples, which of the following describes the sampling distribution of the sample mean?
A: Approximately normal with mean $206,274 and standard deviation $3,788
B: Approximately normal with mean $206,274 and standard deviation $37,881
C: Approximately normal with mean $206,274 and standard deviation $520
D: Strongly right-skewed with mean $206,274 and standard deviation $3,788
E: Strongly right-skewed with mean $206,274 and standard deviation $37,881
A: Approximately normal with mean $206,274 and standard deviation $3,788
Define Independence
a concept where the occurrence of one event or the behavior of one variable does not influence, or provide information about, the probability of another
A nutrition researcher is hoping to evaluate the claimed sugar content on the new McDonald's
sandwich. McDonald's claims that their sandwich has 20g of sugar and a sample of 5 sandwiches shows the
following sugar contents: 15, 22, 18, 17, and 23. What assumption(s) do we have to make in order to carry out a
legitimate statistical test of the nutritionist’s claim?
I. The 5 sandwiches are from a normally distributed population.
II. The 5 sandwiches can be viewed as coming from a simple random sample.
III. The standard deviation of the population of all McDonald sandwich sugar content is known.
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I, II and III
(D) I and II
An experiment was conducted to assess the effect of baking temperature on the density of bread. A large batch of white bread dough and a large batch of whole wheat bread dough were prepared. Each of the batches was formed into loaves, resulting in a total of loaves. Each of the white bread loaves was randomly assigned to one of three baking temperatures (low, medium, and high), so that loaves were baked at the low temperature, were baked at the medium temperature, and were baked at the high temperature. A similar process of random assignment was carried out for the whole wheat bread loaves.
Which of the following are the treatments in the experiment?
A: The loaves of bread
B: The type of bread (white, whole wheat)=
C: The density of the bread
D: The baking temperatures (low, medium, high)
E: The two batches of bread dough
D: The baking temperatures (low, medium, high)
When will the standard deviation be zero?
When there is no variance in the data set, all the data is the same number.
For which of the following conditions is it not appropriate to assume that the sampling distribution of the sample mean is approximately normal?
A: A random sample of 8 taken from a normally distributed population
B: A random sample of 50 taken from a normally distributed population
C: A random sample of 10 taken from a population distribution that is skewed to the right
D: A random sample of 75 taken from a population distribution that is skewed to the left
E: A random sample of 100 taken from a population that is uniform
C: A random sample of 10 taken from a population distribution that is skewed to the right
Define Mutually Exclusive
Refers to outcomes that cannot occur at the same time.
Michelin claims that their new snow tires for SUVs have a shorter skid distance than the current
skid distance for their regular snow tires. The current mean skid distance for their snow tires is 140 feet. A tire
testing company is hired to evaluate their claim. If μ represents the true mean skid distance for these new snow
tires, which of the following states the null hypothesis and alternative hypothesis that should be tested?
(A) H0: μ < 140; Ha: μ ≥ 140
(B) H0: μ ≤ 140; Ha: μ > 140
(C) H0: μ = 140; Ha: μ < 140
(D) H0: μ = 140; Ha: μ ≤ 140
(E) H0: μ = 140; Ha: μ ≠ 140
(C) H0: μ = 140; Ha: μ < 140
Which of the following is a benefit to using a random sample for an observational study?
A: The random sample allows for different treatments to be assigned.
B: A causal relationship can be determined.
C: The results of the observational study can be generalized to the population.
D: A random sample is the easiest method of data collection.
E: The distribution of the sample will match the distribution of the population.
C: The results of the observational study can be generalized to the population.
What are the summary statistics that are resistant to outliers?
Median, IQR, Mode
A: The bias will decrease and the variance will remain the same.
B: The bias will increase and the variance will remain the same.
C: The bias will remain the same and the variance will decrease.
D: The bias will remain the same and the variance will increase.
E: The bias will decrease and the variance will decrease.
C: The bias will remain the same and the variance will decrease.
Define Standard error
measures the accuracy of a sample mean
A large sample hypothesis test with σ known of a null hypothesis μ = 15 against the alternative
hypothesis μ ≠ 15 results in the test statistic value of z = 1.37. Assuming σ is known, the corresponding p-value
is approximately
(A) 0.0853
(B) 0.1707
(C) 0.4147
(D) 0.8293
(E) 0.9147
(B) 0.1707
______ 1) Why do we use control groups in experiments?
(A) To eliminate confounding variables
(B) To control the subjects to make sure everyone participates equally
(C) To control how the experiment is conducted and make sure that the results are what we expect
(D) To ensure that randomized assignment is achieved
(E) To reduce the variability in the response variable between the two groups so that any difference is due to the treatment alone
(E) To reduce the variability in the response variable between the two groups so that any difference is due to the treatment alone
What are the four measures of spread?
Range, IQR, Variance, Standard Deviation
A: The distribution of the number of recharge cycles for the sample is approximately normal because the population mean of 400 is greater than 30.
B: The distribution of the number of recharge cycles for the sample is approximately normal because the sample size of 100 is greater than 30.
C: The distribution of the number of recharge cycles for the population is approximately normal because the sample size of 100 is greater than 30.
D: The distribution of the sample means of the number of recharge cycles is approximately normal because the sample size of 100 is greater than 30.
E: The distribution of the sample means of the number of recharge cycles is approximately normal because the population mean of 400 is greater than 30.
D: The distribution of the sample means of the number of recharge cycles is approximately normal because the sample size of 100 is greater than 30.
Define Interval
a range of estimated values or a level of measurement
Looking online, you find the salaries of all 25 players for the Chicago Cubs as of opening day of
the 2021 baseball season. The club total was $128 million, 12th in the major leagues. Which inference
procedure would you use to estimate the average salary of the Cubs players?
(A) One-sample z interval for μ
(B) One-sample t interval for μ
(C) One-sample t test
(D) One-sample z test
(E) None of these—this is not a situation that calls for inference.
(E) None of these—this is not a situation that calls for inference.