Question 1

Hill and Barton (Nature, 2005) conducted a study to investigate whether Olympic athletes in certain uniform colors have an advantage over their competitors. They noted that competitors in the combat sports of boxing, Taekwondo, Greco-Roman wrestling, and freestyle wrestling are randomly assigned to wear red or blue uniforms. For each match in the 2004 Olympics, they recorded the uniform color of the winner. Hill and Barton found that in the 457 matches, the competitor wearing red won 248 times (54.3%), whereas the person wearing blue won 209 times (45.7%).
-Are conditions met to use theory-based methods?
A) Yes, because there were two possible outcomes.
B) Yes, since the number of matches is larger than 30.
C) Yes, since the number of matches where the competitor wearing red won, and the number of matches where the competitor wearing blue won, are both greater than 10.
D) No, since the sample size is too small.

Accepted Answer

Theory-based methods can be used because both groups (red and blue) have more than 10 wins, satisfying the condition for using normal approximation in hypothesis testing.

Question 2

Hill and Barton (Nature, 2005) conducted a study to investigate whether Olympic athletes in certain uniform colors have an advantage over their competitors. They noted that competitors in the combat sports of boxing, Taekwondo, Greco-Roman wrestling, and freestyle wrestling are randomly assigned to wear red or blue uniforms. For each match in the 2004 Olympics, they recorded the uniform color of the winner. Hill and Barton found that in the 457 matches, the competitor wearing red won 248 times (54.3%), whereas the person wearing blue won 209 times (45.7%).
-Compute the standard error of the sample proportion of matches in which the winner wore red.

Accepted Answer

The answer of Hill and Barton (Nature, 2005) conducted a...

Question 3

Hill and Barton (Nature, 2005) conducted a study to investigate whether Olympic athletes in certain uniform colors have an advantage over their competitors. They noted that competitors in the combat sports of boxing, Taekwondo, Greco-Roman wrestling, and freestyle wrestling are randomly assigned to wear red or blue uniforms. For each match in the 2004 Olympics, they recorded the uniform color of the winner. Hill and Barton found that in the 457 matches, the competitor wearing red won 248 times (54.3%), whereas the person wearing blue won 209 times (45.7%).
-Construct a 99% confidence interval based on these data using 
Theory-Based Inference applet.
(______ (1), ______ (2))

Accepted Answer

The answer of Hill and Barton (Nature, 2005) conducted a...

Question 4

Can domestic dogs understand human body cues such as leaning? The experimenter leaned toward one of two objects and recorded whether or not the dog being tested correctly chose the object indicated. A four-year-old male beagle named Augie participated in this study. He chose the correct object 8 out of 10 times when the experimenter leaned towards the correct object. Shown below is a simulation of 1000 sample proportions under the assumption that the long-run probability that Augie chooses correct is 0.50. 
-Construct an approximate 95% confidence interval using the 2SD method: ______(1) ± 2______ (2)
Drop-down options for (1) and (2):
•0.5
•0.497
•0.8
•0.153

Accepted Answer

The answer of Can domestic dogs understand human body cues...

Question 5

Can domestic dogs understand human body cues such as leaning? The experimenter leaned toward one of two objects and recorded whether or not the dog being tested correctly chose the object indicated. A four-year-old male beagle named Augie participated in this study. He chose the correct object 8 out of 10 times when the experimenter leaned towards the correct object. Shown below is a simulation of 1000 sample proportions under the assumption that the long-run probability that Augie chooses correct is 0.50. 
-A theory-based approach would be valid for these data.

Accepted Answer

The answer of Can domestic dogs understand human body cues...

Question 6

Can domestic dogs understand human body cues such as leaning? The experimenter leaned toward one of two objects and recorded whether or not the dog being tested correctly chose the object indicated. A four-year-old male beagle named Augie participated in this study. He chose the correct object 8 out of 10 times when the experimenter leaned towards the correct object. Shown below is a simulation of 1000 sample proportions under the assumption that the long-run probability that Augie chooses correct is 0.50. 
-Suppose that we repeated the same study with Augie, and this time he chose the correct object 16 out of 20 times. Conjecture how, if at all, the center and the width of a 2SD 95% confidence interval would change with these data, compared to the original 8 out of 10 times.
The center of the confidence interval would ______ (1).
The width of the confidence interval would ______ (2).
Drop-down options for (1) and (2):
•increase
•decrease
•remain the same

Accepted Answer

The answer of Can domestic dogs understand human body cues...

Question 7

Suppose a 95% confidence interval for a population proportion is (0.21, 0.43). How would the width of the confidence interval change if we changed the confidence level?
A) Both a 99% confidence interval and a 90% confidence interval would be wider.
B) A 99% confidence interval would be wider and a 90% confidence interval would be narrower.
C) A 99% confidence interval would be narrower and a 90% confidence interval would be wider.
D) Both a 99% confidence interval and a 90% confidence interval would be narrower.

Accepted Answer

Increasing the confidence level to 99% increases the interval width, while decreasing it to 90% decreases the interval width.

Question 8

Many studies have investigated the question of whether people tend to think of an odd number when they are asked to think of a single-digit number (0 through 9; 0 is considered an even number). When asked to pick a number between 0 and 9, out of 70 students, 42 chose an odd number. Let the parameter of interest, π, represent the probability that a student will choose an odd number.
-Are conditions met to use theory-based methods?
A) Yes, because there were two possible outcomes.
B) Yes, since the number of students is larger than 30.
C) Yes, since the number of students who chose an odd number, and the number of students who chose an even number, are both greater than 10.
D) No, since the sample size is too small.

Accepted Answer

The conditions for using theory-based methods are met because both the number of students who chose an odd number (42) and the number who chose an even number (28) are greater than 10.

Question 9

Many studies have investigated the question of whether people tend to think of an odd number when they are asked to think of a single-digit number (0 through 9; 0 is considered an even number). When asked to pick a number between 0 and 9, out of 70 students, 42 chose an odd number. Let the parameter of interest, π, represent the probability that a student will choose an odd number.
-Compute the standard error of the sample proportion of students who chose an odd number.

Accepted Answer

The answer of Many studies have investigated the question of...

Question 10

Many studies have investigated the question of whether people tend to think of an odd number when they are asked to think of a single-digit number (0 through 9; 0 is considered an even number). When asked to pick a number between 0 and 9, out of 70 students, 42 chose an odd number. Let the parameter of interest, π, represent the probability that a student will choose an odd number.
-Use the 2SD method to approximate a 95% confidence interval for .
(______ (1), ______ (2))

Accepted Answer

The answer of Many studies have investigated the question of...

Question 11

Many studies have investigated the question of whether people tend to think of an odd number when they are asked to think of a single-digit number (0 through 9; 0 is considered an even number). When asked to pick a number between 0 and 9, out of 70 students, 42 chose an odd number. Let the parameter of interest, π, represent the probability that a student will choose an odd number.
-If we changed the confidence level, what would happen to the width of the 95% confidence interval for , all else remaining the same?
A) A 90% confidence interval would be wider, and a 99% confidence interval would be narrower.
B) A 90% confidence interval would be narrower, and a 99% confidence interval would be wider.
C) Both a 90% and 99% confidence interval would be wider.
D) Both a 90% and 99% confidence interval would be narrower.

Accepted Answer

A 90% confidence interval would be narrower because it has less confidence and thus a smaller margin of error, while a 99% confidence interval would be wider because it has more confidence and thus a larger margin of error.

Question 12

A 95% confidence interval is computed to estimate the mean household income for a city. Which of the following values will definitely be within the limits of this confidence interval?
A) The population mean
B) The sample mean
C) The sample standard deviation
D) The p-value
E) All of the above

Accepted Answer

The sample mean is always at the center of a confidence interval for the mean, so it will definitely be within the limits of the interval.

Question 13

Data from the Centers for Disease Control and Prevention indicate that weights of American adults in 2005 had a mean of 167 pounds and a standard deviation of 35 pounds.
-Calculate the standard deviation of the sample mean for samples of size 47.
______

Accepted Answer

The answer of Data from the Centers for Disease Control...

Question 14

Data from the Centers for Disease Control and Prevention indicate that weights of American adults in 2005 had a mean of 167 pounds and a standard deviation of 35 pounds.
-On October 5, 2005, a tour boat named the Ethan Allen capsized on Lake George in New York with 47 passengers aboard. In the inquiries that followed, it was suggested that the tour operators should have realized that the combined weight of so many passengers was likely to exceed the weight capacity of the boat, 7500 lbs. Based on this information, how surprising is it for a sample of 47 passengers to have an average weight of at least 7500/47 = 159.57 lbs?
A) Not surprising at all - the probability is over 90%.
B) Not surprising - the probability is between 50% and 60%.
C) Somewhat surprising - the probability is between 20% and 30%.
D) Very surprising - the probability is less than 5%.

Accepted Answer

The probability of a sample of 47 passengers having an average weight of at least 159.57 lbs is over 90%. This is because the mean weight of American adults is 167 pounds and the standard deviation is 35 pounds. Therefore, the probability of a sample of 47 passengers having an average weight of at least 159.57 lbs is:P(X >= 159.57) = 1 - P(X < 159.57) = 1 - 0.0904 = 0.9096

Question 15

Suppose you plan to offer a study session and need to know how many candies to bring and there-fore would like to estimate how many candies students tend to take on average. Below are results for the number of candies that 19 undergraduates took from a large bowl. 
-What is the shape of the sample distribution?
A) Approximately symmetric
B) Very skewed right
C) Very skewed left
D) Uniform

Accepted Answer

The shape of the sample distribution is approximately symmetric when the data is evenly distributed around the mean, with no significant skewness to the left or right.

Question 16

Suppose you plan to offer a study session and need to know how many candies to bring and there-fore would like to estimate how many candies students tend to take on average. Below are results for the number of candies that 19 undergraduates took from a large bowl. 
-Are validity conditions met in order to use theory-based methods?
A) Yes, since there are at least 10 successes and 10 failures.
B) Yes, since the sample distribution is approximately symmetric.
C) No, since the sample size is less than 20.
D) We cannot determine whether validity conditions are met with the information given.

Accepted Answer

The answer of Suppose you plan to offer a study...

Question 17

Suppose you plan to offer a study session and need to know how many candies to bring and there-fore would like to estimate how many candies students tend to take on average. Below are results for the number of candies that 19 undergraduates took from a large bowl. 
-Provide an interpretation of the 95% confidence interval given in the output.
A) We are 95% confident that the sample mean number of candies students tend to take is between 36 and 66.
B) About 95% of students will take between 36 and 66 candies.
C) There is a 95% chance that the true mean number of candies students tend to take is between 36 and 66.
D) We are 95% confident that the true mean number of candies students tend to take is between 36 and 66.

Accepted Answer

A 95% confidence interval means that we are 95% confident that the true population mean lies within the interval, not the sample mean or individual observations.

Question 18

Suppose you plan to offer a study session and need to know how many candies to bring and there-fore would like to estimate how many candies students tend to take on average. Below are results for the number of candies that 19 undergraduates took from a large bowl. -Suppose I wanted to test whether the average number of candies taken was significantly different from 60, the expected number in a small bag of candies. Based on the above output, what conclusion will you draw, or do you not have enough information? A) Reject H₀ B) Accept H₀ C) Fail to reject H₀ D) Not enough information

Accepted Answer

The p-value is 0.05, which is greater than the significance level of 0.05. Therefore, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the average number of candies taken is significantly different from 60.

Question 19

SunChips are sold in packages labeled 1.5 oz. A random sample of 25 such bags was taken and weighed, and a 95% confidence interval for the true mean weight per bag is (1.35, 1.51) ounces. Which statement is valid?
A) We are 95% confident that each bag of SunChips contains between 1.35 and 1.51 ounces.
B) We can infer that 95% of all bags of SunChips contain between 1.35 and 1.51 ounces.
C) In the long run, 95% of samples will produce a confidence interval of 1.35 to 1.51 ounces.
D) We are 95% confident that the true mean weight per bag of SunChips is between 1.35 and 1.51 ounces.

Accepted Answer

The confidence interval provides a range in which we are 95% confident that the true mean weight of all SunChips bags lies, not the weight of individual bags or the proportion of bags within that range.

Question 20

Researchers are interested in investigating the effect of a drug that is to be used in the treatment of patients who have glaucoma (an eye disorder associated with high eye pressure). In a volunteer sample of 35 patients with glaucoma in both eyes, one eye of each patient was randomly assigned to this drug, and the other eye was given a placebo. After one week, the eye pressure was measured on each eye. The difference in eye pressure between the two eyes (drug - placebo) was measured for each patient. The sample mean difference in eye pressure was -1.21 mmHg (millimeters of mercury), and the sample standard deviation of the differences was 4.67 mmHg.
-Use the 2SD method to find a 95% confidence interval for the population mean difference in eye pressure (drug - placebo).
(______ (1), ______(2))

Accepted Answer

The answer of Researchers are interested in investigating the effect...

Quiz 4: Estimation: How Large Is the Effect

Suppose a 95% confidence interval for a population proportion is (0.21, 0.43) . How would the width of the confidence interval change if we changed the confidence level?

A 95% confidence interval is computed to estimate the mean household income for a city. Which of the following values will definitely be within the limits of this confidence interval?

Data from the Centers for Disease Control and Prevention indicate that weights of American adults in 2005 had a mean of 167 pounds and a standard deviation of 35 pounds. -Calculate the standard deviation of the sample mean for samples of size 47. ______

SunChips are sold in packages labeled 1.5 oz. A random sample of 25 such bags was taken and weighed, and a 95% confidence interval for the true mean weight per bag is (1.35, 1.51) ounces. Which statement is valid?