Question 1

Suppose I am trying to construct a confidence interval using repeated tests of significance to develop an interval of plausible values. I am doing two-sided tests each time with the following null hypotheses and resulting p-values. Using the results, give a 95% confidence interval.
  (______ (1), ______ (2))

Accepted Answer

(1) 0.47; (2) 0.57

Question 2

Suppose I am trying to construct a confidence interval using repeated tests of significance to develop an interval of plausible values. I am doing two-sided tests each time with the following null hypotheses and resulting p-values. Using the results, give a 99% confidence interval.
  (______ (1), ______ (2))

Accepted Answer

(1) 0.46; (2) 0.59

Question 3

Suppose I am trying to construct a confidence interval using repeated tests of significance to develop an interval of plausible values. I am doing two-sided tests each time with the following null hypotheses and resulting p-values. Using the results, give a 95% confidence interval.
  (______ (1), ______ (2))

Accepted Answer

(1) 0.45; (2) 0.53

Question 4

Suppose I am trying to construct a confidence interval using repeated tests of significance to develop an interval of plausible values. I am doing two-sided tests each time with the following null hypotheses and resulting p-values. Using the results, give a 99% confidence interval.
  (______ (1), ______ (2))

Accepted Answer

The answer of Suppose I am trying to construct a...

Question 5

Let be some population proportion of interest and suppose a 99% confidence interval for is calculated to be (0.37, 0.43) and a 95% confidence interval is calculated to be (0.38, 0.42). Suppose also that you are testing the hypotheses H₀: = 0.33 and H_a: ? 0.33. What can you say about the corresponding p-value for this test? A) The corresponding p-value will be less than 0.01. B) The corresponding p-value will be between 0.01 and 0.05. C) The corresponding p-value will be greater than 0.05.

Accepted Answer

The 99% confidence interval does not include 0.33, so the p-value for the test will be less than 0.01.

Question 6

Let be some population proportion of interest and suppose a 99% confidence interval for is calculated to be (0.15, 0.26) and a 95% confidence interval is calculated to be (0.18, 0.23). Suppose also that you are testing the hypotheses H₀: = 0.17 and H_a: ? 0.17. What can you say about the corresponding p-value for this test? A) The corresponding p-value will be less than 0.01. B) The corresponding p-value will be between 0.01 and 0.05. C) The corresponding p-value will be greater than 0.05.

Accepted Answer

The answer of Let be some population proportion of interest...

Question 7

Suppose I am conducting a test of significance with H₀: = 0.50 and H_a: ? 0.50 and I end up with a p-value of 0.07. I also construct 99% and 95% confidence intervals from my data. What will be true about my confidence interval? A) Both the 99% and the 95% intervals will contain 0.50. B) Neither the 99% nor the 95% intervals will contain 0.50. C) The 99% interval will contain 0.50, but the 95% interval will not contain 0.50. D) The 99% interval will not contain 0.50, but the 95% interval will contain 0.50.

Accepted Answer

The answer of Suppose I am conducting a test of...

Question 8

Commercial fisherman working certain parts of the Atlantic Ocean sometimes find their efforts being hindered by the presence of whales. Ideally, they would like to scare away the whales without frightening the fish. Experience has shown that whales leave the sight of a fishing boat 40% of the time. One of the strategies being experimented with is to transmit underwater the sounds of a killer whale. On the 52 occasions that this technique has been tried, it worked 24 times (that is, the whales immediately left the area). -A test of the hypotheses H₀: versus H₀: yields a p-value of 0.3968. Based on this result, would you expect a 95% confidence interval to contain the value 0.40? A) Yes, since the p-value is larger than 0.05. B) Yes, since the p-value is smaller than 0.05. C) No, since the p-value is larger than 0.05. D) No, since the p-value is smaller than 0.05.

Accepted Answer

The answer of Commercial fisherman working certain parts of the...

Question 9

Commercial fisherman working certain parts of the Atlantic Ocean sometimes find their efforts being hindered by the presence of whales. Ideally, they would like to scare away the whales without frightening the fish. Experience has shown that whales leave the sight of a fishing boat 40% of the time. One of the strategies being experimented with is to transmit underwater the sounds of a killer whale. On the 52 occasions that this technique has been tried, it worked 24 times (that is, the whales immediately left the area).
-A 99% confidence interval for is (0.29, 0.65). How would you interpret this interval?
A) When underwater sounds of killer whales are transmitted, we are 99% confident that whales leave the sight of a fishing boat 46% of the time.
B) When underwater sounds of killer whales are transmitted, we are 99% confident that whales leave the sight of a fishing boat between 29% and 65% of the time.
C) 99% of whales will leave the sight of a fishing boat if they hear sounds of a killer whale.
D) If we collect another sample of 52 occasions, there is a 99% chance that the sample proportion of whales who leave the sight of a fishing boat will be between 0.29 and 0.65.

Accepted Answer

We are 99% confident that the true proportion of times whales leave when killer whale sounds are transmitted is between 29% and 65%.

Question 10

The spinning dancer (or silhouette illusion) is a moving image of a woman that appears to be spinning. Some people see her spinning clockwise and some see her spinning counterclockwise. A student showed other students this and found that 30 out of 50 (or 60%) saw her spinning clockwise. A 95% theory-based confidence interval for π is (0.45, 0.73).
-Which of the following statements correctly interprets this interval?
A) We are 95% confident that the proportion of the 50 students sampled that saw the spinning dancer spinning clockwise is between 0.45 and 0.73.
B) We are 95% confident that the probability a randomly chosen student would see the spinning dancer spinning clockwise is between 0.45 and 0.73.
C) If we were to collect another sample of 50 students, there is a 95% probability that the sample proportion who see the spinning dancer spinning clockwise would be between 0.45 and 0.73.
D) We are 95% confident that the long-run proportion of students who would see the spinning dancer spinning clockwise is 0.60.

Accepted Answer

A 95% confidence interval estimates the range in which the true population proportion (π) lies, meaning we are 95% confident that the probability a randomly chosen student would see the spinning dancer spinning clockwise is between 0.45 and 0.73.

Question 11

The spinning dancer (or silhouette illusion) is a moving image of a woman that appears to be spinning. Some people see her spinning clockwise and some see her spinning counterclockwise. A student showed other students this and found that 30 out of 50 (or 60%) saw her spinning clockwise. A 95% theory-based confidence interval for π is (0.45, 0.73).
-Based on this interval, is there statistical evidence that the long-run probability a randomly chosen student would see the woman spinning clockwise is larger than 50%?
A) Yes, since most of the interval is larger than 50%.
B) Yes, since 0.50 is not contained in the interval.
C) No, since 0.50 is contained in the interval.
D) No, since our sample size was not large enough.

Accepted Answer

The interval (0.45, 0.73) contains 0.50, indicating there is no statistical evidence that the probability is larger than 50%.

Question 12

Let the parameter of interest, , represent the probability that a student will choose an odd number. Fill in the blanks for the null and alternative hypotheses below. H₀: $\pi$= _______ (1) H_a: $\pi$ ______ (2) ______ (3) (1) and (3) are numerical text entry. Drop-down menu item for (2): • = • ? • > •<

Accepted Answer

The answer of Let the parameter of interest, , represent...

Question 13

To investigate whether students tend to think of an odd number when they are asked to think of a single-digit number, you used the One Proportion applet and ran a simulation with 100 trials under the null hypothesis. Given below is a dotplot with results from that simulation.
  Based on this dotplot, would a 95% confidence interval for contain the value 0.5?
A) No, since 0.5 is not on the plot.
B) No, since only 9 points fall at or above the observed sample result.
C) Yes, since the p-value is 0.09.
D) Yes, since we are assuming the null hypothesis is true.

Accepted Answer

The answer of To investigate whether students tend to think...

Question 14

In a different class of 80 students, 51 chose an odd number. A 95% confidence interval for based on these data is (0.522, 0.740), and a 99% confidence interval is (0.487, 0.766). What would be true about the p-value for testing whether differs from 0.5?
A) The p-value would be less than 0.01.
B) The p-value would be less than 0.05 but greater than 0.01.
C) The p-value would be less than 0.10 but greater than 0.05.
D) The p-value would be greater than 0.10.
E) There is not enough information provided to answer this question.

Accepted Answer

The answer of In a different class of 80 students,...

Question 15

A 95% confidence interval for is (0.522, 0.740), based on data where 51 students chose an odd number out of a class of 80 students. Which of the following is a correct interpretation of this interval?
A) About 95% of students would choose an odd number.
B) In 95% of all classes of 80 students, the proportion that choose an odd number would be between 0.522 and 0.740.
C) We are 95% confident that the probability a student chooses an odd number is between 0.522 and 0.740.
D) We do not have statistically significant evidence that the true proportion of students who would choose an odd number differs from 0.5.

Accepted Answer

A 95% confidence interval means we are 95% confident that the true proportion of students who would choose an odd number is between 0.522 and 0.740.

Question 16

The spinning dancer (or silhouette illusion) is a moving image of a woman that appears to be spinning. Some people see her spinning clockwise and some see her spinning counterclockwise. A student showed other students this and found that 30 out of 50 (or 60%) saw her spinning clockwise. The student researcher was interested in the probability of a randomly chosen student that would see the dancer spinning clockwise. He created the following null distribution for this.   Using the information provided above, determine a 2SD confidence interval for the long-run probability a randomly chosen student would see the woman spinning clockwise. (Don't use any other applet to do this, just the applet output and information above.)
A) (0.36, 0.64)
B) (0.46, 0.74)
C) (0.53, 0.67)
D) (0.43, 0.57)

Accepted Answer

The answer of The spinning dancer (or silhouette illusion) is...

Question 17

A 95% confidence interval for a population proportion is (0.67, 0.83). What is the sample proportion?
A) 0.67
B) 0.83
C) 0.75
D) 0.08
E) It cannot be determined given the information provided.

Accepted Answer

The sample proportion is the midpoint of the confidence interval, calculated as (0.67 + 0.83) / 2 = 0.75.

Question 18

A 95% confidence interval for a population proportion is (0.67, 0.83). What is the margin of error?
A) 0.67
B) 0.83
C) 0.75
D) 0.08
E) It cannot be determined given the information provided.

Accepted Answer

The margin of error is half the width of the confidence interval, which is (0.83 - 0.67) / 2 = 0.08.

Question 19

A 95% confidence interval for a population proportion is 0.20 ± 0.09. What are the endpoints of the interval?
(______ (1), ______ (2))

Accepted Answer

The answer of A 95% confidence interval for a population...

Question 20

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%).
-Below are the results of 1000 samples from a process with QUOTE = .50.
   Using the 2SD method, construct a 95% confidence interval for the long-run proportion of matches where the competitor wearing red wins.
(______ (1), ______ (2))

Accepted Answer

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

Quiz 4: Estimation: How Large Is the Effect

Suppose I am trying to construct a confidence interval using repeated tests of significance to develop an interval of plausible values. I am doing two-sided tests each time with the following null hypotheses and resulting p-values. Using the results, give a 95% confidence interval. ( (1), (2))

Suppose I am trying to construct a confidence interval using repeated tests of significance to develop an interval of plausible values. I am doing two-sided tests each time with the following null hypotheses and resulting p-values. Using the results, give a 99% confidence interval. ( (1), (2))

Suppose I am trying to construct a confidence interval using repeated tests of significance to develop an interval of plausible values. I am doing two-sided tests each time with the following null hypotheses and resulting p-values. Using the results, give a 95% confidence interval. ( (1), (2))

Suppose I am trying to construct a confidence interval using repeated tests of significance to develop an interval of plausible values. I am doing two-sided tests each time with the following null hypotheses and resulting p-values. Using the results, give a 99% confidence interval. ( (1), (2))

Suppose I am conducting a test of significance with H₀: = 0.50 and H_a: ? 0.50 and I end up with a p-value of 0.07. I also construct 99% and 95% confidence intervals from my data. What will be true about my confidence interval?

In a different class of 80 students, 51 chose an odd number. A 95% confidence interval for based on these data is (0.522, 0.740) , and a 99% confidence interval is (0.487, 0.766) . What would be true about the p-value for testing whether differs from 0.5?

A 95% confidence interval for is (0.522, 0.740) , based on data where 51 students chose an odd number out of a class of 80 students. Which of the following is a correct interpretation of this interval?

A 95% confidence interval for a population proportion is (0.67, 0.83) . What is the sample proportion?

A 95% confidence interval for a population proportion is (0.67, 0.83) . What is the margin of error?

A 95% confidence interval for a population proportion is 0.20 ± 0.09. What are the endpoints of the interval? ( (1), (2))