Exam 4: Estimation: How Large Is the Effect

A 2012 survey of 1,254 American cell phone owners indicates that 17% of those surveyed do their browsing on their phone rather than a computer or other device. You use these data to calculate a 95% confidence interval for the proportion of all American cell phone owners that do their browsing on their phone rather than a computer or other device. -Suppose another survey was done on 532 American cell phone owners, and again, 17% of those surveyed do their browsing on their phone rather than a computer or other device. How would the 95% confidence interval from this survey compare to yours? This survey's interval would be:

As the standard deviation of a quantitative variable increase, the width of a confidence interval for the population mean also increases, all else being equal.

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

Suppose we have a collection of the heights of all students at your college. Each of the 250 people taking statistics randomly takes a sample of 40 of these heights and constructs a 95% confidence interval for mean height of all students at the college. Which of the following statements about the confidence intervals is most accurate?

Adult male polar bears are expected to weigh, on average, 370 kg. A polar bear's primary source of food are seals and other marine animals, which they hunt from a platform of sea ice. Scientists are concerned that global warming is melting these platforms earlier in the year, reducing the time polar bears are able to hunt and forcing them inland without the necessary fat reserves built up to survive summer and fall. The US Geological Survey (USGS) conducted a study in the Southern Beaufort Sea to investigate whether climate change has appeared to negatively impact the weight of polar bears, on average. Eighty-three adult male polar bears were captured between March and May of the years 1990 and 2006 and their weights were recorded. The sample mean weight was 324.6 kg and the sample standard deviation was 88.3 kg. -Does the confidence interval in question 45 provide statistically significant evidence that the true mean weight of adult male polar bears in the Southern Beaufort Sea is less than 370 kg?

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))

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?

Coulrophobia, or the extreme or irrational fear of clowns, is considered to be relatively rare. A 2018 study conducted by Chapman University found that, in a representative sample of 1190 American adults, 3% indicated they were "very afraid" of clowns. A 99% confidence level created from these data is (0.0173, 0.0426). Which of the following statements best interpret the 99% confidence level?

Suppose you take a random sample of 100 students at a university, ask them how many hours they slept last night, and find a mean of 7.1hours and a standard deviation of 1.2hours. You then calculate a 95% confidence interval for the mean number of hours all students from that university slept last night. -Suppose your friend took a random sample of150 students (and had the same sample mean and standard deviation as your sample). How would your friend's 95% confidence interval compare to yours? The friend's interval would be:

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))

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?

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))

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?

As the sample size decreases, the width of a confidence interval also decreases, all else being equal.

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. ______

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?

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

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))