Exam 4: Estimation: How Large Is the Effect

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): • = • ? • > •<

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. -Use the 2SD method to find a 95% confidence interval for parameter of interest. (______ (1), ______ (2))

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. -What is the parameter of interest?

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?

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.

Researchers are studying a new weight-loss program. Using a sample of 9,812 volunteers with a desire to lose weight, they construct a 95% confidence interval for the true mean amount of weight loss after six months on the program to be (0.12, 0.20) pounds. -Are these results practically important?

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. -Are validity conditions met in order to use theory-based methods?

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?

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 you constructed a 99% confidence interval with your data instead. How would your 99% confidence interval compare to your 95% confidence interval? Your 99% confidence interval would be:

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 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 1,254 American cell phone owners, but this time, 23% 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:

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?

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?

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 you took another sample of 100 students and this time find a mean of 7.1 and a standard deviation of 1.4 for the hours slept. You then used these new statistics to create another 95% confidence interval for the mean hours slept. How would your new 95% confidence interval compare to your old one? Your new 95% confidence interval would be:

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%?

Studies that have a very large sample size will nearly always yield statistically significant results, but may not yield practically important results.

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?

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 you took another sample of 100 students and this time find a mean of 6.8 and a standard deviation of 1.2 for the hours slept. You then used these new statistics to create another 95% confidence interval for the mean number of hours slept for all students. How would your new 95% confidence interval compare to your old one? Your new 95% confidence interval would be:

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))

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?