Exam 3: Generalization: How Broadly Do the Results Apply

If your p-value is very large, your results prove the null hypothesis.

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. 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, the sam-ple median weight was 339.4 kg, and the sample standard deviation was 88.3 kg. A box plot of the data is shown below. -Fill in the blanks below to explain how to use bootstrapping to create one simulated sample which assumes the null hypothesis is true. Create ______ (1) cards. On each card, you should write the ________ (2) after ________ (3) the value ________ (4). Then draw ______ (5) cards ______ (6) replacement. Plot the ______ (7). Repeat 1000 times to create the simulated null distribution. Drop-down options for (1), (4), and (5): •83 •45.4 •370 •324.6 Drop-down options for (2) and (7): •weight of each sampled polar bear •mean weight of the resampled polar bears Drop-down options for (3): •adding •subtracting Drop-down options for (6): •with •without

The following 19 test scores are based on a random sample of final exam scores (sorted in increasing order) for the population of students who took an elementary statistics course at a large university over a 5 year period: Answer the following questions without performing any calculations. -Suppose the largest test score in the sample changed from a 94 to a 90. Describe how each of the following statistics would change. The median would ______. (1) The mean would ______. (2) The standard deviation would ______. (3) Drop-down options for (1), (2), and (3): •increase •decrease •remain the same

For a survey on affirmative action, researchers selected a random sample of 20 faculty members from a large research university. Faculty in the sample were asked, "Do you favor or oppose using race, religion, sex, color, ethnicity, or national origin as a criterion for college admission?" -The proportion of all faculty at this large research university that would have answered "Yes" to the survey question if asked is the___.

Suppose that the proportion of all American adults that fit the medical definition of being obese is 0.23. A large medical clinic would like to determine if the proportion of their patients that are obese is higher than that of all American adults. The clinic takes a simple random sample of 30 of their patients and finds that 9 patients in the sample are obese. -If the clinic had collected a sample of 100 patients instead of 30, would the standard deviation of the simulated null distribution increase, decrease, or remain the same?

Suppose that the proportion of all American adults that fit the medical definition of being obese is 0.23. A large medical clinic would like to determine if the proportion of their patients that are obese is higher than that of all American adults. The clinic takes a simple random sample of 30 of their patients and finds that 9 patients in the sample are obese. -Write the null and alternative hypotheses in proper notation.

Adult male polar bears are expected to weigh, on average, 370 kg. A polar bear's primary source of food is 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. 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 Theory-Based Inference applet to determine the p-value to investigate whether climate change has appeared to negatively impact the weight of polar bears.

Most experts recommend college students get at least 8 hours of sleep per night. You collect a random sample of 112 students at your college and ask how many hours of sleep they got last night. The sample mean amount of sleep last night was 7.6 hours, with a sample standard deviation of 2.1 hours. The sample distribution of hours of sleep was slightly skewed right. Does this provide evidence that students at your college are getting less than the recommended amount of sleep per night? -What are the observational units?

Adult male polar bears are expected to weigh, on average, 370 kg. A polar bear's primary source of food is 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. 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 sample results to estimate the standard error of the sampling distribution of sample mean weight.

In June of 2012, New York City Mayor Michael Bloomberg proposed banning the sale of any reg-ular soda or other sugary drinks in containers larger than 16 oz. A fast food chain polled a random sample of 2500 of its regular customers and found that 63% opposed the ban, 28% supported the ban, and 9% had no opinion. -To which population should this sample be generalized?

Most experts recommend college students get at least 8 hours of sleep per night. You collect a random sample of 112 students at your college and ask how many hours of sleep they got last night. The sample mean amount of sleep last night was 7.6 hours, with a sample standard deviation of 2.1 hours. The sample distribution of hours of sleep was slightly skewed right. Does this provide evidence that students at your college are getting less than the recommended amount of sleep per night? -Is a theory-based approach reasonable for these data?

Most experts recommend college students get at least 8 hours of sleep per night. You collect a random sample of 112 students at your college and ask how many hours of sleep they got last night. The sample mean amount of sleep last night was 7.6 hours, with a sample standard deviation of 2.1 hours. The sample distribution of hours of sleep was slightly skewed right. Does this provide evidence that students at your college are getting less than the recommended amount of sleep per night? -Use the sample results to estimate the standard error of the sampling distribution of sample means.

Suppose that the proportion of all American adults that fit the medical definition of being obese is 0.23. A large medical clinic would like to determine if the proportion of their patients that are obese is higher than that of all American adults. The clinic takes a simple random sample of 30 of their patients and finds that 9 patients in the sample are obese. -Where is the distribution centered? Explain why this makes sense.

Noxious weeds are invasive plants that quickly spread and deplete the soil of nutrients that are required for all aspects of farming and ranching. With much at stake, the state of Montana has hired a team of researchers to explore the issue. They want to know the average number of noxious weeds per acre in North Central Montana. To do so, researchers divided the area of interest into 1,000,000 acres and randomly selected 24 of these acres. For each selected acre, they counted and removed the noxious weeds. The sample mean was 103.47 weeds, and the sample standard deviation was 46.034 weeds. Below is the simulated bootstrap distribution of 1,000 sample means they created from resampling the observed data. -Suppose we had selected 240 acres rather than 24, but the values of our sample statistics were the same. Describe how each of the following would change. The sample standard deviation would ______. (1) The standard error of the sample mean would ______. (2) The standard deviation of the bootstrap distribution would ______. (3) The p-value would ______. (4) Drop-down options for (1)-(4): •decrease •increase •remain the same •unable to determine

Noxious weeds are invasive plants that quickly spread and deplete the soil of nutrients that are required for all aspects of farming and ranching. With much at stake, the state of Montana has hired a team of researchers to explore the issue. They want to know the average number of noxious weeds per acre in North Central Montana. To do so, researchers divided the area of interest into 1,000,000 acres and randomly selected 24 of these acres. For each selected acre, they counted and removed the noxious weeds. The sample mean was 103.47 weeds, and the sample standard deviation was 46.034 weeds. Below is the simulated bootstrap distribution of 1,000 sample means they created from resampling the observed data. -What is the population of interest?

Adult male polar bears are expected to weigh, on average, 370 kg. A polar bear's primary source of food is 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. 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. -To which population can we generalize these results?

The following 19 test scores are based on a random sample of final exam scores (sorted in increasing order) for the population of students who took an elementary statistics course at a large university over a 5 year period: Answer the following questions without performing any calculations. -Suppose we removed the smallest test score (61) from the sample. Describe how each of the following statistics would change. The median would ______. (1) The mean would ______. (2) The standard deviation would ______. (3) Drop-down options for (1), (2), and (3): •increase •decrease •remain the same

Suppose that the proportion of all American adults that fit the medical definition of being obese is 0.23. A large medical clinic would like to determine if the proportion of their patients that are obese is higher than that of all American adults. The clinic takes a simple random sample of 30 of their patients and finds that 9 patients in the sample are obese. -Based on this p-value, what is your conclusion for the hypothesis test in the context of this problem?

Most experts recommend college students get at least 8 hours of sleep per night. You collect a random sample of 112 students at your college and ask how many hours of sleep they got last night. The sample mean amount of sleep last night was 7.6 hours, with a sample standard deviation of 2.1 hours. The sample distribution of hours of sleep was slightly skewed right. Does this provide evidence that students at your college are getting less than the recommended amount of sleep per night? -What are the measurement units?

A histogram of a bootstrapped null distribution is shown below. Since the bootstrapped null distribution is bell-shaped, the population of polar bear weights must also be bell-shaped.