Exam 3: Generalization: How Broadly Do the Results Apply

The following histogram shows the distribution of the difference between the actual and "ideal" weights for 119 female students. Ideal weights are responses to the question "What is your ideal weight"? The difference = actual - ideal. -Most of the women in this sample felt that their actual weight was

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 population of test scores is skewed right. What would be the shape of the sampling distribution for sample mean test scores from samples of 50 students?

A rental car company has noticed that the distribution of the number of miles customers put on rental cars per day is skewed to the right, with some occasional high outliers. The distribution has a mean of 80 miles and a standard deviation of 50 miles. -Which of the following distributions would have the smallest mean?

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. -Describe the parameter of interest in the context of this problem. What is the appropriate statistical symbol for this parameter?

The following histogram shows the distribution of the difference between the actual and "ideal" weights for 119 female students. Ideal weights are responses to the question "What is your ideal weight"? The difference = actual - ideal. -If the observation at -20 pounds was removed from the data set, the mean would___

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. -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 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. -Identify the appropriate parameter of interest for this study.

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 is the null hypothesis?

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. -Calculate the p-value using the table of counts provided.

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? -The sample mean of 7.6 hours lies _______ (1) standard errors ______ (2) the recommended value of 8 hours. (1) = blank for calculation (2) = drop-down menu with options: •above •below

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? -Using the Theory-Based Inference applet to determine the probability of observing a sample mean of 7.6 hours or less, assuming the true mean hours of sleep per night is 8 hours.

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. -Can we use this study to generalize our results to the population of interest?

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?" -Is this sample representative of the entire population of faculty at this large research university?

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? -Suppose that instead of measuring the amount of sleep each student got last night, you measured whether each student got at least 8 hours of sleep last night in your sample. Could you use these data to carry out a one-sample t-test to determine if students at your college are getting less than the recommended amount of sleep per night?

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. -The sample mean of 324.6 kg lies _______(1) standard errors ______ (2) the expected average polar bear weight of 370 kg. (1) = blank for calculation (2) = drop-down menu with options: •above •below

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? -Do these results provide evidence that students at your college are getting less than the recommended amount of sleep per night?

A hot dog manufacturer asserts that one of its brands of hot dogs has an average fat content of 18grams per hot dog. Fat contents in hot dogs from this manufacturer follow an approximately normal distribution with a standard deviation of 1.1grams. Define the statisticx ̅ = mean fat content in a random sample of 10 hot dogs. -If the hot dog manufacturer's claim is true, what would be the mean of the sampling distribution of ? ________ grams

The following histogram shows the distribution of the difference between the actual and "ideal" weights for 119 female students. Ideal weights are responses to the question "What is your ideal weight"? The difference = actual - ideal. -The median of the distribution is approximately___

If your p-value is very small, you have proven the alternative hypothesis.

If a distribution is skewed left, then the mean will be smaller than the median.