Exam 4: Hypothesis Tests

Identify the error in the following hypotheses: versus .

Use the following There are 24 students enrolled in an introductory statistics class at a small university. As an in-class exercise the students were asked how many hours of television they watch each week. Their responses, broken down by gender, are summarized in the provided table. Assume that the students enrolled in the statistics class are representative of all students at the university. -Describe how you would generate a single randomization sample in this situation, and identify (using the appropriate notation) the sample statistic you would record for each sample.

Use the following A student in an introductory statistics course investigated if there is evidence that the proportion of milk chocolate M&M's that are green differs from the proportion of dark chocolate M&M's that are green. She purchased a bag of each variety, and her data are summarized in the following table. -Use technology to create a randomization distribution with at least 1,000 values for testing these hypotheses. Use your randomization distribution to estimate the p-value for this sample.

Use the following The owner of a small pet supply store wants to open a second store in another city, but he only wants to do so if more than one-third of the city's households have pets (otherwise there won't be enough business). He samples 150 of the households and finds that 64 have pets. -Use technology to create a randomization distribution with at least 1,000 values for testing these hypotheses. Use your randomization distribution to estimate the p-value for this sample.

Use the following A study recently described in Attention, Perception, and Psychophysics investigated the impacts of mult-tasking on people who play video games and those who don't. Participants in the study were asked to perform three visually demanding tasks with (dual-task) and without (single-task) answering unrelated questions over the phone. One of the tasks involved tracking multiple circles moving around on a computer monitor. At the 5% significance level, the authors of the study concluded "tracking accuracy was significantly worse in the dual-task condition" for both people who play video games and those who do not. -What conclusion would the authors have made at the 10% significance level?

Use the following The owner of a small pet supply store wants to open a second store in another city, but he only wants to do so if more than one-third of the city's households have pets (otherwise there won't be enough business). He samples 150 of the households and finds that 64 have pets. -Use your p-value and a 5% significance level to make a decision about these hypotheses. Be sure to word your decision in the context of the problem.

Use the following A certain species of tree has an average life span of 130 years. A researcher has noticed a large number of trees of this species washing up along a beach as driftwood. She takes core samples from 27 of those trees to count the number of rings and measure the widths of the rings. Counting the rings allows the researcher to determine the age of each tree. Her data are displayed in the provided table. One of her interests is determining if this sample provides evidence that the average age of the driftwood is less than the 130 year life span expected for this type of tree. If the average age is less than 130 years it might suggest that the trees have died from unusual causes, such as invasive beetles or logging. -Use technology and the provided data to determine if this sample provides evidence that the average age of the driftwood along this beach is less than 130 years. Use a 5% significance level to make your conclusion.

Use the following Consider testing the hypotheses H_o: p = 0.4 versus H_a: p > 0.4. Four possible sample statistics, along with four possible p-values, are given. Match the statistics to their p-values. -________ p-value = 0.138

Use the following A Division III college men's basketball team is interested in identifying factors that impact the outcomes of their games. They plan to use "point spread" (their score minus their opponent's score) to quantify the outcome of each game this season; positive values indicate games that they won while negative values indicate games they lost. They want to determine if "steal differential" (the number of steals they have in the game minus the number of steals their opponent had) is related to point spread; positive values indicate games where they had more steals than their opponent. The data for the n = 25 games they played this season displayed in the provided table. Assuming that this season was a typical season for the team, they want to know if steal differential is positively correlated with point spread. -Use technology to determine if this sample provides evidence that point spread and steal differential are positively correlated. Be sure to include all of the steps of the test. Use a 10% significance level to make your conclusion.

Decreasing the significance level of a hypothesis test (say, from 5% to 1%) will cause the p-value of an observed test statistic to

Use the following There are 24 students enrolled in an introductory statistics class at a small university. As an in-class exercise the students were asked how many hours of television they watch each week. Their responses, broken down by gender, are summarized in the provided table. Assume that the students enrolled in the statistics class are representative of all students at the university. -Use technology to create a randomization distribution with at least 1,000 values for testing these hypotheses. Use your randomization distribution to estimate the p-value for this sample.

Use the following A study recently described in Attention, Perception, and Psychophysics investigated the impacts of mult-tasking on people who play video games and those who don't. Participants in the study were asked to perform three visually demanding tasks with (dual-task) and without (single-task) answering unrelated questions over the phone. One of the tasks involved tracking multiple circles moving around on a computer monitor. At the 5% significance level, the authors of the study concluded "tracking accuracy was significantly worse in the dual-task condition" for both people who play video games and those who do not. -Which type of error, Type I or Type II, could have occurred in this situation? Briefly justify your answer.

Use the following As of August 8, 2012, the national average price for a gallon of regular unleaded gasoline was $3.63. The prices for a sample of n = 10 gas stations in the state of Illinois are provided. It is of interest to use this sample to compare the average gas price in Illinois to the national average. -Describe how you would generate a single randomization sample in this situation, and identify (using the appropriate notation) the sample statistic you would record for each sample.

Use the following There are 24 students enrolled in an introductory statistics class at a small university. As an in-class exercise the students were asked how many hours of television they watch each week. Their responses, broken down by gender, are summarized in the provided table. Assume that the students enrolled in the statistics class are representative of all students at the university. -Use the provided randomization distribution (based on 100 samples) to estimate the p-value for this sample.

Use the following A Division III college men's basketball team is interested in identifying factors that impact the outcomes of their games. They plan to use "point spread" (their score minus their opponent's score) to quantify the outcome of each game this season; positive values indicate games that they won while negative values indicate games they lost. They want to determine if "steal differential" (the number of steals they have in the game minus the number of steals their opponent had) is related to point spread; positive values indicate games where they had more steals than their opponent. The data for the first five games are in the provided table as an example. The correlation between point spread and steal differential for the n = 25 games they played this season is about r = 0.35. Assuming that this season was a typical season for the team, they want to test if this sample provides evidence that steal differential is positively correlated with point spread. -Use the provided randomization distribution (based on 100 samples) to estimate the p-value for this sample.

Briefly explain the difference between a "bootstrap distribution" and a "randomization distribution".

Use the following A certain species of tree has an average life span of 130 years. A researcher has noticed a large number of trees of this species washing up along a beach as driftwood. She takes core samples from 27 of those trees to count the number of rings and measure the widths of the rings. Counting the rings allows the researcher to determine the age of each tree. Her data are displayed in the provided table. One of her interests is determining if this sample provides evidence that the average age of the driftwood is less than the 130 year life span expected for this type of tree. If the average age is less than 130 years it might suggest that the trees have died from unusual causes, such as invasive beetles or logging. -What conclusion would you make at the 10% significance level?

Use the following The owner of a small pet supply store wants to open a second store in another city, but he only wants to do so if more than one-third of the city's households have pets (otherwise there won't be enough business). He samples 150 of the households and finds that 64 have pets. -Use your p-value and a 5% significance level to make a decision about these hypotheses. Be sure to word your decision in the context of the problem.

In a test of the hypotheses versus , the observed sample results in a p-value of 0.0256. Would you expect a 95% confidence interval for based on this sample to contain 0? Briefly explain why or why not.