Exam 4: Hypothesis Tests

Use the following to answer the questions below: 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 your p-value to make a decision about these hypotheses. Be sure to word your decision in the context of the problem.

Use the following to answer the questions below: 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 games they played this season is about 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. -Describe how you would generate a single randomization sample in this situation, and identify the statistic you would calculate for each sample.

- p-value = 0.293

Identify the error in the following hypotheses: versus

Use the following to answer the questions below: 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 to answer the questions below: 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 games they played this season is about 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. -Define the appropriate parameter(s) and state the hypotheses for testing if this sample provides evidence that steal differential is positively correlated with point spread.

The provided figure displays the randomization distribution for testing versus The p-value for the sample mean = 112 is closest to

When generating a randomization sample, the sample should be consistent with the ________ hypothesis.

The average SAT-Critical Reading score for college bound students taking the exam in the 2018-2019 academic year was 501 531. A highly selective university wants to know if their 2020 incoming class had an average SAT-Critical Reading score that was higher than the national average. Which of the following possible samples provides the most evidence for this claim?

Use the following to answer the questions below: 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. -Define the appropriate parameter(s) and state the hypotheses for testing if the proportion of green M&M's differs for milk chocolate and dark chocolate M&M's.

Use the following to answer the questions below: -Define the appropriate parameter(s) and state the hypotheses for testing if this sample provides evidence that the average gas price in Illinois exceeds the national average.

Use the following to answer the questions below: A study conducted by the National Center of Health Statistics collects data on Vitamin D levels. In 2011-2014, in a sample of 3,929 non-Hispanic Blacks showed that 17.5% were Vitamin D deficient. A 95% confidence interval based on the sample is (0.152, 0.200). -Does this confidence interval provide evidence that among non-Hispanic Blacks Vitamin D deficiency occurs at a rate other than 8%? What significance level is being used to make this decision? Briefly justify your answer.

Use the following to answer the questions below: 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. -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 to answer the questions below: 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 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 to answer the questions below: 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. The average age of the trees in the sample is approximately 120 years. 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. -Describe how you would generate a single randomization sample in this situation, and identify the statistic you would calculate for each sample.

A statistical test uses data from a sample to assess a claim about a population.

Use the following to answer the questions below: 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 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 create a randomization distribution with at least 1,000 values for testing these hypotheses and estimate the p-value. Use your p-value to make a decision about these hypotheses. Be sure to word your decision in the context of the problem.

Use the following to answer the questions below: A study described in Attention, Perception, and Psychophysics investigated the impacts of multi-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 does the phrase "significantly worse" mean in this context?

Use the following to answer the questions below: 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 and the provided data to test if this sample provides evidence that the proportion of candies that are green differs for the two types of M&M's. Include an assessment of the strength of your evidence.

Use the following to answer the questions below: 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 determine if this sample provides evidence that, on average, male students watch more television than female students at this university. Include an assessment of the strength of the evidence.