Exam 4: Hypothesis Tests

Use the following to answer the questions below: -Use technology and the provided data to test if this sample provides evidence that the average gas price in Illinois exceeds the national average. Include an assessment of the strength of your evidence.

The null and alternative hypotheses for a test are vs. Give the notation for a sample statistic we might record for each simulated sample to create the randomization distribution.

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. -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.

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. -Use the provided randomization distribution (based on 100 samples) to estimate the p-value for this sample. What conclusion would you make at the 10% significance level?

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.

- p-value = 0.019

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. -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: The makers of a popular brand of laundry detergent have discovered a new secret ingredient that they believe will boost the cleaning power of their detergent. The new ingredient is expensive, and if they use it, they would have to increase the retail price of the detergent (and they worry that the price increase will cause them to lose customers). However, they believe that if the improved detergent gets clothes drastically cleaner, customers will recognize that it is worth the extra cost. They conduct an experiment to compare the performance of the new and old formulas at removing grass stains, red wine, and chocolate from white t-shirts. Each cleaned shirt was rated on a scale from 1 (stain did not get removed) to 10 (no evidence of the stain) by trained experts. They compared the average rating for the new and old formulas. -Suppose, at the 5% significance level, they find that the new formula cleaned the shirts significantly better than the old formula, with a p-value of 0.046. Interpret the p-value, in terms of the probability of the results happening by random chance, in this context.

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 technology 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.

Use the following to answer the questions below: -Describe how you could 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: -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: Match each p-value to the most appropriate conclusion. - "There is really no evidence supporting the alternative hypothesis."

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 conclusion would the authors have made at the 1% significance level?

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 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.

The randomization distribution for testing the hypotheses versus is provided. The sample statistic is Use the provided randomization distribution (based on 100 samples) to estimate the p-value for this test.

Use the following to answer the questions below: -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. 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. -Define the appropriate parameter(s) and state the hypotheses for testing if this sample provides evidence that, on average, male students watch more television than female students at this university.

- p-value = 0.72

Use the following to answer the questions below: 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 to answer the questions below: 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. -Describe how you could generate a single randomization sample in this situation, and identify the statistic that you would calculate for each sample.