Exam 4: Hypothesis Tests

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. -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 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. -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 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 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. -Use the provided randomization distribution (based on 1,000 samples) to estimate the p-value for this sample.

Use the following In 2012 the Centers for Disease Control and Prevention reported that in a sample of 4,349 African Americans 31% were Vitamin D deficient. A 90% confidence interval based on this sample is (0.30, 0.32). It is believed that among the general population of Americans 8% suffer from Vitamin D deficiency. -Does this confidence interval provide evidence that among African Americans 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 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 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. -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 In May 2012, President Obama made history by revealing his support of gay marriage. Around that time, the Gallup Organization polled 1,024 U.S. adults about their opinions on gay/lesbian relations and gay marriage. They found that 54% of those sampled viewed gay/lesbian relations as "morally acceptable" and that 50% felt that gay marriage should be legal. -Use technology to determine if this sample provides evidence that the majority of Americans find gay/lesbian relations "morally acceptable". Be sure to state the hypotheses, give the p-value, and clearly state the conclusion in context. Include an assessment of the strength of the evidence.

Use the following In May 2012, President Obama made history by revealing his support of gay marriage. Around that time, the Gallup Organization polled 1,024 U.S. adults about their opinions on gay/lesbian relations and gay marriage. They found that 54% of those sampled viewed gay/lesbian relations as "morally acceptable" and that 50% felt that gay marriage should be legal. -A 90% confidence interval for the proportion of American adults who support gay marriage is (0.475, 0.524). Does this confidence interval provide evidence that the percentage of American adults who support gay marriage differs from 50%? Briefly justify your answer and state the significance level you are using.

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 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 the evidence.

An article published in the Canadian Journal of Zoology presented a method for estimating the body fat percentage of North American porcupines; the method was illustrated with a sample of n = 25 porcupines. Based on this sample, a 95% bootstrap confidence interval for the average body fat percentage of porcupines is 17.4% to 25.8%. Which of the following null hypotheses would be rejected based on this confidence interval?

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. -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.

It is of interest to test the hypotheses H_o: p = 0.8 versus H_a: p < 0.8. The sample outcome, based on n = 10 observations, is $\hat{p}$ = 0.7, and the randomization statistic to be calculated is $\hat{p}$ . The p-value for this test was found to be 0.322. If the test was performed correctly, where should the randomization distribution be centered?

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. 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. -Define the appropriate parameter(s) and state the hypotheses for testing if this sample provides evidence that the average age of the driftwood along this beach is less than 130 years.

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 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 In 2012 the Centers for Disease Control and Prevention reported that in a sample of 4,349 African Americans 31% were Vitamin D deficient. A 90% confidence interval based on this sample is (0.30, 0.32). It is believed that among the general population of Americans 8% suffer from Vitamin D deficiency. -Define the appropriate parameter and state the appropriate hypotheses for testing the claim that, among African Americans, Vitamin D deficiency occurs at a rate other than 8%.

Use the following 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. -Briefly explain what a Type II error would mean in this situation.

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 know if 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.

Identify the error in the following hypotheses: versus .

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. 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 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.