Exam 4: Hypothesis Tests

Use the following to answer the questions below: -Use the provided randomization distribution (based on 1,000 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. Include an assessment of the strength of your evidence.

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 the provided randomization distribution (based on 100 samples) to estimate the p-value for this sample. 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 to answer the questions below: 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 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 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. -Use the provided randomization distribution (based on 100 samples) 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 about 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.

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. -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.

Identify the error in the following hypotheses: versus

Identify the error in the following hypotheses: of versus

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 the provided randomization distribution (based on 100 samples) to estimate the p-value for this sample.

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. -Does this sample provide evidence that, on average, male students watch more television than female students at this university? Describe how you could generate a single randomization sample in this situation, and identify the statistic that you would calculate for each sample.

Use the following to answer the questions below: Match each p-value to the most appropriate conclusion. - "The evidence against the null and in favor of the alternative is very strong."

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 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: 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 the provided randomization distribution (based on 1,000 samples) 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 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.

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

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 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 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.

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 the provided randomization distribution (based on 100 samples) to determine if this sample provides evidence that more than one-third of households in this city own pets. Use a 5% significance level.

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). -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%.