Question

A test of H0: p = 0.4 versus Ha: p > 0.4 has the test statistic z = 2.52. Part A: What conclusion can you draw at the 5% significance level? At the 1% significance level? (6 points) Part B: If the alternative hypothesis is Ha: p ≠ 0.4, what conclusion can you draw at the 5% significance level? At the 1% significance level? (4 points) 2. At a Clover City Council meeting, a plan to fund more sign language programs was presented. The reasoning behind the request was that less than 25% of parents with hearing-impaired children have the ability to pass a sign-language exam. If this is true, the council will agree to fund more programs for these parents. The council decides to take a 175-person volunteer sample of parents in Clover City that have children with auditory issues and conduct a significance test for H0: p = 0.25 and Ha: p < 0.25, where p is the proportion of these parents that can pass the sign language exam. They will perform the significance test at a significance level of α = 0.05 for the hypotheses. Part A: Describe a Type II error that could occur. What impact could this error have on the situation? (3 points) Part B: Out of the 175 volunteer parents of children with hearing problems, 54 passed, resulting in a p-value of 0.96. What can you conclude from this p-value given the data of the 175 parents is sufficient to perform a significance test for the hypotheses? (4 points) Part C: What possible defect in the study can you find in Part B? Explain. (3 points) 3. A study is performed involving two methods for removing harmful bacteria in 350 lakes in Florida. The lakes were treated randomly using one of two methods. Specifically, 150 were treated using Method A and 200 were treated using Method B. A total of 250 of the 350 lakes were bacteria-free after treatment, 95 from the Method A group and 155 from the Method B group. A significance test was performed for the following hypotheses and resulted in a p-value of 0.0018: H0: Bacteria removal rates are the same for Method A and B Ha: Method B has a higher bacteria removal rate Part A: Interpret the p-value in terms of the context. (3 points) Part B: Using a significance level of α = 0.05, what can you conclude from the context of this study? (4 points) Part C: Based on your conclusion in part B, which type of error—Type I or Type II—could have been made? What is one potential consequence of this error? (3 points) 4. A recent study of high school students shows the percentage of females and males who took advanced math courses. A simple random sample of high school students was interviewed. The students were asked whether they had taken an advanced math course. Of the 150 females, 53 answered yes, as did 89 of the 275 males. Part A: Construct and interpret a 98% confidence interval for the difference in population proportions of females and males who took advanced math courses. Be sure to state the parameter, check conditions, perform calculations, and make conclusion(s). (8 points) Part B: Does your interval from part A give convincing evidence of a difference between the population proportions? Explain. (2 points) 5. A survey of 450 randomly chosen US adults found that 35% of the 200 men and 40% of the 250 women attended a college football game during the past month. Do these data provide statistical evidence at the α = 0.01 level that men are more likely than women to attend football games? Be sure to state the parameter, check conditions, perform calculations, and make conclusion(s). (10 points)

A test of H0: p = 0.4 versus Ha: p > 0.4 has the test statistic z = 2.52.

Part A: What conclusion can you draw at the 5% significance level? At the 1% significance level? (6 points)

Part B: If the alternative hypothesis is Ha: p ≠ 0.4, what conclusion can you draw at the 5% significance level? At the 1% significance level? (4 points)

2. At a Clover City Council meeting, a plan to fund more sign language programs was presented. The reasoning behind the request was that less than 25% of parents with hearing-impaired children have the ability to pass a sign-language exam. If this is true, the council will agree to fund more programs for these parents. The council decides to take a 175-person volunteer sample of parents in Clover City that have children with auditory issues and conduct a significance test for H0: p = 0.25 and Ha: p < 0.25, where p is the proportion of these parents that can pass the sign language exam. They will perform the significance test at a significance level of α = 0.05 for the hypotheses.

Part A: Describe a Type II error that could occur. What impact could this error have on the situation? (3 points)

Part B: Out of the 175 volunteer parents of children with hearing problems, 54 passed, resulting in a p-value of 0.96. What can you conclude from this p-value given the data of the 175 parents is sufficient to perform a significance test for the hypotheses? (4 points)

Part C: What possible defect in the study can you find in Part B? Explain. (3 points)

3. A study is performed involving two methods for removing harmful bacteria in 350 lakes in Florida. The lakes were treated randomly using one of two methods. Specifically, 150 were treated using Method A and 200 were treated using Method B. A total of 250 of the 350 lakes were bacteria-free after treatment, 95 from the Method A group and 155 from the Method B group.

A significance test was performed for the following hypotheses and resulted in a p-value of 0.0018:

H0: Bacteria removal rates are the same for Method A and B
Ha: Method B has a higher bacteria removal rate

Part A: Interpret the p-value in terms of the context. (3 points)

Part B: Using a significance level of α = 0.05, what can you conclude from the context of this study? (4 points)

Part C: Based on your conclusion in part B, which type of error—Type I or Type II—could have been made? What is one potential consequence of this error? (3 points)

4. A recent study of high school students shows the percentage of females and males who took advanced math courses. A simple random sample of high school students was interviewed. The students were asked whether they had taken an advanced math course. Of the 150 females, 53 answered yes, as did 89 of the 275 males.

Part A: Construct and interpret a 98% confidence interval for the difference in population proportions of females and males who took advanced math courses. Be sure to state the parameter, check conditions, perform calculations, and make conclusion(s). (8 points)

Part B: Does your interval from part A give convincing evidence of a difference between the population proportions? Explain. (2 points)

5. A survey of 450 randomly chosen US adults found that 35% of the 200 men and 40% of the 250 women attended a college football game during the past month. Do these data provide statistical evidence at the α = 0.01 level that men are more likely than women to attend football games? Be sure to state the parameter, check conditions, perform calculations, and make conclusion(s). (10 points)

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Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Ivan Kochetkov

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Part A: With a test statistic of z = 2.52, we can reject the null hypothesis at the 5% significance level, but not at the 1% significance level. Therefore, we can conclude that there is evidence to suggest that the true proportion is greater than 0.4, but we Show more…

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A test of H0: p = 0.4 versus Ha: p > 0.4 has the test statistic z = 2.52. Part A: What conclusion can you draw at the 5% significance level? At the 1% significance level? (6 points) Part B: If the alternative hypothesis is Ha: p ≠ 0.4, what conclusion can you draw at the 5% significance level? At the 1% significance level? (4 points) 2. At a Clover City Council meeting, a plan to fund more sign language programs was presented. The reasoning behind the request was that less than 25% of parents with hearing-impaired children have the ability to pass a sign-language exam. If this is true, the council will agree to fund more programs for these parents. The council decides to take a 175-person volunteer sample of parents in Clover City that have children with auditory issues and conduct a significance test for H0: p = 0.25 and Ha: p < 0.25, where p is the proportion of these parents that can pass the sign language exam. They will perform the significance test at a significance level of α = 0.05 for the hypotheses. Part A: Describe a Type II error that could occur. What impact could this error have on the situation? (3 points) Part B: Out of the 175 volunteer parents of children with hearing problems, 54 passed, resulting in a p-value of 0.96. What can you conclude from this p-value given the data of the 175 parents is sufficient to perform a significance test for the hypotheses? (4 points) Part C: What possible defect in the study can you find in Part B? Explain. (3 points) 3. A study is performed involving two methods for removing harmful bacteria in 350 lakes in Florida. The lakes were treated randomly using one of two methods. Specifically, 150 were treated using Method A and 200 were treated using Method B. A total of 250 of the 350 lakes were bacteria-free after treatment, 95 from the Method A group and 155 from the Method B group. A significance test was performed for the following hypotheses and resulted in a p-value of 0.0018: H0: Bacteria removal rates are the same for Method A and B Ha: Method B has a higher bacteria removal rate Part A: Interpret the p-value in terms of the context. (3 points) Part B: Using a significance level of α = 0.05, what can you conclude from the context of this study? (4 points) Part C: Based on your conclusion in part B, which type of error—Type I or Type II—could have been made? What is one potential consequence of this error? (3 points) 4. A recent study of high school students shows the percentage of females and males who took advanced math courses. A simple random sample of high school students was interviewed. The students were asked whether they had taken an advanced math course. Of the 150 females, 53 answered yes, as did 89 of the 275 males. Part A: Construct and interpret a 98% confidence interval for the difference in population proportions of females and males who took advanced math courses. Be sure to state the parameter, check conditions, perform calculations, and make conclusion(s). (8 points) Part B: Does your interval from part A give convincing evidence of a difference between the population proportions? Explain. (2 points) 5. A survey of 450 randomly chosen US adults found that 35% of the 200 men and 40% of the 250 women attended a college football game during the past month. Do these data provide statistical evidence at the α = 0.01 level that men are more likely than women to attend football games? Be sure to state the parameter, check conditions, perform calculations, and make conclusion(s). (10 points)