Question

Part 1A: A machine in a factory is supposed to fill vials with approximately 50 mL of a liquid. The quality control manager wants to test whether the machine is working properly. If the machine is found to be over or under-filling, then the assembly line will need to be shut down so that it can be recalibrated. a. State the Null and Alternative Hypotheses to the scenario using the correct symbols. Null Hypothesis (H0): The machine is working properly and filling vials with approximately 50 mL of liquid. Alternative Hypothesis (Ha): The machine is not working properly and is either over-filling or under-filling the vials. b. What would it mean to make a Type 1 error in this situation? Making a Type 1 error would mean rejecting the null hypothesis when it is actually true. In this scenario, it would mean concluding that the machine is not working properly and shutting down the assembly line for recalibration, even though the machine is actually filling the vials with approximately 50 mL of liquid. c. What would it mean to make a Type 2 error in this situation? Making a Type 2 error would mean failing to reject the null hypothesis when it is actually false. In this scenario, it would mean not shutting down the assembly line for recalibration, even though the machine is either over-filling or under-filling the vials. d. Why might it be worse to make a Type 1 error in this scenario? Making a Type 1 error in this scenario would result in unnecessary shutdowns of the assembly line for recalibration, which can be costly in terms of time and resources. It may disrupt the production process and lead to delays or inefficiencies. e. Suppose that we fail to reject the null hypothesis. Write a conclusion statement in the context of the problem. Assume no errors were made. Based on the data and analysis, we fail to reject the null hypothesis. This suggests that the machine is working properly and filling the vials with approximately 50 mL of liquid. No further action or recalibration is required at this time. Part 1B: The proportion of Americans who have frequent migraines is 15.2% according to the CDC. An acupuncturist claims that her treatment can reduce this figure significantly. A random sample of 315 Americans is administered the acupuncturist's treatment, and 35 report experiencing migraines. a. State Hypotheses to the scenario using the correct symbols. Null Hypothesis (H0): The acupuncturist's treatment does not significantly reduce the proportion of Americans who have frequent migraines. Alternative Hypothesis (Ha): The acupuncturist's treatment significantly reduces the proportion of Americans who have frequent migraines. b. What is the sample proportion? (Round to 2 decimal places) p^ = 35/315 = 0.11 c. Suppose the P-value is calculated to be 0.0332. What would your decision be for this test using α = 0.025? (multiple choice) 3. reject the null d. Write a conclusion in terms of the acupuncturist's claim. Use the model provided by the instructor. Assume no errors were made. Based on the analysis and the calculated P-value of 0.0332, which is less than the significance level of α = 0.025, we reject the null hypothesis. This provides evidence to support the acupuncturist's claim that her treatment significantly reduces the proportion of Americans who have frequent migraines.

Name: part 1a a machine in a factory is supposed to fill vials with approximately 50ml of a liquid the quality control manager wants to test whether the machine is working properly if the machine 38876
Uploaded: 2023-09-03T19:53:11-08:00
Duration: 5 min 42 s
Channel: Kari Hasz
Description: part 1a a machine in a factory is supposed to fill vials with approximately 50ml of a liquid the quality control manager wants to test whether the machine is working properly if the machine 38876

a. State the Null and Alternative Hypotheses to the scenario using the correct symbols.

Null Hypothesis (H0): The machine is working properly and filling vials with approximately 50 mL of liquid.
Alternative Hypothesis (Ha): The machine is not working properly and is either over-filling or under-filling the vials.

b. What would it mean to make a Type 1 error in this situation?

Making a Type 1 error would mean rejecting the null hypothesis when it is actually true. In this scenario, it would mean concluding that the machine is not working properly and shutting down the assembly line for recalibration, even though the machine is actually filling the vials with approximately 50 mL of liquid.

c. What would it mean to make a Type 2 error in this situation?

Making a Type 2 error would mean failing to reject the null hypothesis when it is actually false. In this scenario, it would mean not shutting down the assembly line for recalibration, even though the machine is either over-filling or under-filling the vials.

d. Why might it be worse to make a Type 1 error in this scenario?

Making a Type 1 error in this scenario would result in unnecessary shutdowns of the assembly line for recalibration, which can be costly in terms of time and resources. It may disrupt the production process and lead to delays or inefficiencies.

e. Suppose that we fail to reject the null hypothesis. Write a conclusion statement in the context of the problem. Assume no errors were made.

Based on the data and analysis, we fail to reject the null hypothesis. This suggests that the machine is working properly and filling the vials with approximately 50 mL of liquid. No further action or recalibration is required at this time.

Part 1B:
The proportion of Americans who have frequent migraines is 15.2% according to the CDC. An acupuncturist claims that her treatment can reduce this figure significantly. A random sample of 315 Americans is administered the acupuncturist's treatment, and 35 report experiencing migraines.

a. State Hypotheses to the scenario using the correct symbols.

Null Hypothesis (H0): The acupuncturist's treatment does not significantly reduce the proportion of Americans who have frequent migraines.
Alternative Hypothesis (Ha): The acupuncturist's treatment significantly reduces the proportion of Americans who have frequent migraines.

b. What is the sample proportion? (Round to 2 decimal places)

p^ = 35/315 = 0.11

c. Suppose the P-value is calculated to be 0.0332. What would your decision be for this test using α = 0.025? (multiple choice)

3. reject the null

d. Write a conclusion in terms of the acupuncturist's claim. Use the model provided by the instructor. Assume no errors were made.

Based on the analysis and the calculated P-value of 0.0332, which is less than the significance level of α = 0.025, we reject the null hypothesis. This provides evidence to support the acupuncturist's claim that her treatment significantly reduces the proportion of Americans who have frequent migraines.

Added by Olivia J.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Kari Hasz

09/03/2023

Step 1

Null hypothesis: The machine fills vials with approximately 50mL of liquid (μ = 50mL). Alternative hypothesis: The machine does not fill vials with approximately 50mL of liquid (μ ≠ 50mL). b. Making a Type 1 error in this situation would mean rejecting the null Show more…

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Part 1A: A machine in a factory is supposed to fill vials with approximately 50 mL of a liquid. The quality control manager wants to test whether the machine is working properly. If the machine is found to be over or under-filling, then the assembly line will need to be shut down so that it can be recalibrated. a. State the Null and Alternative Hypotheses to the scenario using the correct symbols. Null Hypothesis (H0): The machine is working properly and filling vials with approximately 50 mL of liquid. Alternative Hypothesis (Ha): The machine is not working properly and is either over-filling or under-filling the vials. b. What would it mean to make a Type 1 error in this situation? Making a Type 1 error would mean rejecting the null hypothesis when it is actually true. In this scenario, it would mean concluding that the machine is not working properly and shutting down the assembly line for recalibration, even though the machine is actually filling the vials with approximately 50 mL of liquid. c. What would it mean to make a Type 2 error in this situation? Making a Type 2 error would mean failing to reject the null hypothesis when it is actually false. In this scenario, it would mean not shutting down the assembly line for recalibration, even though the machine is either over-filling or under-filling the vials. d. Why might it be worse to make a Type 1 error in this scenario? Making a Type 1 error in this scenario would result in unnecessary shutdowns of the assembly line for recalibration, which can be costly in terms of time and resources. It may disrupt the production process and lead to delays or inefficiencies. e. Suppose that we fail to reject the null hypothesis. Write a conclusion statement in the context of the problem. Assume no errors were made. Based on the data and analysis, we fail to reject the null hypothesis. This suggests that the machine is working properly and filling the vials with approximately 50 mL of liquid. No further action or recalibration is required at this time. Part 1B: The proportion of Americans who have frequent migraines is 15.2% according to the CDC. An acupuncturist claims that her treatment can reduce this figure significantly. A random sample of 315 Americans is administered the acupuncturist's treatment, and 35 report experiencing migraines. a. State Hypotheses to the scenario using the correct symbols. Null Hypothesis (H0): The acupuncturist's treatment does not significantly reduce the proportion of Americans who have frequent migraines. Alternative Hypothesis (Ha): The acupuncturist's treatment significantly reduces the proportion of Americans who have frequent migraines. b. What is the sample proportion? (Round to 2 decimal places) p^ = 35/315 = 0.11 c. Suppose the P-value is calculated to be 0.0332. What would your decision be for this test using α = 0.025? (multiple choice) 3. reject the null d. Write a conclusion in terms of the acupuncturist's claim. Use the model provided by the instructor. Assume no errors were made. Based on the analysis and the calculated P-value of 0.0332, which is less than the significance level of α = 0.025, we reject the null hypothesis. This provides evidence to support the acupuncturist's claim that her treatment significantly reduces the proportion of Americans who have frequent migraines.