# Hypothesis Testing and Type Errors Module 5 Case (Math Problem Sample)

# Module 5 - Case

## Hypothesis testing and type errors

### Case Assignment

**By submitting this assignment, you affirm that it contains all original work, and that you are familiar with Trident University’s Academic Integrity policy in the Trident ****Policy Handbook****. You affirm that you have not engaged in direct duplication, copy/pasting, sharing assignments, collaboration with others, contract cheating and/or obtaining answers online, paraphrasing, or submitting/facilitating the submission of prior work. Work found to be unoriginal and in violation of this policy is subject to consequences such as a failing grade on the assignment, a failing grade in the course, and/or elevated academic sanctions. You affirm that the assignment was completed individually, and all work presented is your own.**

Problems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible.

**Answer the following problems showing your work and explaining (or analyzing) your results.**

- Explain Type I and Type II errors. Use an example if needed.
- Explain a one-tailed and two-tailed test. Use an example if needed.
- Define the following terms in your own words.
- Null hypothesis
- P-value
- Critical value
- Statistically significant

- A homeowner is getting carpet installed. The installer is charging her for 250 square feet. She thinks this is more than the actual space being carpeted. She asks a second installer to measure the space to confirm her doubt. Write the null hypothesis H
_{o}and the alternative hypothesis H_{a}. - Drug A is the usual treatment for depression in graduate students. Pfizer has a new drug, Drug B, that it thinks may be more effective. You have been hired to design the test program. As part of your project briefing, you decide to explain the logic of statistical testing to the people who are going to be working for you.
- Write the research hypothesis and the null hypothesis.
- Then construct a table like the one below, displaying the outcomes that would constitute Type I and Type II error.
- Write a paragraph explaining which error would be more severe, and why.

- Cough-a-Lot children’s cough syrup is supposed to contain 6 ounces of medicine per bottle. However since the filling machine is not always precise, there can be variation from bottle to bottle. The amounts in the bottles are normally distributed with σ = 0.3 ounces. A quality assurance inspector measures 10 bottles and finds the following (in ounces):

5.95 | 6.10 | 5.98 | 6.01 | 6.25 | 5.85 | 5.91 | 6.05 | 5.88 | 5.91 |

Are the results enough evidence to conclude that the bottles are not filled adequately at the labeled amount of 6 ounces per bottle?

- State the hypothesis you will test.
- Calculate the test statistic.
- Find the P-value.
- What is the conclusion?

- Calculate a Z score when X = 20, μ = 17, and σ = 3.4.
- Using a standard normal probabilities table, interpret the results for the Z score in Problem 7.
- Your babysitter claims that she is underpaid given the current market. Her hourly wage is $12 per hour. You do some research and discover that the average wage in your area is $14 per hour with a standard deviation of 1.9. Calculate the Z score and use the table to find the standard normal probability. Based on your findings, should you give her a raise? Explain your reasoning as to why or why not.
- Tutor O-rama claims that their services will raise student SAT math scores at least 50 points. The average score on the math portion of the SAT is μ = 350 and σ = 35. The 100 students who completed the tutoring program had an average score of 385 points. Is the average score of 385 points significant at the 5% level? Is it significant at the 1% level? Explain why or why not.

Module 5 Case

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Answer the following problems showing your work and explaining (or analyzing) your results.

Explain Type I and Type II errors. Use an example if needed.

The Type I error (false positive) occurs when one wrongly rejects a true null hypothesis, and it signifies the level of significance that a researcher is willing to risk when they reject the null hypothesis. For instance, concluding that a blood sample has hepatitis C, while it does not.

The Type II error (false negative) is made when one accepts a false null hypothesis. For instance, blood tests that shows that a patient does not have hepatitis C, while in reality they are infected is a false negative.

Explain a one-tailed and two-tailed test. Use an example if needed.

The one-tailed test is based on a directional hypothesis of an effect being studied, and is on one side of the normal distribution after having identified the critical value and level of significance. For instance, testing two samples and determining whether one has a higher mean than the other.

In the two-tailed test, after identifying the critical region, there are two tails of the distribution. For instance, a hypothesis test determining whether two mean samples are either from the same or different populations.

Define the following terms in your own words.

Null hypothesis- This is the general proposition that there is no relationship between a dependent and independent variable.

P-value- This is a probability measure that determines the strength of evidence for which to reject the null hypothesis.

Critical value- This is a value of the test statistics beyond which the null hypothesis is invalid. It is necessary to determine whether to accept or reject the null hypothesis by comparing results between the calculated value and the critical value.

Statistically significant- This indicates that a finding of a sample compared to the population is unlikely to have been experienced merely by chance.

A homeowner is getting carpet installed. The installer is charging her for 250 square feet. She thinks this is more than the actual space being carpeted. She asks a second installer to measure the space to confirm her doubt. Write the null hypothesis Ho and the alternative hypothesis Ha.

Null hypothesis Ho: The space = for 250 square feet

Alternative hypothesis Ha: The space is < for 250 square feet

Drug A is the usual treatment for depression in graduate students. Pfizer has a new drug, Drug B, that it thinks may be more effective. You have been hired to design the test program. As part of your project briefing, you decide to explain the logic of statistical testing to the people who are going to be working for you.

Write the research hypothesis and the null hypothesis.

N...

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