# Hypothesis Testing and Type Errors (Math Problem Sample)

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 Ho and the alternative hypothesis Ha.

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.

State of the World

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 HYPOTHESIS TESTING AND TYPE ERRORS

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

Type I error (false-positive) - This is an incorrect judgment made when one rejects a null hypothesis that is true.

Type II error (false-negative) - This is an incorrect judgment made when one fails to reject a null hypothesis that is not true

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

In hypothesis testing, when a proposition identifies the direction of the difference it is a one-tailed test. One has either to accept or reject one tail of the normal distribution. For instance, if one receives 20 calls per month, then it is possible to test whether the call volume is above 20 calls per month. On the other hand, when there is no emphasis on direction of difference, then the hypothesis test performed is a to-tailed test. In the call example if the hypothesis is to test whether the call volume is above or below 20 calls per month, then this is a tow-tailed test.

Define the following terms in your own words.

Null hypothesis- This is the default hypothesis that a prediction has no difference between two variables. The rejection or acceptance of a null hypothesis forms the basis to establish whether a relationship exists.

P-value- This represents the probability that represents the plausibility of the null hypothesis being true.

Critical value- This represents the level of significance that determines whether the evidence is strong enough to accept the null hypothesis.

Statistically significant- This is the likelihood that the relationship between variables is caused by other factors and not random chance, and it is established through statistical hypothesis.

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.

Ho- The space being carpeted is 250 square feet

Ha –The space being carpeted is less than 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.

Ho- There is no difference between effectiveness of Drug B and Drug A

Ha – The effectiveness of Drub B is better compared to Drug A

Then construct a table like the one below, displaying the outcomes that would constitute Type I and Type II error.

Actual Drug effectivenessNo d...

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