Hypothesis Testing3. The director of admissions at the University of Maryland, University College is concerned about the high cost of textbooks for the students each semester. A sample of 45 students enrolled in the university indicates that X (bar) = $285.4 and s = $42.20.a. Using the 0.05 level of significance, is there evidence that the population mean is above $300?b. What is your answer in (a) if s = $90 and the 0.10 level of significance is used?c. What is your answer in (a) if X (bar) = $310.10 and s = $40.20?d. Based on the information in part (a), what decision should the director make about the books used for the courses if the goal is to keep the cost below $300?

3. The director of admissions at the University of Maryland, University College is concerned about the high cost of textbooks for the students each semester. A sample of 45 students enrolled in the…

 

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Hypothesis Testing

For each of the following three research scenarios:

a) state the null hypothesis

b) specify whether a one- or a two-tailed test was used

1. A study on the gender income gap among older adults where the main researcher believes that the

average income of elderly women is lower than the average income of elderly men.

2. A survey-based study trying to determine if there is a difference in the amount of study time oncampus

and off-campus students devote to their schoolwork during an average week.

3. A study testing that stress (measured on an ordinal scale) is lower for adults who own dogs (or other

pets) than for non-pet owners.

4. What is the difference between a Type I error and a Type II error?

5. If a two-tailed probability is 0.07, what is the one-tailed probability if the effect were in the specified

direction?

6. True or False: it is easier to reject the null hypothesis using an alpha of 0.05 than an alpha of 0.01.

7. True or False: it is easier to reject the null with a two-tailed test than with a one-tailed test using the

same confidence level.

 

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Student Profile

You are a statistician working for a drug company. A few new scientists have been hired by your company. They are experts in pharmacology, but are not experts in doing statistical studies, so you will explain to them how statistical studies are done when testing two samples for the effectiveness of a new drug. The two samples can be dependent or independent, and you will explain the difference.

Concept being Studied

Your focus is on hypothesis tests and confidence intervals for two populations using two samples, some of which are independent and some of which are dependent. These concepts are an extension of hypothesis testing and confidence intervals which use statistics from one sample to make conclusions about population parameters.

What to Submit

To complete this assignment, you must first download the worksheet and then complete it.

You will also develop a PowerPoint presentation for the newly hired scientists on these topics, and you have been asked to provide two real-life examples that you will describe step-by-step. Your boss has asked you to include the following slides:

Slide 1: Title slide

Slide 2: Describes the two differences between independent and dependent samples

Slide 3: Provides an example of independent samples when testing a new drug

Slide 4: Shows how to set up a hypothesis test for two independent proportions: One to test whether they are equal and another one to test whether one proportion is larger than the other

Slide 5: Shows the formula for the test statistic for two independent proportions and lists what each variable in the formula represents

Slide 6: Shows the formula for the margin of error (E) when doing a confidence interval on two proportions and explains what each variable stands for

Slide 7: Other than proportions, describes what other types of hypothesis tests can be done for two independent samples

Slide 8: Provides an example of dependent samples (also known as matched pairs) when testing a new drug. The two samples should be a before and after test with the same group

Slide 9: Shows the t formula for the test statistic for matched pairs and explains what each variable represents

Slide 10: Show what a confidence interval for matched pairs would look like using only variables. Also, include the formula for the Margin of Error and state what each variable represents

To show the formulas above, you may need to use the following variables which you can copy from here:

x̅, p̂, q̂, p̅, q̅, d̅, ∑, μ, σ, σ2, α

 

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a. Suppose the price or cost of hiring a security guard increases from $450 to $600 per week.

 Using the data in Table above, show how this will affect the Lindahl equilibrium.

b. Use the data above to show how a decrease in the demand for security protection by any one voter will affect the Lindahl equilibrium.

—Hypothetical Marginal Benefits of Security Protection for a Community of Three People + av. Suppose the price or cost of hiring a security guard increases from $450 to $600 per week. Using the data in Table above, Show how this will affect the Lindahl equilibrium. In. Use the data above to Show how a decrease in the demand for security protection by any one NURIBER OF SECURITY GUARDS PER WEEK 1 $300$250$200$750 2 $250$200$150$600 voter will affect the Lindahl equilibrium. 3 $200$150$100$450 4$150$100$50 $300 L

 

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