Hypothesis Testing on a Competency Template

The following table summarizes the different hypothesis test distributions and when each is used. Use this table when completing this Assessment.

Which Statistical Test Do I Use?
Test Requirement
Z Test
Normal distribution
Population mean known
Population standard deviation known
Sample size is greater than 30 if not normal
Quantitative variables
t Test Normal distribution
Population mean known
Population standard deviation unknown
Sample size is a) nearly normal with sample less than 15; b) at least 15 with no outliers; c) greater than 30 even if skewed or not normal
Quantitative variables
Chi Square Variables are qualitative
Testing if observed results agree with claimed (Goodness of Fit Unequal Frequencies)
Testing if outcomes occur with the same frequency (Goodness of Fit Equal Frequencies)
Testing if outcomes are independent of treatment (Goodness of Fit Test of Independence)
Used to test the relationship between variables
Data in two-way table of counts of outcomes
ANOVA Compares whether several populations have the same mean

Scenario 1: Presidential Ratings

College students are asked to rate two presidential candidates, Mr. Smith and Ms. Jones on how trustworthy their faces appear.The scale was zero to seven with zero being not at all trustworthy and seven being extremely trustworthy.Below are 29 ratings.Is there significant evidence at the 5% level that the mean rating is greater than 3.5 (a neutral rating)? Assume that this is a simple random sample of all U.S. college students.

2.6 3.2 4.7 3.3 3.4 3.6 3.7 3.9 3.9 4.1
4.2 4.9 5.7 4.2 3.9 3.2 4.1 5.0 5.0 4.6
4.6 3.9 3.9 2.8 2.6 3.0 3.3 3.7 5.3

Which type of test would you use, and why?
State the null and alternative hypothesis. Use Statdisk to solve the problem describing the steps that you used (options in Statdisk) and paste your results here. Write a conclusion statement.

Scenario 2: Weekly Births

Are births evenly distributed across the days of the week?A sample of 700 birth days was collected with the following results.

Day Sun. Mon. Tues. Wed. Thur. Fri. Sat.
Births 84 110 124 104 94 112 72

Test the hypothesis that the births are equally distributed across the days of the week using an alpha of 0.05.

Which type of test would you use, and why?
State the null and alternative hypothesis. Use Statdisk to solve the problem describing the steps that you used (options in Statdisk) and paste your results here. Write a conclusion statement.

 
Scenario 3: Nursing Job Satisfaction and Retention

A nursing magazine reported the results of a survey of more than 1800 nurses from across the country on job satisfaction and retention.Nurses from magnet hospitals (an award given by the American Nurses Credentialing Center to hospitals that satisfy a certain level of criteria designed to measure the strength and quality of nursing) describe staffing as follows:

Staffing Situation Percent
Short of help—patient care has suffered 12
Short of help—patient care hasn’t suffered 32
Adequate 38
More than adequate 12
Excellent 6

A survey of 500 nurses from non-magnet hospitals gave the following results.
Staffing Situation Number
Short of help—patient care has suffered 165
Short of help—patient care hasn’t suffered 140
Adequate 125
More than adequate 50
Excellent 20

Determine if the data indicates that the nurses from the non-magnet hospitals have a different distribution of opinions.
Use α = 0.05.

Which type of test would you use, and why?

State the null and alternative hypothesis. Use Statdisk to solve the problem describing the steps that you used (options in Statdisk) and paste your results below. Write a conclusion statement.

Scenario 4: Drug Effectiveness

To test the effectiveness of a new drug, a researcher gives one group of individuals the new drug and another group a placebo. The results of the study are shown below.At the 0.01 level of significance, can the researcher conclude that the drug is effective? In other words, are the results independent of the method of treatment?

Medication Effective Not Effective
Drug 32 9
Placebo 12 18

Which type of test would you use, and why?
State the null and alternative hypothesis. Use Statdisk to solve the problem describing the steps that you used (options in Statdisk) and paste your results here. Write a conclusion statement.

Scenario 5: Sodium Content

The amount of sodium (in milligrams) in one serving for a random sample of three different foods is listed in the table below.At the 0.10 level of significance, is there sufficient evidence to conclude that a difference in mean sodium amounts exists among the condiments, cereals, and desserts?

Condiments Cereal Desserts
270 260 100
130 220 180
230 290 250
180 290 250
80 200 300
70 320 360
200 140 300

Which type of test would you use, and why?
State the null and alternative hypothesis. Use Statdisk to solve the problem describing the steps that you used (options in Statdisk) and paste your results here. Write a conclusion statement.