Question: 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
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.
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.
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 helppatient care has suffered
12
Short of helppatient 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 helppatient care has suffered
165
Short of helppatient 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 = 0.05.
Which type of test would you use, and why?
State the null and alternative hypothesis.
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.
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.
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