Assignment -No Plagiarism PLEASE read before accepting assignment. Assignment is Due Sunday, October 18, 2015 by 1pm EST

Hypothesis Testing Proportions

A survey of the morning beverages shows that the primary breakfast beverage or 17% of Americans is milk. A milk producer in Wisconsin, where milk is plentiful, believes that the figure is higher for Wisconsin. To test this idea, she contacts a random sample of 550 Wisconsin residents and asked them which primary beverage they consume for breakfast that day area close 115 replied that milk was the primary beverage. Using a level of significance of .05, test the idea that milk figure is higher in Wisconsin.

Minitab Output

Test of p = 0.17 vs p > 0.17

95%

Lower

Sample X N Sample p Bound Z-Value P-Value

1 115 550 0.209091 0.180569 2.44 0.007

Problem Statement:

HO:

H1

Decision Rule

Test Statistic:

Decision

Notes:

Answer

HO: Proportion who drink milk is less than or equal to 17%

H1: Proportion who drink milk is greater than 17%

Decision Rule: If the probability value calculated is less than .05, we will reject the null hypothesis

Test Statistic: .007

Decision: Since the probability value calculated of .007 is less than the critical value of .05, we will reject the null hypothesis and conclude that there is strong evidence that the people living in Wisconsin consume more milk than the national average.

Plagiarism

Given the advent of online paper sources, an instructor finds that two sections of the paper word for word from the source and that the total count of 176 words out of the 1,000 word paper match identical as well. The rule of thumb is that 15% or less matching on papers sent to plagiarism.com and other cites is acceptable and not considered plagiarism. Did the student plagiarize?

HO :

H1:

Decision Rule:

Test Stat.

Decision;

Test and CI for One Proportion

Test of p = 0.15 vs p > 0.15

95% Lower

Sample X N Sample p Bound Z-Value P-Value

1 176 1000 0.176000 0.156192 2.30 0.011

Given the advent of online paper sources, an instructor finds that two sections of the paper word for word from the source and that the total count of 176 words out of the 1,000 word paper match identical as well. The rule of thumb is that 15% or less matching on papers sent to plagiarism.com and other cites is acceptable and not considered plagiarism. Did the student plagiarize?

HO : Word count is less than or equal to 15%

H1: Word count exceeds 15%

Decision Rule: If the p value calculated is less than .05, reject HO

Test Stat. P value .011

Decision; Since the p value calculated of .011 is less than .05, we reject HO and conclude there is enough evidence to warrant a plagiarism sanction.

Test and CI for One Proportion

Test of p = 0.15 vs p > 0.15

95% Lower

Sample X N Sample p Bound Z-Value P-Value

1 176 1000 0.176000 0.156192 2.30 0.011

Two Sample Proportions

Americans drink or use milk with various meals and dishes. A recent poll in California and Wisconsin seems to indicate that people living in California consume different levels of milk at breakfast. To test this idea, she contacts a random sample of 550 people in California and105 replied they drank milk at breakfast where as 550 Wisconsin residents and asked them which primary beverage they consume for breakfast that day area close 115 replied that milk was the primary beverage. Using a level of significance of .05, test the idea that milk figure is higher in Wisconsin than in California.

HO :

H1:

Decision Rule:

Test Stat.

Decision;

Difference = p (1) - p (2)

Estimate for difference: 0.0181818

95% lower bound for difference: -0.0214833

Test for difference = 0 (vs > 0): Z = 0.75 P-Value = 0.225

Fisher's exact test: P-Value = 0.249

Americans drink or use milk with various meals and dishes. A recent poll in California and Wisconsin seems to indicate that people living in California consume different levels of milk at breakfast. To test this idea, she contacts a random sample of 550 people in California and105 replied they drank milk at breakfast where as 550 Wisconsin residents and asked them which primary beverage they consume for breakfast that day area chose 115 replied that milk was the primary beverage. Using a level of significance of .05, test the idea that milk figure is higher in Wisconsin than in California.

HO : Wisconsin Rate is less than or equal to California Rate

H1: Wisconsin Rate is greater than California Rate

Decision Rule: If P calculated is less than .05, reject HO

Test Stat. P calculated is .225

Decision; Since the probability value calculated of .225 is larger than .05 level of significance, we fail to reject the HO and conclude we have strong evidence that the rate of milk drinkers in Wisconsin is less than or equal to California.

Difference = p (1) - p (2)

Estimate for difference: 0.0181818

95% lower bound for difference: -0.0214833

Test for difference = 0 (vs > 0): Z = 0.75 P-Value = 0.225

Fisher's exact test: P-Value = 0.249

Minitab Directions

Step 1: choosing the test

Start by clicking on Basic Stats, then since we are doing a one sample proportion, we choose one sample proportion.

Step 2

Location of Data

Since our data is summarized, we choose the summarize data and that allows us to enter the data

Step 3

Enter Data

You enter in the summarized data with

Number of Trials: In this case it is the total number of people surveyed

Number of Events: This is the number of success, in this case the people who drink milk

Step 3

Set Test Parameters

Level of Significance: You set the level of significance by changing the value in the confidence interval box, thus a .05 level of significance equates with a 95% confidence interval.

Test Proportion: This is where the null hypothesis value is entered, in this case it is the 17% which is the national average for milk drinkers.

Alternative: This is where you enter the alternative hypothesis H1

Step 4

Test Results

Two Proportion Test

Step One

Step Two

The key point is to know your HO and H1 prior to entering numbers in first and second. Since we are comparing Wisconsin (115/550) is greater than California (105/550) we enter it first.

HO: Wisconsin is less than or equal to California

H1: Wisconsin is greater than California

Step Three

H1 Is greater than, then click OK.

Megastat for Single Proportion

Step one

Select Single Proportion Test

· Click on Add Ins

· Choose megastat

· Choose Hypothesis test

· Choose Proportion versus hypothesized value

Step Two

Enter in the number of success and trials

· You will enter in the number of successes

· Enter in the number of trials

· Enter in the proportion you are using in the test.

· Enter in the H1

· Choose a level of significance

· A survey of the morning beverages shows that the primary breakfast beverage or 17% of Americans is milk. A milk producer in Wisconsin, where milk is plentiful, believes that the figure is higher for Wisconsin. To test this idea, she contacts a random sample of 550 Wisconsin residents and asked them which primary beverage they consume for breakfast that day area close 115 replied that milk was the primary beverage. Using a level of significance of .05, test the idea that milk figure is higher in Wisconsin.

Step Three

Output

Hypothesis test for proportion vs hypothesized value
	Observed	Hypothesized
	0.2091	0.17	p (as decimal)
	115/550	94/550	p (as fraction)
	115.	93.5	X
	550	550	n
		0.016	std. error
		2.44	z
		.0073	p-value (one-tailed, upper)

Megastat for Two Proportion Test

Step one

Select Compare Two Independent Proportions

· Click on Add Ins

· Choose megastat

· Choose Hypothesis test

· Choose Two Independent Proportions

Step Two

Enter in the number of success and trials

Americans drink or use milk with various meals and dishes. A recent poll in California and Wisconsin seems to indicate that people living in California consume different levels of milk at breakfast. To test this idea, she contacts a random sample of 550 people in California and105 replied they drank milk at breakfast where as 550 Wisconsin residents and asked them which primary beverage they consume for breakfast that day area chose 115 replied that milk was the primary beverage. Using a level of significance of .05, test the idea that milk figure is higher in Wisconsin than in California. Be sure to enter group one for the first proportion listed in your HO statement and use group 2 for the second group in your HO

HO : Wisconsin Rate is less than or equal to California Rate

H1: Wisconsin Rate is greater than California Rate

Decision Rule: If P calculated is less than .05, reject HO

Results

Hypothesis test for two independent proportions
	p1	p2	pc
	0.2091	0.1909	0.2	p (as decimal)
	115/550	105/550	220/1100	p (as fraction)
	115.	105.	220.	X
	550	550	1100	n
		0.0182	difference
		0.	hypothesized difference
		0.0241	std. error
		0.75	z
		.2255	p-value (one-tailed, upper)

HO : Wisconsin Rate is less than or equal to California Rate

H1: Wisconsin Rate is greater than California Rate

Decision Rule: If P calculated is less than .05, reject HO

Test Stat. P calculated is .225

Decision; Since the probability value calculated of .225 is larger than .05 level of significance, we fail to reject the HO and conclude we have strong evidence that the rate of milk drinkers in Wisconsin is less than or equal to California.

Start with basic stats

1 sample proportion

Total amount surveyed

Success

P value

Choose 2 Proportions

2nd in H1

First in H1

H1 setting

Proportion vs hypothesized value

Level of significance

H1

Hypothesized proportion

# of trials

# of success

Two independent proportions

California

Wisconsin