Montgomery College Probability Null Hypothesis Statistics

Completely solve and answer each problem. Use technology when directed to. Submit completed assignment as a document or spreadsheet file in one of the following formats (.pdf .doc .docx .xls. xlsx)

Problem 1 (15 points possible – 3 points for each part)

a. Two hypotheses with correct symbols and numbers

b. Correct application of type 1 error to this situation

c. Correct application of type 2 error to this situation

d. Explanation of why part b could be worse than part c

e. Correct interpretation of the decision “fail to reject the null” in the context given

Problem 2 (15 points possible)

a. Two hypotheses with correct symbols and numbers (4.5 points)

b. Automatically graded (1.5 points)

c. Automatically graded (4.5 points)

d. Correct interpretation of the decision in part c in the context given (4.5 points)

Experience 11&12 – Hypothesis Testing

A machine in a factory is supposed to fill vials with approximately 50mL of a liquid. The quality control manager wants to test whether the machine is working properly. If the machine is found to be over or under-filling then the assembly line will need to be shut down so that it can be re-calibrated.

a. State the Null and Alternative Hypotheses to the scenario using the correct symbols

Note: You can access special symbols by clicking on the button.

b. What would it mean to make a Type 1 error in this situation?

c. What would it mean to make a Type 2 error in this situation?

d. Why might it be worse to make a Type 1 error in this scenario?

e. Suppose that we fail to reject the null hypothesis. Write a conclusion statement in the context of the problem. Assume no errors were made.

Question 2

The proportion of Americans who have frequent migraines is 15.2% according to the CDC. An acupuncturist claims that her treatment can reduce this figure significantly. A random sample of 465 Americans is administered the acupuncturists treatment and 51 report experiencing migraines.

a. State Hypotheses to the scenario using the correct symbols.

b. What is the sample proportion? (Round to 2 decimal places) ˆp=

c. Suppose the P-value is calculated to be 0.0052

What would your decision be for this test using ?=?= 0.05?

• accept the null
• reject the null
• fail to reject the null

d. Write a conclusion in terms of the acupuncturist’s claim. Use the model provided by the instructor. Assume no errors were made.

You are conducting a study to see if the proportion of men over 50 who regularly have their prostate examined is significantly different from 0.2. You use a significance level of ?=0.002?=0.002.

H0_p=0.2
H1:p?0.2

You obtain a sample of size n=745n=745 in which there are 181 successes.

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

The p-value is…

• less than (or equal to) ??
• greater than ??

This p-value leads to a decision to…

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that…

• There is sufficient evidence to warrant rejection of the claim that the proportion of men over 50 who regularly have their prostate examined is different from 0.2.
• There is not sufficient evidence to warrant rejection of the claim that the proportion of men over 50 who regularly have their prostate examined is different from 0.2.
• The sample data support the claim that the proportion of men over 50 who regularly have their prostate examined is different from 0.2.
• There is not sufficient sample evidence to support the claim that the proportion of men over 50 who regularly have their prostate examined is different from 0.2.

You wish to test the following claim (Ha) at a significance level of ?=0.10

Ho: ?=57.5
Ha: ??57.5

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=28 with mean M=59.8 and a standard deviation of SD=10.1

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

The p-value is…

• less than (or equal to) ?
• greater than ?

This p-value leads to a decision to…

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that…

• There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 57.5.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 57.5.
• The sample data support the claim that the population mean is not equal to 57.5.
• There is not sufficient sample evidence to support the claim that the population mean is not equal to 57.5.