STATSTISTICS

QUESTION 1

1. A user survey is completed by 35 individuals testing a new interface. They each score the interface on a 1 to 100 scale. The average score is 71 with a standard deviation of 4. The designer wants to test the hypothesis that the rating is above 70 with 95% confidence.  Which of these is the appropriate null hypothesis? (Ho: μ < 70 , Ho: μ ≥ 70 , Ho: μ < 72, or Ho: μ ≥ 72)  What z-value is calculated as the test statistic for this hypothesis?  What is the p-value associated with this z?  What is the decision? (fail to reject null hypothesis , reject null hypothesis)  With 95% confidence, is the mean greater than 70?

8 points   

QUESTION 2

1. A programmer has developed a random number generator that gives a normally distributed set of results based on an input population mean and population standard deviation. To test the program, he inputs a mean of 20 and a standard deviation of 5. He generates 14 random numbers with a sample mean of 21.7 and a sample deviation of 5. He wants to test with 95% confidence whether or not this sample has the correct mean of 20.  Which of these is the appropriate null hypothesis? (Ho: μ = 20 or Ho: μ =21.7)  What z-value is calculated as the test statistic for this hypothesis?  What is the p-value associated with this z?  What is the decision? (fail to reject null hypothesis or reject null hypothesis)  With 95% confidence based on this measurement, is the program working correctly? (yes or no)

8 points   

QUESTION 3

1. A performance specification requires a variance of less than 0.20 (σ2≤0.20). A sample of 15 batches have an average variance of 0.23 (s2=0.23). For a 90% confidence, is this sample out of spec?  Which of these is the appropriate null hypothesis? (Ho: μ = 0.20 , Ho: μ =0.23, Ho: σ2 = 0.20 or Ho: σ2 =0.23)  What is the chi-squared (χ2) cut-off value for rejecting the null hypothesis given n=15 and α=0.10?  What χ2-value is calculated as the sample statistic for this hypothesis?  What is the decision? (fail to reject null hypothesis or reject null hypothesis)  With 95% confidence based on this measurement, do these batches need to investigated for not meeting the variance spec?

8 points   

QUESTION 4

1. The table below gives process times for two different systems running a series of computation tasks. A system administrator wishes to utilize a t-test with 95% confidence to assess whether or not the two systems perform differently.

	Test A	Test B	Test C	Test D	Test E
System Alpha	45	92	21	33	74
System Beta	56	86	24	42	80

2. Are these samples independent, dependent, or paired?

	a.	independent
	b.	dependent
	c.	paired

2 points   

QUESTION 5

1. Fill in the remaining values in the difference table:

	Test A	Test B	Test C	Test D	Test E
Beta-Alpha Difference	11			9

3 points   

QUESTION 6

1. What is the t-statistic value for this test?

1 points   

QUESTION 7

1. What is the average difference?

1 points   

QUESTION 8

1. What is the standard deviation of the difference?

1 points   

QUESTION 9

1. What are the bounds of the 95% confidence interval for difference with values to the nearest tenth: _  ____≤ d ≤ _  ____.

2 points   

QUESTION 10

1. Based on this analysis, is there a significant difference between System Alpha and System Beta?

	a.	yes
	b.	no

1 points   

QUESTION 11

1. If testing the null hypothesis d=0 at 95% confidence, what is the resulting conclusion?

	a.	fail to reject null hypothesis
	b.	reject null hypothesis

1 points   

QUESTION 12

1. A hypothesis test wishes to assess the difference between two means for independent samples. Which equation gives the correct calculation for t for this test?

		Equation A
		Equation B
		Equation C
		Equation D