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Engineering Probability and Inference Homework 6 The dynamic modulus of concrete is obtained for two different concrete mixes

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Engineering Probability and Inference Homework 6

1. The dynamic modulus of concrete is obtained for two different concrete mixes. For the first mix, 13 samples yielded a mean of 115.1 and a standard deviation of 0.47. For the second mix, 16 samples yielded a mean of 114.6 and a standard deviation of 0.38.

1. Use a 0.05 significance level to test if the two mixes have the same average dynamic modulus. Make sure you test the variances first and then use the appropriate test of means.
2. Find a 95% confidence interval for the variance of the second mix.
3. Find a 90% confidence interval for the mean dynamic modulus of the second mix.

 

2. The following data come from a study in which random samples of employees of three government agencies were asked questions about their retirement plan.

 

	Agency 1	Agency 2	Agency 3
For the plan	67	84	109
Against the plan	33	66	41

 

 

1. Use a 0.01 significance level to test the claim that the actual proportions of employees favoring the retirement plan are the same for the three agencies.
2. Find a 90% confidence interval for the proportion of employees favoring the retirement plan for the third agency.

 

3. The following data pertain to the amount of hydrogen present, y, in parts per million in core drillings made at 1-foot intervals along the length of a vacuum-cast ingot, x, core location in feet from base.

 

x	1	3	4	6	8	9	10
Y	1.28	1.83	2.75	2.09	3.21	3.89	3.49

 

1. Do the data provide sufficient evidence to indicate that the slope is not 0? Use a significance level of 0.05.
2. Calculate the correlation coefficient for the data.
3. Calculate Spearman’s Rank correlation coefficient for the data.

 

 

 

4. The following are the numbers of mistakes made in 5 successive days for 4 technicians working for a photo lab.

 

Technician
1	6	14	10	8	11
2	14	9	12	10	14
3	10	12	7	15	11
4	9	12	8	10	11

 

Use a 0.05 significance level to test whether the 4 technicians have the same mean number of mistakes. Construct the full ANOVA table. Which test is this?

 

 

 

5. Three different disinfecting solutions are being compared to study their effectiveness in stopping the growth of bacteria in milk containers. Because days could represent a potential source of variability, the experimenter decides to use the days as blocks. Observations are taken for four days. The inside of the milk containers are covered with a certain amount of bacteria. The response is the percentage of bacteria remaining after rinsing the container with a disinfecting solution. Use a 0.01 significance level to test if there is a difference in three solutions. Construct the full ANOVA table.

 

	Day
Solution	1	2	3	4
A	13	22	18	39
B	16	24	17	44
C	5	8	11	22