Estimate the mean coil characteristic for all machines

Assignment Help Applied Statistics

Reference no: EM132294032

Assignment -

Instructions: Solve all problems.

Problem 1 - Annual dues

The board of directors of a professional association conducted a random sample survey of 30 members to assess the effects of several possible amounts of dues increase. The sample results follow. X denotes the dollar increase in annual dues posited in the survey interview, and Y = 1 if the interviewee indicated that the membership will not be renewed at that amount of dues increase and 0 if the membership will be renewed.

i:	1	2	3	. . .	28	29	30
X_i:	30	30	30	. . .	49	50	50
Y_i:	0	1	0	. . .	0	1	1

Logistic regression model is assumed to be appropriate.

a. Find the maximum likelihood estimates of β₀ and β₁. State the fitted response function.

b. Obtain a scatter plot of the data with both the fitted logistic response function from part (a) and a lowess smooth superimposed. Does the fitted logistic response function appear to fit well?

c. Obtain exp(b₁) and interpret this number.

d. What is the estimated probability that association members will not renew their membership if the dues are increased by $40?

e. Estimate the amount of dues increase for which 75 percent of the members are expected not to renew their association membership.

Problem 2 - Coil winding machines

A plant contains a large number of coil winding machines. A production analyst studied a certain characteristic of the wound coils produced by these machines by selecting four machines at random and then choosing 10 coils at random from the day's output of each selected machine. The results follow.

	j
i	1	2	3	4	5	6	7	8	9	10
1	205	204	207	202	208	206	209	205	207	206
2	201	204	198	203	209	207	199	206	205	204
3	198	204	196	201	199	203	202	198	202	197
4	210	209	214	215	211	208	210	209	211	210

Assume that ANOVA model is appropriate.

a. Test whether or not the mean coil characteristic is the same for all machines in the plant; use α = .10. State the alternatives, decision rule, and conclusion. What is the P-value of the test?

b. Estimate the mean coil characteristic for all coil winding machines in the plant; use a 90 percent confidence interval.

Problem 3 - Imitation pearls

Preliminary research on the production of imitation pearls entailed studying the effect of the number of coats of a special lacquer (factor A) applied to an opalescent plastic bead used as the base of the pearl on the market value of the pearl. Four batches of 12 beads (factor B) were used in the study, and it is desired to also consider their effect on the market value. The three levels of factor A (6, 8, and 10 coats) were fixed in advance, while the four batches can be regarded as a random sample of batches from the bead production process. The market value of each pearl was determined by a panel of experts. The market value data (coded) follow.

Factor A (number of coats)		Factor B (batch)
Factor A (number of coats)		j =1	j =2	j =3	j =4
i = 1	6	72.0	72.1	75.2	70.4
		. . .	. . .	. . .	. . .
		72.8	73.3	77.8	72.4
i = 2	8	76.9	80.3	80.2	74.3
		. . .	. . .	. . .	. . .
		74.2	77.2	79.9	72.9
i = 3	10	76.3	80.9	79.2	71.6
		. . .	. . .	. . .	. . .
		75.0	80.2	81.2	74.4

Assume that mixed ANOVA model is applicable.

a. Test for interaction effects; use α = .05. State the alternatives, decision rule, and conclusion. What is the P-value of the test?

b. Test for factor A and factor B main effects. For each test, use α = .05 and state the alternatives, decision rule, and conclusion. What is the P-value for each test?

c. Estimate D₁ = μ₂. - μ₁. and D₂ = μ₃. - μ₂. By means of the Bonferroni procedure with a 90 percent family confidence coefficient. State your findings.

d. Use the Satterthwaite procedure to obtain an approximate 95 percent confidence interval for μ₂.. Interpret your confidence interval.

e. Use the MLS procedure to obtain an approximate 90 percent confidence interval for σ_β². Does σ_β²appear to be large compared to σ²?

Note - For problem 1 use attached logistics SAS file.

Attachment:- Assignment File.rar

Reference no: EM132294032

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