Plasma etching is essential to the fineline pattern transfer

Plasma etching is essential to the fine-line pattern transfer in current semiconductor processes. An article gives the accompanying data (read from a graph) on chlorine flow (x, in SCCM) through a nozzle used in the etching mechanism and etch rate (y, in 100 A/min).

The summary statistics are

(a) Does the simple linear regression model specify a useful relationship between chlorine flow and etch rate? (Use = 0.05.)
State the appropriate null and alternative hypotheses.

H₀: ₁ = 0
H_a: ₁ < 0H₀: ₁ 0
H_a: ₁ = 0    H₀: ₁ = 0
H_a: ₁ 0H₀: ₁ = 0
H_a: ₁ > 0

Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)

State the conclusion in the problem context.

Reject H₀. This model does not specify a useful relationship between chlorine flow and etch rate.

Fail to reject H₀. This model does not specify a useful relationship between chlorine flow and etch rate.    

Fail to reject H₀. This model does specify a useful relationship between chlorine flow and etch rate.

Reject H₀. This model does specify a useful relationship between chlorine flow and etch rate.

(b) Estimate the true average change in etch rate associated with a 1-SCCM increase in flow rate using a 95% confidence interval. (Round your answers to three decimal places.)

(c) Calculate a 95% CI for _{Y · 3.0},

the true average etch rate when flow = 3.0. (Round your answers to three decimal places.)

(d) Calculate a 95% PI for a single future observation on etch rate to be made when flow = 3.0. (Round your answers to three decimal places.)

(e) Would the 95% CI and PI when flow = 2.5 be wider or narrower than the corresponding intervals of parts (c) and (d)? Answer without actually computing the intervals.

Solution

a) the appropriate null and alternative hypotheses.is

Ha: 1 0H0: 1 = 0

t-value = 11.33

P-value = 0.000

conclusion: Reject H0. This model does specify a useful relationship between chlorine flow and etch rate.

b)

The 95% CI for Y · 3.0, is (36.253,40.183)

c) Predicted value = 7.2564+(10.3205*3)= 38.2179

A 95% PI for a single future observation on etch rate to be made when flow = 3.0 is (32.388, 44.048)

d)

The predicted value at x=2.5 is 7.2564+(10.3205*2.5)= 33.0577

the 95% CI and PI when flow = 2.5 be narrower than the corresponding intervals of parts (c) and (d)