(a) Is there evidence to support the claim that the high- er baking temperature results in wafers with a lower mean photoresist thickness? Use ? = 0.05. (b) What is the P-value for the test conducted in part (a)? (c) Find a 95 percent confidence interval on the difference in means. Provide a practical interpretation of this interval. (d) Draw dot diagrams to assist in interpreting the results from this experiment. (e) Check the assumption of normality of the photoresist thickness. (f) Find the power of this test for detecting an actual dif- ference in means of 2.5 kA. (g) What sample size would be necessary to detect an actual difference in means of 1.5 kA with a power of at least 0.9?
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Calculate the mean photoresist thickness for the wafers that were baked at a higher temperature (170°C) versus the wafers that were baked at a lower temperature (130°C). Show more…
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Q1: Photoresist is a light-sensitive material applied to semiconductor wafers so that the circuit pattern can be imaged onto the wafer. After application, the coated wafers are baked to remove the solvent in the photoresist mixture and to harden the resist. Here are measurements of photoresist thickness (in kÅ) for eight wafers baked at two different temperatures. Assume that all of the runs were made in random order. Temperature (ºC): 95 100 Photoresist Thickness (kÅ): 11.176 5.263 7.089 6.748 8.097 7.461 11.739 7.015 11.291 8.133 10.759 7.418 6.467 3.772 8.515 8.963 (a) Is there evidence to support the claim that the higher baking temperature results in wafers with a lower mean photoresist thickness? Use α = 0.05. (b) What is the P-value for the test conducted in part (a)? P = 0.008 (c) Find a 95% confidence interval on the difference in means. Provide a practical interpretation of this interval. (d) Find the power of this test for detecting an actual difference in means of 2.5 kÅ. (e) What sample size would be necessary to detect an actual difference in means of 1.5 kÅ with a power of at least 0.9? (f) What is your conclusion on the hypothesis test result?
Ameer S.
A new process has been developed for applying photoresist to 125-mm silicon wafers used in manufacturing integrated circuits. Ten wafers were tested, and the following photoresist thickness measurements (in angstroms x1000) were observed: 13.3987, 13.3957, 13.3902, 13.4015, 13.4001, 13.3918, 13.3965, 13.3925, 13.3946, and 13.4002. (a) Test the hypothesis that mean thickness is 13.4 x 1000Å. Use α = 0.05 and assume a two-sided alternative. (b) Find a 99% two-sided confidence interval on mean photoresist thickness. Assume that thickness is normally distributed. (c) Does the normality assumption seem reasonable for these data?
Adi S.
Photoresist is a light-sensitive material applied to semiconductor wafers so that the circuit pattern can be imaged on to the wafer. After application, the coated wafers are baked to remove the solvent in the photoresist mixture and to harden the resist. Here are measurements of photoresist thickness (in kÅ) for eight different wafers baked at two different temperatures. Assume that all of the runs were made in random order. 95 °C 100 °C 11.176 5.623 7.089 6.748 8.097 7.461 11.739 7.015 11.291 8.133 10.759 7.418 6.467 3.772 8.315 8.963 Find the absolute value of the test statistic to test if the higher baking temperature results in wafers with a lower mean photoresist thickness.
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