The standard deviation of critical dimension thickness in semiconductor manufacturing is a = 15 nm. (a) State the null and alternative hypotheses used to demonstrate that the standard deviation is reduced. (b) Assume that the previous test does not reject the null hypothesis. Does this result provide strong evidence that the standard deviation has not been reduced? (a) Ho: 0= 1 (b) .H₂:0
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- Time left 0:57:32 Toll Brothers is a luxury home builder that would like to test the hypothesis that the variance for the size of new homes exceeds 160000 (square feet). The square footage for a random sample of 25 new homes was recorded. The standard deviation for this sample was found to be 390 square feet. Test this hypothesis using a = 0.10. a) What is the parameter of interest? ( b) State the null and the alternative hypotheses. (1 c) What is the appropriate test statistic? d) Calculate the test statistic. ( e) What is the degrees of freedom? Find the required table value(s) to test the hypothesis by using the critical value approach. f) State the rejection criterion (use the critical value approach) g) Write your decision and draw your conclusion. **2. An engineer who is studying the tensile strength of a steel alloy intended for use in golf club shafts knows that tensile strength is approximately normally distributed with s=25 psi. A random sample of 25 specimens has a mean tensile strength of x = 3490 psi. (a) Test the hypothesis that the mean strength is NOT 3500 psi by using the p-value. Use α=0.05. (b) Test the hypothesis in part (a) using a two-sided confidence interval on mean tensile strength.5.5.4. Let Y1, Y2, ..., Yn be a random sample from the uniform pdf fy(y; 0) = 1/0, 0 ≤ y ≤ 0. Compare the
- The viscosity of a liquid detergent is supposed to average 800 centistokes at 25°C. A random sample of 16 batches of detergent is collected, and the average viscosity is 812. Suppose we know that the standard deviation of viscosity is σ = 25 centistokes. (a) State the hypotheses that should be tested. (b) Test these hypotheses using α = 0.05. What are your conclusions?A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compressive strength of more than 1,300 KN/m². The mixture will not be used unless experimental evidence indicates conclusively that the strength specification has been met. Suppose compressive strength for specimens of this mixture is normally distributed with o = 67. Let u denote the true average compressive strength. (a) What are the appropriate null and alternative hypotheses? Ho: μ 1,300 H₂: μ = 1,300 Ho: μ = 1,300 H a: μ> 1,300 ○ Ho: μ = 1,300 H₂: μ< 1,300 (b) Let X denote the sample average compressive strength for n = 15 randomly selected specimens. Consider the test procedure with test statistic X itself (not standardized). What is the probability distribution of the test statistic when Ho is true? O The test statistic has a gamma distribution. O The test statistic has an exponential distribution. O The test statistic has a binomial distribution. The test statistic has a normal…To test Ho: o=2.8 versus H₁: <2.8, a random sample of size n=21 is obtained from a population that is known to be normally distributed. CITE (a) If the sample standard deviation is determined to be s = 1.3, compute the test statistic. = 4.311 (Round to three decimal places as needed.) (b) If the researcher decides to test this hypothesis at the α=0.10 level of significance, determine the critical value. The critical value is (Round to three decimal places needed.) 4 Clear all View an example Get more help. a Et H Help me solve this Type here to search 4 R F 5 T 7 8 96°F Mostly sunny Check answ G 3:54 PM 6/18/202
- A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compressive strength of more than 1,300 KN/m. The mixture will not be used unless experimental evidence indicates conclusively that the strength specification has been met. Suppose compressive strength for specimens of this mixture is normally distributed with o= 65. Let u denote the true average compressive strength. (a) What are the appropriate null and alternative hypotheses? H:H= 1,300 H:H= 1,300 Ho: H > 1,300 H:H= 1,300 O Hg: H = 1,300 H: H > 1,300 O Hg: H< 1,300 H H = 1,300 O Ho: H = 1,300 H: H < 1,300 (b) Let X denote the sample average compressive strength for n = 11 randomly selected specimens. Consider the test procedure with test statistic X itself (not standardized). What is the probability distribution of the test statistic when H, is true? O The test statistic has a normal distribution. O The test statistic has a binomial distribution. O The test statistic has a gamma distribution.…A simple random sample of size n=40 is drawn from a population. The sample mean is found to be 107.6, and the sample standard deviation is found to be 20.2. Is the population mean greater than 100 at the α=0.025 level of significance? Determine the null and alternative hypotheses. H0: mu equals 100μ=100 mu less than 100μ<100 mu equals 100μ=100 mu greater than 100μ>100 mu less than 107.6μ<107.6 mu equals 107.6μ=107.6 mu greater than 107.6μ>107.6 H1: mu greater than 100μ>100 mu less than 100μ<100 mu equals 100μ=100 mu greater than 100μ>100 mu less than 107.6μ<107.6 mu equals 107.6μ=107.6 mu greater than 107.6μ>107.6 Compute the test statistic. t 0t0 t 0t0 z 0z0 = (Round to two decimal places as needed.) Determine the P-value. The P-value is . (Round to three decimal places as needed.) What is the result of the hypothesis test? the null hypothesis because the P-value is the level of significance.…A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compressive strength of more than 1,300 KN/m2. The mixture will not be used unless experimental evidence indicates conclusively that the strength specification has been met. Suppose compressive strength for specimens of this mixture is normally distributed with o = 69. Let u denote the true average compressive strength. (a) What are the appropriate null and alternative hypotheses? O Ho: H > 1,300 H: u = 1,300 Ο H,: μ= 1,300 H: u 1,300 (b) Let X denote the sample average compressive strength for n = 15 randomly selected specimens. Consider the test procedure with test statistic X itself (not standardized). What is the probability distribution of the test statistic when Ho is true? O The test statistic has a binomial distribution. O The test statistic has a gamma distribution. The test statistic has a normal distribution. O The test statistic has an exponential distribution. If X = 1,340, find the…
- Suppose that the pdf of a random variable is given by f(y)=1/10 , -5<y<5 For what value of y does the cdf equals 0.6?To test Ho: o = 4.1 versus H,: 0±4.1, a random sample of size n = 14 is obtained from a population that is known to be normally distributed. (a) If the sample standard deviation is determined to bes=5.9, compute the test statistic. (b) If the researcher decides to test this hypothesis at the a = 0.05 level of significance, use technology to determine the P-value. (c) Will the researcher reject the null hypothesis? ..... (a) The test statistic is x =. (Round to two decimal places as needed.)To test Ho: o = 2.1 versus H: 0+2.1, a random sample of size n = 17 is obtained from a population that is known to be normally distributed. (a) If the sample standard deviation is determined to be s = 1.8, compute the test statistic. = 11.755 (Round to three decimal places as needed.) (b) If the researcher decides to test this hypothesis at the a = 0.05 level of significance, determine the critical values. .2 The critical values are x6 025 and x6.975 %3D %3D (Round to three decimal places as needed.)