Question

my question contains 4 points kindly answer the all, if u won't don't solve , answer clear and if u r not sure from answer don't solve plz , thank u , sir

An analyst wants to test if the mean peak loads (in MPa) of two alloys are different. He takes a random sample of n peak load measurements from alloy 1 and finds a sample average #7 =9.5 MPa, and a sample standard deviation s =0.82 MPa. He takes another random sample of size n peak load measurements from alloy 2 and finds a sample average Iz = 7.8 MPa, and a sample standard deviation S, =1.6 MPa. Both samples have the same size n. It is known that the population distributions of the peak load measurements of the two alloys have unequal variances. Hint : n=11 (a) What test statistic the analyst should use to make the test described above? State any necessary assumptions about the data for conducting the test. (b) Use the obtained sample values to test the hypothesis of the analyst, at the significance level a=0.05, with a fixed-level test. State clearly all the necessary steps. What is your conclusion in the context of the problem? c) Use the appropriate statistical table to provide bounds for the p-value of the test. (a) Which confidence interval you would use to do the hypothesis test of part (b) at the significance level o=0.012 Calculate the confidence interval and state your conclusion regarding the test of hypothesis.

Answer 1

ORTE we have given that a = 9.5 MPa 7.8 MPa 52= 1.6 MPa For alloy ! Si=0.82 Tipa hall For alloy 2 a) Here we use the test for testing equality of means of two population For this the test statistic is t = # - 22 ~ thith-2 d. f s ni ni where s² = (n-1) s? +(12-1) sa nithz-2. Assumtions :- i) The parent population from which the samples have been drawn are normally distributed ii) The two samples are random and independent of each other. iii) The population variance 6² and o² are unknown but equal. 67 Here we have to test Ho: Ni= 42 ip, The mean peak loads (in Mpa) of two alloys are not different. vis Hi : Mi & M2 of two ie the mean peak loads (in Mipa) alloys." ave different. CS Scanned with CamScannen

DATE Under Ho the test statistic is t x -X2 th KI hi ho I (n-1) sp +(12-1) 322 hitna-2 (11-1) (0.82)2 + (11-1 (1-622 11 + 1 - 2 1.6162 1.2713 t = 9.5 7.8 1-2713 x ft 1) 3.1360 Now- p-value Here we use two sided alternative hypothesis le test is two tailed test then the p value with test statistic 3.1360 and with degrees of freedom from the t-table it lies between 0.002 to o.ol Exact - pualue is given by excel p-value: TDISC degrees freedom tails) = TDIST( 3-1360, 20, 2) 20 0.0052 CS Scanned with CamScanner

Here p-value < I level of significance 0.0052 L 10.05 Hence reject Ho al 5% level of significance and conclude that the mean peak loads (in ripa) of two alloys different are is o ol then we d) Here significance level have to find 99% confidence interval for given problem. S we know lool 1-2) % confidence interval for different between two populdion mean is de 82)- thitha-2 2/2 (x-2) + thith-2, 2/2 sf for 99% confidence interval hi h) ni h2 tnitm-2 dl2 = tutil-2 og t 200.005 = 1.725 : lower bound = ci-dez) - thitha 2,6 s Jr the for ct = (9.5-7-8) - (1.725x 1-2713 It = 0-7649 upper bound for c. I (2. Paz) + thithe-2 do sth - (9.5-7.8) + (1725x 1-2713* + - na CH 2.6351 CS Scanned with CamScanner

99% confidence interval for a given problem is (0.7649, 2.6351) Hence out 2 and he are does not belong to the confidence interval - Hence we reject Ho at 1 % level of level of significance and conclude that the mea peak loads (in MPa 1 of two alloys are different. gg% CS Scanned with CamScanner

c)

p value for 2 tailed test=2*p value for one tailed test

p value table for one tailed test as follows:

9:34 Hull , ROSE © * 36 Edit 37 Х Cover pen, shapes and stamps are available X PDF Annotation 0.0.0-0.13.0.0 0.046 0.04.14 0.146 0 0.04 0.046 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.046 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.042 1.84 1.86 1.88 1.90 1.92 1.94 1.96 1.98 2.00 2.02 2.04 0.044 0.044 0.043 0.042 0.042 0.041 0.041 0.040 0.040 0.040 0.039 0.039 0.043 0.042 0.041 0.041 0.040 0.040 0.039 0.039 0.038 0.038 0.038 0.038 0.041 0.041 0.040 0.039 0.039 0.038 0.038 0.037 0.037 0.037 0.036 0.036 0.040 0.039 0.038 0.038 0.037 0.037 0.036 0.036 0.036 0.035 0.035 0.035 0.039 0.038 0.037 0.036 0.036 0.035 0.035 0.035 0.034 0.034 0.034 0.033 0.037 0.036 0.036 0.035 0.035 0.034 0.034 0.033 0.033 0.033 0.032 0.032 0.036 0.035 0.034 0.034 0.033 0.033 0.032 0.032 0.032 0.031 0.031 0.031 0.035 0.034 0.033 0.033 0.032 0.032 0.031 0.031 0.030 0.030 0.030 0.030 0.033 0.033 0.032 0.031 0.031 0.030 0.030 0.030 0.029 0.029 0.029 0.028 0.032 0.031 0.031 0.030 0.030 0.029 0.029 0.028 0.028 0.028 0.028 0.027 0.031 0.030 0.030 0.029 0.029 0.028 0.028 0.027 0.027 0.027 0.026 0.026 Note: <.001 indicates P<001. 4 Table 1 (cont'd). One-sided P-values from () distribution: P[r(v) > u). df- 11 13 15 16 17 18 19 20 21 22 23 24 2.06 0.030 0.029 0.029 0.028 0.028 0.027 0.027 0.026 0.026 0.026 0.025 0.025 2.08 0.029 0.028 0.028 0.027 0.026 0.026 0.026 0.025 0.025 0.025 0.024 0.024 2.10 0.028 0.027 0.027 0.026 0.025 0.025 0.025 0.024 0.024 0.024 0.023 0.023 2.12 0.027 0.026 0.026 0.025 0.025 0.024 0.024 0.023 0.023 0.023 0.023 0.022 2.14 0.026 0.025 0.025 0.024 0.024 0.023 0.023 0.022 0.022 0.022 0.022 0.021 2.16 0.025 0.024 0.024 0.023 0.023 0.022 0.022 0.022 0.021 0.021 0.021 0.020 2.18 0.024 0.023 0.023 0.022 0.022 0.021 0.021 0.021 0.020 0.020 0.020 0.020 2.20 0.023 0.023 0.022 0.021 0.021 0.021 0.020 0.020 0.020 0.019 0.019 0.019 2.22 0.022 0.022 0.021 0.021 0.020 0.020 0.019 0.019 0.019 0.019 0.018 0.018 2.24 0.022 0.021 0.020 0.020 0.019 0.019 0.019 0.018 0.018 0.018 0.018 0.017 2.26 0.021 0.020 0.020 0.019 0.019 0.018 0.018 0.018 0.017 0.017 0.017 0.017 2.28 0.020 0.019 0.019 0.018 0.018 0.018 0.017 0.017 0.017 0.016 0.016 0.016 2.30 0.019 0.019 0.018 0.018 0.017 0.017 0.016 0.016 0.016 0.016 0.015 0.015 2.32 0.019 0.018 0.017 0.017 0.017 0.016 0.016 0.016 0.015 0.015 0.015 0.015 2.34 0.018 0.017 0.017 0.016 0.016 0.016 0,015 0,015 0,015 0.014 0.014 0.014 2.36 0.017 0.017 0.016 0.016 0.015 0,015 0,015 0.014 0.014 0.014 0.014 0.013 2.38 0.017 0.016 0.016 0.015 0.015 0.014 0.014 0.014 0.013 0.013 0.013 0.013 2.40 0.016 0.015 0.015 0.014 0.014 0.014 0.013 0.013 0.013 0.013 0.012 0.012 2.42 0.015 0.015 0.014 0.014 0.014 0.013 0.013 0.013 0.012 0.012 0.012 0.012 2.44 0.015 0.014 0.014 0.013 0.013 0.013 0.012 0.012 0.012 0.012 0.011 0.011 2.46 0.014 0.014 0.013 0.013 0.012 0.012 0.012 0.012 0.011 0.011 0.011 0.011 2.48 0.014 0.013 0.013 0.012 0.012 0.012 0.011 0.011 0.011 0.011 0.010 0.010 2.50 0.013 0.013 0.012 0.012 0.011 0.011 0.011 0.011 0.010 0.010 0.010 0.010 2.52 0.013 0.012 0.012 0.011 0.011 0.011 0.010 0.010 0.010 0.010 0.010 0.009 2.54 0.012 0.012 0.011 0.011 0.011 0.010 0.010 0.010 0.010 0.009 0.009 0.009 2.56 0.012 0.011 0.011 0.010 0.010 0.010 0.010 0.009 0.009 0.009 0.009 0.009 2.58 0.011 0.011 0.010 0.010 0.010 0.009 0.009 0.009 0.009 0.009 0.008 0.008 2.60 0.011 0.010 0.010 0.010 0.009 0.009 0.009 0.009 0.008 0.008 0.008 0.008 2.70 0.009 0.009 0.008 0.008 0.008 0.007 0.007 0.007 0.007 0.007 0.006 0.006 2.80 0.008 0.007 0.007 0.006 0.006 0.006 0.006 0.006 0.005 0.005 0.005 0.005 2.90 0.006 0.006 0.005 0.005 0.005 0.005 0.005 0.004 0.004 0.004 0.004 0.004 3.00 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.003 0.003 0.003 0.003 3.10 0.004 0.004 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.002 3.20 0.003 0.003 0.003 0.003 0.003 0.002 0.002 0.002 0.002 0.002 0.002 0.002 3.30 0.003 0.003 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 3.40 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.001 0.001 0.001 0.001 0.001 3.50 0.002 0.002 0.002 0.001 0.001 0.001 0.001 0.001 0.001 0.001 <.001 <.001 df-v II 25 26 27 28 29 30 40 50 60 80 100 1.30 0.103 0.103 0.102 0.102 0.102 0.102 0.101 0.100 0.099 0.099 0.098 0.097 1.32 0.099 0.099 0.099 0.099 0.099 0.098 0.097 0.096 0.096 0.095 0.095 0.093 1.34 0.096 0.096 0.096 0.096 0.095 0.095 0.094 0.093 0.093 0.092 0.092 0.090 1.36 0.093 0.093 0.093 0.092 0.092 0.092 0.091 0.092 0.092 0.092 0.091 0.090 0.089 0.089 0.088 0.087 1.38 0.090 0.090 0.089 0.089 0.089 0.089 0.088 0.087 0.086 0.086 0.085 0.084 1.40 0.087 0.087 0.086 0.086 0.086 0.086 0.085 0.084 0.083 0.083 0.082 0.081 1.42 0.084 0.084 0.084 0.083 0.083 0.083 0.082 0.081 0.080 0.080 0.079 0.078 1.44 0.081 0.081 0.081 0.080 0.080 0.080 0.079 0.078 0.078 0.077 0.076 0.075 1.46 0.078 0.078 0.078 0.078 0.078 0.077 0.076 0.075 0.075 0.074 0.074 0.072 1.48 0.076 0.075 0.075 0.075 0.075 0.075 0.073 0.073 0.072 0.071 0.071 0.069 1.50 0.073 0.073 0.073 0.072 0.072 0.072 0.071 0.070 0.069 0.069 0.068 0.067 1.52 0.071 0.070 0.070 0.070 0.070 0.069 0.068 0.067 0.067 0.066 0.066 0.064 1.54 0.068 0.068 0.068 0.067 0.067 0.067 0.066 0.065 0.064 0.064 0.063 0.062 1.56 0.066 0.065 0.065 0.065 0.065 0.065 0.063 0.063 0.062 0.061 0.061 0.059 1.58 0.063 0.063 0.063 0.063 0.062 0.062 0.061 0.060 0.060 0.059 0.059 0.057 1.60 0.061 0.061 0.061 0.060 0.060 0.060 0.059 0.058 0.057 0.057 0.056 0.055 1.62 0.059 0.059 0.058 0.058 0.058 0.058 0.057 0.056 0.055 0.055 0.054 0.053 1.64 0.057 0.057 0.056 0.056 0.056 0.056 0.054 0.054 0.053 0.052 0.052 0.051 Note: <.001 indicates P<001. w DD DD Tools Mobile View Share PDF to DOC