htmlCanvasXw Elementary Statistics with Integra XBaseCamp+<8-4 Testing a Claim About a Stan... >the claim that birth weights of girls have the same standard deviationas birth weights of boys, which is 660.2 hg (based on Data Set 4"Births" in Appendix BLO).9. Cola Cans A random sample of 20 aluminum cola cans with thickness0.0109 in. is selected and the axial loads are measured and the stan-dard deviation is 18.6 lb. The axial load is the pressure applied to thetop that causes the can to crush. Use a 0.05 significance level to testthe claim that cans with thickness 0.0109 in. have axial loads with thesame standard deviation as the axial loads of cans that are 0.0111 in.thick. The thicker cans have axial loads with a standard deviation of27.8 lb (based on Data Set 30 "Aluminum Cans" in Appendix B).Does the thickness of the cans appear to affect the variation of the ax-ial loads?10. Statistics Test Scores Tests in the author's statistics classes have

Given Information: Sample size n=20 Standard deviation is 18.6 Significance level α=0.05 Standard deviation of thicker cans is 27.8 State the hypotheses as follows: Null Hypothesis H0:μ1=μ2 i.e., mean thickness of the cans of type 1 is equal to the mean thickness of cans of type 2. Alternative Hypothesis Ha:μ1≠μ2 i.e., mean thickness of the cans of type 1 is different than the mean thickness of cans of type 2. This a two-tailed test. The test statistic is given by the formula: z=x¯1-x¯2σ12n1+σ22n2=0.0109-0.011118.6220+27.8220=-0.000217.298+38.642≈-0.00003 Using the standard normal table, look for α2=0.052=0.025 in the entries of the table. The value corresponding to it is 1.96. Thus, the critical values for a two-tailed test are: -1.96 and +1.96 Since the value of the test statistic (-0.00003) lies between the two critical values, we fail to reject the null hypothesis. Therefore at 0.05 significance level, there is not enough evidence to warrant rejection of the claim that the mean thickness of the cans of type 1 is equal to the mean thickness of cans of type 2. In other words, the thickness of cans does not appear to affect variation of the axial loads. OR Conduct a variance test as shown below: Null Hypothesis H0:σ21=σ22 i.e., thickness of cans does not appear to affect variation of the axial loads, so the standard deviations of two types of cans are equal. Alternative Hypothesis H1:σ12≠σ22 i.e., thickness of cans appears to affect variation of the axial loads. The test statistic is given by the formula: F=s12s22=(18.6)2(27.8)2=0.448 Use Excel function "=2*F.DIST(0.448,19,19,TRUE)", the p-value obtained is 0.08788 Since the p-value is greater than the significance level (0.05), we fail to reject the null hypothesis. Therefore at 0.05 significance level, there is not enough evidence to warrant rejection of the claim that the thickness of cans does not appear to affect variation of the axial loads.