A report included the following information on the heights (in.) for non-Hispanic white females. Sample Sample Std. Error Size Mean Mean 0.09 0.11 Age 20-39 866 935 60 and older (a) Calculate a confidence interval at confidence level approximately 95% for the difference between population mean height for the younger women and that for the older women. (Use #20-39 - #60 and older") 64.9 63.4 Interpret the interval. We are 95% confident that the true average height of younger women is greater than that of older women by an amount outside the confidence interval. O We cannot draw a conclusion from the given information. We are 95% confident that the true average height of younger women is less than that of older women by an amount within the confidence interval. We are 95% confident that the true average height of younger women is greater than that of older women by an amount within the confidence interval. (b) Let , denote the population mean height for those aged 20-39 and 4₂ denote the population mean height for those aged 60 and older. Interpret the hypotheses Ho: #₁ #₂ = 1 and H₂: H₁ H₂ > 1. O The null hypothesis states that the true mean height for younger women is more than 1 inch higher than for older women. The alternative hypothesis states that the true mean height for younger women is 1 inch higher than for older women. The null hypothesis states that the true mean height for older women is more than 1 inch higher than for younger women. The alternative hypothesis states that the true mean height for older women is 1 inch higher than for younger women. O The null hypothesis states that the true mean height for older women is 1 inch higher than for younger women. The alternative hypothesis states that the true mean height for older women is more than 1 inch higher than for younger women. O The null hypothesis states that the true mean height for younger women is 1 inch higher than for older women. The alternative hypothesis states that the true mean height for younger women is more than 1 inch higher than for older women. Carry out a test of these hypotheses at significance level 0.001. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value four decimal places.) z = P-value = (c) Based on the P-value calculated in (b) would you reject the null hypothesis at any reasonable significance level? Explain your reasoning. O Fail to reject Ho. The data suggests that the difference in the true average heights exceeds 1. O Reject Ho. The data does not suggest that the difference in the true average heights exceeds 1. O Fail to reject Ho. The data does not suggest that the difference in the true average heights exceeds 1. O Reject Ho. The data suggests that the difference in the true average heights exceeds 1.