Q15 Please answer the fill-ins. **Study on Height Differences in Non-Hispanic White Females**A report included the following information on the heights (in.) for non-Hispanic white females.| Age | Sample Size | Sample Mean | Std. Error Mean ||-----------------|-------------|-------------|-----------------|| 20-39 | 863 | 64.5 | 0.09 || 60 and older | 932 | 62.7 | 0.11 |---### (a) Confidence Interval Calculation**Task:** Calculate a confidence interval at a confidence level of approximately 95% for the difference between the population mean height for younger women and that for older women. (Use \(\mu_{20-39} - \mu_{60 \text{ and older}}\))**Answer:** \[ (\_, \_) \]### Interpret the Interval- \(\bigcirc\) 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.- \(\bigcirc\) 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. - \(\bigcirc\) 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.- \(\bigcirc\) We cannot draw a conclusion from the given information.**Correct Interpretation:**- \(\bigcirc\) 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.---### (b) Hypothesis Testing**Task:** Let \(\mu_1\) denote the population mean height for those aged 20-39 and \(\mu_2\) denote the population mean height for those aged 60 and older. Interpret the hypotheses \(H_0: \mu_1 - \mu_2 = 1\) and \(H_a: \mu_1 - \mu_2 > 1\).- \(\bigcirc\) 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.-

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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 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") 863 932 64.5 62.7 Interpret the interval. O 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 greater than that of older women by an amount within the confidence interval. O 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. (b) Let , denote the population mean height for those aged 20-39 and ₂ denote the population mean height for those aged 60 and older. Interpret the hypotheses Ho: M₁ M₂ = 1 and H₂ : ₁ - ₂ > 1. 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. 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. O 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 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. P-value= 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 to four decimal places.)