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Question 4: A persons protein requirement is the amount of protein they must consume in a day to maintain a stable weight, muscle mass, etc. A group of researchers wanted to know if the mean protein requirement (in grams of protein per day per kilogram of body weight) is the same for young adult males and females. The protein requirement of 10 males and 11 females was determined. The protein requirements of the subjects are given below. (Data based on summary statistics in Campbell WW, et. al., Dietary protein requirements of younger and older adults. American Journal of Clinical Nutrition. 2008.) Males: 0.760.590.440.460.51 0.63 0.29 0.430.590.74 Femal 0.80 0.680.510.540.63 0.70 0.80 0.490.740.62 0.82 es: Is there a difference in the mean protein requirement of young adult males and females? Use a 0.025 and be sure to verify the requirements for the test.

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(a) The Computation Table 0.76 0.59 0.44 0.46 0.51 0.63 0.29 0.43 0.59 0.74 0.216 0.046 0.104 0.084 0.034 0.086 0.254 0.114 0.046 0.196 0.046656 0.002116 0.010816 0.007056 0.001156 0.007396 0.064516 0.012996 0.002116 0.038416 10 10 ΣΧ,-5.44 Σ (X-X)2 = 0.19324 The formula for calculating the point estimate of the population mean is il 10 ΣΧ, 0.76+0.59+.. +0.74) (5.44) 0.544 X 0.544 Therefore, the point estimate of the population mean is X544 The formula for calculating the populati on stan dar d deviation is 0.19324 V0.021471111 0.14653024 σ~ 0.14653024 Therefore, the population standard deviation is σ~ 146531

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(c) Let and j/2 be the population means and let x, and x2 be the means of the respective samples. From the given inform ati on Samplel: » 10, x-0.544, s 0.14653024 Sample2: n, = 1 1, = 0.666, s,ー0.1 18766 The level of significance is a 0.025 Step1: State the null and alternative hypotheses The null and alternative hypotheses are, respectively We need to use two-tailed test Ho : μ1-AG (The two population means are equal H1 : μ-μ (The population mean μί is not equal to μ) Step 2: Select the distributi on to use Here, the two samples are independent, and α are unknown but equal, and the sample sizes are sm all but both populations are normally distributed. Hence, all conditions are sati sfied. Consequently, we will use the t distribution Step3: Determine the rejecti on and non-rejection regions The ^ sign in the altenative hypothesis indi cates that the test is two-tailed The significance level is 0.025 From the t distribution table, the critical value of t for df- 19 and 0.025 area in the left-tail of the t distributi on is - 2.093 The critical values of for df 19 and 0.025 area in right-tail of the t distribution curve are 2.093

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