Given X₁, X₂, X3, X4-N(μ, 9) and suppose we have the following hypothesis of interest: Ho:μ = 25 VS H: μ < 25 Jse CR = {XIX ≤ 23) and (0) = P(rei. Ho 10) and determine the significance level and power of a test.
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- If the results of the test with the following hypotheses are statistically significant, we have found evidence that: Hypotheses: h0: u1 = u2 ha: u1>u2 A: X<x2 B: x1 is not equal to x2 c: u1>u2 D: u1=u2 E: x1>x2 F: u1<u2Q1. Let X; and S be the mean and variance of independent random samples of size ni from populations with mean H; and variance of (i = 1,2), respectively where u, = 20. of = 9, n1 = 36 and u2 = 18, ož = 16, n2 = 49. Find (- a) P(X, > 20.98) b) x such that P(X, 12.8062) d) si such that P(S} > s3) = 0.80 e) P(X1 – X2 > 0.2336) n P(SE/S글 > 0.8368) %3DQ1. Let X and S be the mean and variance of independent random samples of size n; from populations with mean H; and variance of (i = 1, 2), respectively where u, = 20, of = 9, n = 36 and 4z = 18, ož = 16, n2 = 49. Find (using MINITAB or Tables of cdf) a) P(X, > 20.98) b) x such that P(X, 12.8062) d) si such that P(S{ > s{) = 0.80 e) P(X, - X2 > 0.2336) ) P(S{/S > 0.8368) %3D %3D
- 3. Let x be a random variable representing the concentration of chemical Z in human blood. Over a long time frame a population mean u = 12% or above is considered unhealthy. A patient has taken %3D 12 blood samples over the last two weeks. The average concentration from these 12 samples is X = 13% and s = 1.32%. a. Do these data suggest a population mean u higher than 12% for this patient? (Use a = 5%) b. Using the sample data, generate a 99% confidence interval for u.Suppose a researcher uses 36 pairs of identical twins (i.e., dependent data) to compare two treatments. For each set of twins, one twin is randomly assigned to Treatment 1 and his/her twin is assigned to Treatment 2. In evaluating the calculated t value, how many degrees of freedom (df) does the researcher have?A. 36B. 72C. 35D. 37Q1. An anthropologist wants to collect data to determine whether the two different cultural groups that occupy an isolated Pacific Island grow to be different heights. The results of his samples of the heights of adult females are as follows Group A Group B n=120 n 150 X 62.7 X 61.8 S 2.5 S2 =2.62 Do these samples constitute enough evidence to reject the null hypothesis that the heights of the two groups are the same? Set alpha to.05. 1. What are the appropriate null and alternative hypothesis? A. Ho: H-Hz = 0 H;: H-H2 # 0 B. Ho: H-H2 20 H: H -H2 0 D. Ho: Hy-Hz # 0 H: H - H2 = 0 E. None of these. 2. What is the Test statistics? A.T = -y-Do B. Z = X-y-Do C. T = 9-Do D-Do D.T = E. Z = -9-Do 1,1 Sp Zu Tu SD n n2 3. What is the value of the test statistic? A. T = 9,20 B.T = 2.86 C.Z = 9.20 D.T = 1.44 E. None of these 4. For a significance level of 0.05, what is the critical value? A. to o5 = 1.645 B.to025 = 1.960 C.Za 0s = 1.645 D.zo025 = 1.960 E.None of these 5. What is the appropriate…
- 38. For a given set of bivariate data, the following results were obtained. X= 53.2, Y= 27.9, Regression coefficient of Y on X = - 1.5. Regression coefficient of X on Y = - 0-2. Find the most probable value of Y when X is 60.The proportion of students who get an undergraduate degree in statistics in four years was compared for meals and females. Random sample of 200 male statistics majors and 200 female statistics majors were taken. Choose the appropriate parameter(s) for this situation. [Hint: The .parameter(s) to be used in your hypothesis] ule u 2.00 jo None of these .A O P1-P2.B O H.C O Hi- H2.D O P.E O إنهاء المحاولة . . . PREVIOUS ACTIVITY Note P Type here to search Ae Ps 近Bb.29.
- 2. Participants were kept awake for a certain number of hours before given a visuospatial task. Researchers measured how many correct responses each participant had. Results are shown below. Use alpha = .01. Number of Correct Hours Kept Awake (X) Responses (Y) 21 X = 10 SS, = 422 SPy= -525 S, -5.70 2 Y = 10 4 19 SS, = 690 13 ху 20 S, = 7.29 9. 11 10 5 5 14 15 17 2 18 1 17 1 13 4 2 18 8 118. For a one-sample problem, suppose that n = 20, x = 315.9, and s = 22.9. The p-value for the hypotheses H, : H> 320 versus HA : H0.80) E. P(t19 > -0.80) E b. For a two-sided t-test, which of the following t-statistics would result in the largest С. 1.43 alue? А. 2.55 В. -2.55 D. -1.33 Е. 3.22 For a one-sided t-test with HA : µ> 10, which of the following t-statistics would result in the largest p-value? С. A. 2.55 В. -2.55 C. 1.43 D. -1.33 Е. 3.223. For the data in the source table, what decision can be made about the hypotheses being tested? Source df F 2 4 Between-groups Subjects Within-groups Total O SS 10.1 7.4 8.5 26 d. 8 14 Oa. Fail to reject the null hypothesis and conclude that there is no effect of the independent variable. Ob. Fail to reject the null hypothesis because the F statistic does not exceed the critical cutoff. Oc. Reject the null hypothesis and conclude that the independent variable has no effect. MS 5.05 1.85 1.063 Reject the null hypothesis and conclude that there are differences among the levels of the independent variable.