An ecologist wishes to mark off a circular sampling region having radius 13 m. However, the radius of the resulting region is actually a random variable R with the following pdf. -0. f(r) = . 1-(13-)²] 12 ≤ r ≤ 14 0 otherwise What is the expected area of the resulting circular region? (Round your answer to two decimal places.) x m²

The graph to the right portrays the decision criterion for a hypothesis test for a population mean u. The null hypothesis for the test is Ho:=Ho- The curve in the graph is the normal curve for the test statistic under the assumption that the null hypothesis is true. Complete parts (a) through (f) below. Reject | Do not reject Ho Ho I 0.04 -1.751 0 a. Determine the rejection region. OA. z> -1.751 O B. z>1.751 O C. zs - 1.751 OD. zs-1.751 or z2 1.751 b. Determine the nonrejection region. A. - 1.751 szS1.751 Question Viewer O B. B. - 1.751 -1.751 c. Determine the critical value(s). (Type integers or decimals. Do not round. Use a comma to separate answers as needed.) Click to select your answer(s). MacBook Pro F1 F2 F3 DII DD F4 F5 F6 F7 F8 F9 F10 23 & 4. 00 %24 2.

To test Ho: µ = 50 versus H,: µ < 50, a random sample of size n = 26 is obtained from a population that is known to be normally distributed. Complete parts (a) through (d) below. E Click here to view the t-Distribution Area in Right Tail. (a) If x = 47.5 and s = 11.9, compute the test statistic. to = (Round to three decimal places as needed.) (b) If the researcher decides to test this hypothesis at the a = 0.05 level of significance, determine the critical value(s). Although technology or a t-distribution table can be used to find the critical value, in this problem use the t-distribution table given. Critical Value: (Round to three decimal places. Use a comma to separate answers as needed.) (c) Draw a t-distribution that depicts the critical region. Choose the correct answer below. OA. OB. Oc. -ta12 ta/2 -ta (d) Will the researcher reject the null hypothesis? O A. Yes, because the test statistic falls in the critical region. B. No, because the test statistic falls in the critical…

26 The table to the right shows the cost per ounce​ (in dollars) for a random sample of toothpastes exhibiting very good stain​ removal, good stain​ removal, and fair stain removal. At α=0.01​, can you conclude that the mean costs per ounce are​ different? Perform a​ one-way ANOVA test by completing parts a through d. Assume that each sample is drawn from a normal​ population, that the samples are independent of each​ other, and that the populations have the same variances. Very good stain removal Good stain removal Fair stain removal   0.37 0.75 0.60   0.49 2.66 1.18   0.33 0.46 0.46   1.64 0.33     0.50 0.58     0.41 1.39           ​(b) Identify the degrees of freedom for the numerator and for the​ denominator, determine the critical​ value, and determine the rejection region. The degrees of freedom for the​ numerator, d.f.N​, is ____ and the degrees of freedom for the​ denominator, d.f.D​, is _____ The critical…