Given the discrete uniform population shown to the right, find the probability that a random sample of size 54, selected with replacement, will yield a sample mean greater than 9.5 but less than 10.3. Assume the means are measured to the nearest tenth. f(x) = 1 x=4, 9, 14 0, elsewhere
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- Suppose X is a normal random variable with mean u = 17.5 and o = 6. A random sample of size n = 24 is selected from this population. a. Find the distribution of b. Find P(X < 14) and P(X < 14) Find P(1526 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…A sample of n = 8 scores has a mean of M = 16. For this sample, ΣX = 128. Is this true or false?A sample of n = 64 scores has a mean of M = 68. Assuming that the population mean is p = 60, find the z-score for this sample: If it was obtained from a population with o = 16 Z = If it was obtained from a population with o = 32 Z = If it was obtained from a population with o = 48 Z =Suppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population favor a charter school for grades K through 5. A simple random sample of 144 is surveyed. a. Find the mean and the standard deviation of X of B(144, 0.49). Round off to 4 decimal places. O = b. Now approximate X of B(144, 0.49) using the normal approximation with the random variable Y and the table. Round off to 4 decimal places. Y - N( c. Find the probability that at most 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X 75) - P(Y > a (Z > e. Find the probability that exactly 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X = 81) - P(The dean of a university estimates that the mean number of classroom hours per week for full-time faculty is 11.0. As a member of the student council, you want to test this claim. A random sample of the number of classroom hours for eightfull-time faculty for one week is shown in the table below. At α=0.10, can you reject the dean's claim? Assume the population is normally distributed. 12.3 9.1 11.8 6.7 6.2 10.6 14.6 9.1 What is the P value? Reject or fail to reject Ho? At α=0.10, can you reject the dean's claim?let Y=5X+10 and X be normally distributed with a mean 10 and varience 25. find P(Y<54).Suppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population favor a charter school for grades K through 5. A simple random sample of 144 is surveyed. a. Find the mean and the standard deviation of X of B(144, 0.49). Round off to 4 decimal places. O = b. Now approximate X of B(144, 0.49) using the normal approximation with the random variable Y and the table. Round off to 4 decimal places. Y - N( c. Find the probability that at most 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X 75) - P(Y > a (Z > e. Find the probability that exactly 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X = 81) - P(A random sample of size n1 =15 is selected from a normal population with a mean of 76 and standard deviation of 9. A second random sample size n2 =10 is taken from another normal population with mean 71 and a standard deviation 13. Let x barı and x bar2 be the sample means. Find: a. The probability that xbar1 – xbar2 exceeds 4.5 b. The probability that 3.5 s xbar1– xbar2 s 5.5A sample of n=4 scores has a mean of M=75. Find the z-score for this sample: a. If it was obtained from a population with u= 80 and o=10. b. If it was obtained from a population with u=80 and o=20.ndependent random samples are selected from two populations and are used to test the hypothesis Hn: (H, - H2) = 0 against the alternative H,: (4, - H2) #0. An analysis of 232 observations from population 1 and 311 from population 2 yielded p-value of 0.113. Complete parts a and b below. a. Interpret the results of the computer analysis. Use as0.10. A. Since this p-value exceeds the given value of a, there is insufficient evidence to indicate that the population means are different. O B. Since the given a value exceeds this p-value, there is insufficient evidence to indicate that the population means are different. OC. Since the given a value exceeds this p-value, there sufficient evidence to indicate that the population means are different. O D. Since this p-value exceeds the given value of , there is sufficient evidence to indicate that the population means are different. b. If the alternative hypothesis had been Ha: (H1 - H2) <0, how would the p-value change? Interpret the p-value…A random sample of size 10 yielded roughly "mound-shaped" data with a sample mean of 63.5 and a sample variance of 60.8. Let (L, OU) be the interval estimate that contains the population mean with 95% probability. Find the width of the interval. 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