The company will not adopt Plastic 1 unless its mean breaking strength exceeds that of Plastic 2 by at least 10 psi. The P-value for the test H0: µ1 - µ2 = 10 versus H1: µ1 - µ2 > 10 is closest to:
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Two types of plastic are suitable for an electronics component manufacturer to use. The breaking strength of this plastic is important. It is known that σ1 = σ2 = 1.0 psi. From a random sample of size n1 = 10 and n2 = 12, the values x̄1 = 162.5 and x̄2 = 155.0 are obtained. The company will not adopt Plastic 1 unless its mean breaking strength exceeds that of Plastic 2 by at least 10 psi. The P-value for the test H0: µ1 - µ2 = 10 versus H1: µ1 - µ2 > 10 is closest to:
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- 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 eight full-time faculty for one week is shown in the table below. At a=0.10, can you reject the dean's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. 10.4 8.2 8.8 12.6 13.1 6.1 9.90 11.3 (a) Write the claim mathematically and identify Ho and Ha Which of the following correctly states Ho and H₂? Ο Α. Ho: με 11.0 H₂>11.0 O D. Ho: 11.0 H: ≤11.0 A O A. Fail to reject Ho because the P-value is greater than the significance level. OB. Reject H, because the P-value is greater than the significance level. OC. Reject Ho because the P-value is less than the significance level. OD. Fail to reject Ho because the P-value is less than the significance level. (d) Interpret the decision in the context of the original claim. O A.…Miller (2008) examined the energy drink consumption of college undergraduates and found that males use energy drinks significantly more often than females. To further investigate this phenomenon, suppose that a researcher selects a random sample of n=36 male undergraduates and s ample of n=25 females. On average, the males reported consuming M=2.45 drinks per month and females had an average of M=1.28. Assume that the overall level of consumption for college undergraduates averages μ=1.85 energy drinks per month, that that the distribution of monthly consumption scores is approximately normal with a standard deviation of σ=1.2. Did this sample of males consume significantly more energy drinks than the overall population average? Use a one-tailed test with α =0.01. Did this sample of females consume significantly fewer energy drinks than the overall population average? Use a one-tailed test with α =0.01.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 eight full-time faculty for one week is shown in the table below. At a = 0.01, can you reject the dean's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. 12.1 8.9 11.8 8.4 7.2 10.1 12.1 8.7
- A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compressive strength of more than 1,300 KN/m2. The mixture will not be used unless experimental evidence indicates conclusively that the strength specification has been met. Suppose compressive strength for specimens of this mixture is normally distributed with σ = 61. Let μ denote the true average compressive strength. For a test with α = 0.01, what is the probability that the mixture will be judged unsatisfactory when in fact μ = 1,350 (a type II error)? (Round your answer to four decimal places.)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(An engineer wants to know if producing metal bars using a new experimental treatment rather than the conventional treatment makes a difference in the tensile strength of the bars (the ability to resist tearing when pulled lengthwise). At α=0.10, answer parts (a) through (e). Assume the population variances are equal and the samples are random. If convenient, use technology to solve the problem. Treatment Tensile strengths (newtons per square millimeter) Experimental 449 354 450 360 433 388 400 Conventional 370 376 374 424 378 450 438 404 352 376 (a) Identify the claim and state H0 and Ha. The claim is "The new treatment ▼ makes a difference does not make a difference in the tensile strength of the bars." What are H0 and Ha? The null hypothesis, H0, is ▼ mu 1 equals mu 2μ1=μ2 mu 1 less than or equals mu 2μ1≤μ2 mu 1 greater than or equals mu 2μ1≥μ2 . The alternative hypothesis, Ha,…The length (in mm) of a spring subjected to a force FNewtons is of the form L = a + BF+ ɛ, where ɛ is assumed normally distributed with mean 0, variance o2. Given the sample statisticsn=D13, E F;= 138, E L; = 577, SEL = -43, SEF= 1735, estimate the expected length of the spring when a force of 11.2 Newtons is applied. (Give your answer correct to 2 decimal places.) Answer: Ti Check 江一 prime viden Type here to search 19 hp ins prt fu f12 f8 f9 f10 f7 f5 f6 『米 " JOI JDI & 6 7 8 5 96 %24 3Suppose 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 36 from a population with known variance, o = 9, yields a sample mean of x = 17. Find ß, for testing the hypothesis H,: u = 15 versus H1 : =16. Assume a 0.05. %3D %3Dndependent 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 population of values has a normal distribution with μ=95.4μ=95.4 and σ=81.4σ=81.4. Find the probability that a single randomly selected value is less than 78.6. Round your answer to four decimal places. P(X<78.6)=P(X<78.6)= Find the probability that a randomly selected sample of size n=225n=225 has a mean less than 78.6. Round your answer to four decimal places. P(M<78.6)=P(M<78.6)=Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON