A new concrete mix is being designed to provide adequate compressive strength for concrete blocks. The specification for a particular application calls for the blocks to have a
a. Find the P-value.
b. Do you believe it is plausible that the blocks do not meet the specification, or are you convinced that they do? Explain your reasoning.
Want to see the full answer?
Check out a sample textbook solutionChapter 6 Solutions
Statistics for Engineers and Scientists
Additional Math Textbook Solutions
Introductory Statistics
APPLIED STAT.IN BUS.+ECONOMICS
University Calculus
Mathematics for the Trades: A Guided Approach (11th Edition) (What's New in Trade Math)
Elementary Algebra For College Students (10th Edition)
College Algebra (7th Edition)
- The compressive strength, in kilopascals, was measured for concrete blocks from five different batches of concrete, both three and six days after pouring. The data are as follows. Can you conclude that the mean strength after three days is greater than the mean strength after six days? Let μ1 represent the mean strength after three days and μd = μ1 - μ2. Use the a = 0.01 level and the P-value method with the table. Block 1 2 3 4 5 After 3 days 1389 1380 1302 1377 1336 After 6 days 1314 1321 1318 1386 1356 Part (a) State the appropriate null and alternate hypotheses. H0: H1: This is a ___ test. Part (b); _ < P-value <= _ Part (c);There __ enough evidence to conclude that the mean strength after three days differs from the mean strength after six days.(is/is not)arrow_forwardThe annual rainfall in a certain region is modeled using the normal distribution shown below.arrow_forwardThe stem-leaf diagram below shows compressive strength of concrete cubes measured in (Kpa). Determine * .the medianarrow_forward
- The compressive strength of concrete is normally distributed with u = 2507 psi and o = 51 psi. A random sample of n = 4 specimens is collected. What is the standard error of the sample mean? Round your final answer to three decimal places (e.g. 12.345). The standard error of the sample mean is psi.arrow_forwardA pharmaceutical manufacturer forms tablets by compressing a granular material that contains the active ingredient and various fillers. The force in kilograms (kg) applied to the tablet varies a bit and follows the Normal distribution with mean 11.5 kg and standard deviation 0.2 kg. The process specifications call for applying a force between 11.2 and 12.2 kg. i. What percent of tablets are subject to a force that meets the specifications? ii. The manufacturer adjusts the process so that the mean force is at uie center of the specifications, u = 11.7 kg. The standard deviation remains 0.2 kg. What percent now meets the specifications? iii. Calculate the 25th percentile (P2s) and the 75th percentile (P7s) of the distribution.arrow_forwardA pharmaceutical manufacturer forms tablets by compressing a granular material that contains the active ingredient and various fillers. The force in kilograms (kg) applied to the tablet varies a bit and follows the Normal distribution with mean 11.5 kg and standard deviation 0.2 kg. The process specifications call for applying a force between 11.2 and 12.2 kg. 1. Calculate the 25th percentile (P25) and the 75th percentile (P75) of the distribution. 2. ) Suppose the lifetime of a human has an expectation of 72 and variance 36. What is the probability that the average of the lifetime of 100 people exceeds 73?arrow_forward
- A product has a nominal length of 11cm. The tolerance associated with this dimension is +0.5cm and -0.5cm. Inspection is carried out on the length and it is found that the mean length is 10.9cm with the standard deviation of 0.47cm. i. Calculate the natural process limits. ii. State the specification limits.iii. Construct process showing all the four limits. In addition, shade the proportion of the product that is outside specification.iv. Calculate both capability indices.arrow_forwardA photoconductor film is manufactured at a nominal thickness of 25 mils. The product engineer wishes to increase the mean speed of the film, and believes that this can be achieved by reducing the thickness of the film to 20 mils. Eight samples of each film thickness are manufactured in a pilot production process, and the film speed (in microjoules per square inch) is measured. For the 25-mil film, the sample data result is = 1.15 and 81 = 0.11, while for the 20-mil film, the data yield 2 = 1.06 and 82 = 0.09. Note that an increase in film speed vould lower the value of the observation in microjoules per square inch. (a) Do the data support the claim that reducing the film thickness increases the mean speed of the film? Use a = 0.10 and assume that the two population variances are equal and the underlying population of film speed is normally distributed. What is the P-value for this test? Round your answer to three decimal places (e.g. 98.765). The data the claim that reducing the film…arrow_forwardA certain brand produces milk with boxes in a weight of 95 gr. The average weight of 12 samples equals 96.51 gr.Assume that the distribution of the weight of the product is 1.24. Conduct a test about the standart weight of the milk boxes. Does the product still weight 95gr or higher? Write down the z value which you should use for comparison.(Use at least 2 digits after decimal,sensitivity ;0.00)arrow_forward
- How heavy a load (pounds) is needed to pull apart pieces of Douglas fir 4 inches long and 1.5 inches square? Students doing a laboratory exercise sample 20 pieces of wood and find an average load capacity of 30,841 pounds. We are willing to regard the wood pieces prepared for the lab session as an SRS of all similar pieces of Douglas fir. Engineers also commonly assume the characteristics of materials vary normally. Suppose that the strength of pieces of wood like these follow a normal distribution with a population standard deviation of 3,000 pounds (As you can see all three necessary assumptions are met). a. Assuming that all evergreen wood has a known "load" capacity average of 30,000 pounds. Make a two-sided hypothesis (null and alternative statement) about Douglas Fir "load" capacity compared to the overall average. b. Apply the formula for finding our test statistic (show your work or describe the process) Specifically, use the formula for the z-statistic (pasted below and on…arrow_forwardThe "spring-like effect" in a golf club could be determined by measuring the coefficient of restitution (the ratio of the outbound velocity to the inbound velocity of a golf ball fired at the clubhead). Twelve randomly selected drivers produced by two clubmakers are tested and the coefficient of restitution measured. The data follow: Club 1: 0.8406, 0.8104, 0.8234, 0.8198, 0.8235, 0.8562, 0.8123, 0.7976, 0.8184, 0.8265, 0.7773, 0.7871 Club 2: 0.8305, 0.7905, 0.8352, 0.8380, 0.8145, 0.8465, 0.8244, 0.8014, 0.8309, 0.8405, 0.8256, 0.8476 Test the hypothesis that both brands of ball have equal mean overall distance. Use α = 0.05 and assume equal variances. Question: Reject H0 if t0 < ___ or if t0 > ___.arrow_forwardUnfortunately, arsenic occurs naturally in some ground water.t A mean arsenic level of u = 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 36 tests gave a sample mean of x = 7.1 ppb arsenic, with s = 2.2 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use a = 0.01. A USE SALT (a) What is the level of significance? State the null and alternate hypotheses. O Ho: H= 8 ppb; H,: H > 8 ppb O Ho: H 8 ppb; H: H = 8 ppb (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since the sample size is large and a is unknown. O The Student's t, since the sample size is large and a is known. O The standard normal, since the sample size is large and a is known. O The Student's t, since the sample size is large and a is unknown. What is…arrow_forward
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman