4D. Articles are mass-produced to a specified width of 0-15 cm. In order to check that the production process is running satisfactorily, random samples of five articles are taken at regular time intervals, and the widths measured. The following are the means and ranges of the widths in 20 consecutive samples, where the widths are measured from the specified value in units of 0.0001 cm. Sample Sample Sample number mean range Sample Sample Sample number mean range 1 1-0 32 11 -1.6 18 2 2.4 21 12 -2.2 14 3 -2.4 19 13 1.6 6 4 3.2 6 14 0-4 15 1-4 11 15 2-0 18 6 1.2 17 16 3-0 16 7 2-6 13 17 1-6 18 8 0-4 9 18 -7-6 11 9 -2.2 14 19 <-5-4 15 10 -3.8 8 20 -4-2 8 Using these results, convert the average range into an estimate of the standard deviation of the widths of the articles in the population of manufactured articles. (If the range of a random sample of size 5 from a normal population is r, then an estimate of the standard deviation is given by multiplying r by 0-4299.) Hence draw a control chart for means, showing both 2-5% control limits (warning limits) and 0-1% control limits (action limits). Describe how this chart could be used to determine whether or not the manufacturing process is under control. What would your conclusion be for the data provided?

4D. Articles are mass-produced to a specified width of 0-15 cm. In order to check that the production process is running satisfactorily, random samples of five articles are taken at regular time intervals, and the widths measured. The following are the means and ranges of the widths in 20 consecutive samples, where the widths are measured from the specified value in units of 0.0001 cm. Sample Sample Sample number mean range Sample Sample Sample number mean range 1 1-0 32 11 -1.6 18 2 2.4 21 12 -2.2 14 3 -2.4 19 13 1.6 6 4 3.2 6 14 0-4 15 1-4 11 15 2-0 18 6 1.2 17 16 3-0 16 7 2-6 13 17 1-6 18 8 0-4 9 18 -7-6 11 9 -2.2 14 19 <-5-4 15 10 -3.8 8 20 -4-2 8 Using these results, convert the average range into an estimate of the standard deviation of the widths of the articles in the population of manufactured articles. (If the range of a random sample of size 5 from a normal population is r, then an estimate of the standard deviation is given by multiplying r by 0-4299.) Hence draw a control chart for means, showing both 2-5% control limits (warning limits) and 0-1% control limits (action limits). Describe how this chart could be used to determine whether or not the manufacturing process is under control. What would your conclusion be for the data provided?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

See similar textbooks

Similar questions

From a sample of n = 10 of marijuana consignments the tetrahydrocannabidiol (THC) content has been measured, and the mean found to be 9.5% and the variance 8.9%. Assuming x and s2 are good estimates of µ and s2 Calculate the percentage of marijuana samples expected to contain greater than 15.5 % THC. Determine the percentage of marijuana samples expected to contain less than 8.3% THC. iii. Determine the percentage of marijuana samples expected to contain between 10.0 and 15.0 % THC.
Apply the Slovin’s formula to calculate the minimum sample size for a population of 3,658 when e = 0.10.
A sample is selected from a population with μ = 50 and σ = 12. If the sample mean of M = 56 produces a z-score of z = +1.00, then how many scores are in the sample?
A random sample of n = 12 individuals is selected from a population with μ = 70, and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be M = 74.5 with SS = 297.a. How much difference is there between the mean for the treated sample and the mean for the original population? (Note: In a hypothesis test, this value forms the numerator of the t statistic.)b. How much difference is expected just by chance between the sample mean and its population mean? That is, find the standard error for M. (Note: In a hypothesis test, this value is the denominator of the t statistic.)c. Based on the sample data, does the treatment have a significant effect? Use a two-tailed test with α = .05.
The desired percentage of SiO2 in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of SiO2 in a sample is normally distributed with ? = 0.32 and that x = 5.21. (Use ? = 0.05.) (a) Does this indicate conclusively that the true average percentage differs from 5.5?State the appropriate null and alternative hypotheses. H0: ? = 5.5Ha: ? ≠ 5.5H0: ? = 5.5Ha: ? ≥ 5.5 H0: ? = 5.5Ha: ? < 5.5H0: ? = 5.5Ha: ? > 5.5 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State the conclusion in the problem context. Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage.Reject the null hypothesis. There is sufficient evidence…
A sample of n= 64 scores has a mean of M= 68. Assuming that the population mean is u=60, find the z-score for this sample: If it was obtained from a population with o= 16 Z=
Suppose that the weight of an newborn fawn is Uniformly distributed between 2.1 and 3.2 kg. Suppose that a newborn fawn is randomly selected. Round answers to 4 decimal places when possible.
Assume an infinite population and solve the given Given with random samples of size n selected from populations with means and variances, find the mean and standard deviation of the sampling distribution of the sample mean in each case: a. n= 9. µ=15, σ2=4 b. n = 100, µ =34, σ2 =49 The average weight of cats in a particular barangay is 3.9 kg with a standard deviation of 0. 82 kg. If 30 cats are randomly selected, determine the mean, standard deviation and variance of the corresponding sampling distributions of the sample means. The weekly allowance of all the Senior High School students in a particular city has an average of Php 500 with a standard deviation of Php 25. A random sample of 60 students was asked of their weekly allowance. Determine the standard error of the sampling distribution of the mean weekly allowance of Senior High School students in this high city. A normal population has a mean of 120 and variance of 16. How large must ure Size of the random sample be if…
A vehicle with a particular defect in its emission control system is taken to a succession of randomly selected mechanics until r = 16 of them have correctly diagnosed the problem. Suppose that this requires diagnoses by 20 different mechanics (so there were 4 incorrect diagnoses). Let p = P(correct diagnosis), so p is the proportion of all mechanics who would correctly diagnose the problem. What is the mle of p? p̂ = Is it the same as the mle if a random sample of 20 mechanics results in 16 correct diagnoses? Explain. No, the formula for the first one is (number of failures)/(number of trials) and the formula for the second one is (number of successes)/(number of failures). No, the formula for the first one is (number of failures)/(number of trials) and the formula for the second one is (number of successes)/(number of trials). Yes, both mles are equal to the fraction (number of successes)/(number of failures). No, the formula for the first one is (number of…
A population of trees has a mean leaf length of 6.2 inches. A sample of 17 of these trees in a particular neighborhood has a mean length of 3.2 inches. If SS = 144 for this sample, what is Cohen's d for this example, and what is the strength of the treatment effect, which in this case is growing in a particular neighborhood?
Suppose an electric-vehicle manufacturing company estimates that a driver who commutes 50 miles per day in a particular vehicle has a recharging time that has a uniformly distributed between 70 and 110 minutes. What is the expected recharging time in minutes?(Enter your answer with no decimal places).
If We can assert with 95% that the maximum error is 0.05 and p= 0.2 ,find the sample size...