A synthetic fiber used in manufacturing carpet has tensile strenght that is normally distributed with 75.5psi and standard deviation 3.5psi. Find the probability that a random sample of n=6 fiber specimen will have sample mean tensile strength that exceeds 75.75psi.
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- A manufacturer claims that the average tensile strength of thread A exceeds the average tensile strength of thread B by at least 13 kilograms. To test this claim, 51 pieces of each type of thread were tested under similar conditions. Type A thread had an average tensile strength of 89.8 kilograms with a standard deviation of 5.95 kilograms, while type B thread had an average tensile strength of 79.8 kilograms with a standard deviation of 5.37 kilograms. Test the manufacturer's claim using a 0.05 level of significance. Do not assume that the population variances are equal. Click here to view page 1 of the table of critical values of the t-distribution. Click here to view page 2 of the table of critical values of the t-distribution. Let type A thread correspond to population 1 and let type B thread correspond to population 2. Identify the null and alternative hypotheses. Choose the correct answer below. B. Ho: H1 - H2 = 13 Ho: H1 - H2 > 13 H1: H1 - H2 = 13 A. Ho: H1 - H2 = 13 %3D H1: H1…Following maintenance and calibration, an extrusion machine produces aluminum tubing with a mean outside diameter of 2.500 inches, with a standard deviation of 0.027 As the machine functions over an extended number of work shifts, the standard deviation remains unchanged, but the combination of accumulated deposits and mechanical wear causes the mean diameter to “drift” away from the desired 2.500 inches. For a recent random sample of 34 tubes, the mean diameter was 2.509 inches. At the 0.01 level of significance, does the machine appear to be in need of maintenance and calibration?A local company makes snack-size bags of potato chips. The company produces batches of 400 snack-size bags using a process designed to fill each bag with an average of 2 ounces of potato chips. However, due to imperfect technology, the actual amount placed in a given bag varies. Assume the population of filling weights is normally distributed with a standard deviation of 0.1 ounce. The company periodically weighs samples of 10 bags to ensure the proper filling process. The last five sample means, in ounces, were 1.99, 2.02, 2.07, 1.96, and 2.01. Is the production process under control? Group of answer choices A. No, because the sample means show a downward trend. B. Yes, because the sample means show a downward trend. C. No, because the sample means fall within the upper and lower control limits. D. Yes, because the sample means fall within the upper and lower control limits.
- A machine that cuts corks for wine bottles operates in such a way that the distribution of the diameter of corks is well approximated by a Normal distribution with mean 3 cm and standard deviation 0.1 cm. The specififications call for corks with diameters between 2.9 and 3.1 cm. A cork not meeting the specififications is considered defective (a cork that is too small leaks and causes the wine to deteriorate; a cork that is too large does not fifit in the bottle). (a) What proportion of corks produced by this machine are defective? (b) If you choose 15 corks at random produced by this machine, what is the probability that 5 of them will be defective?A synthetic fiber used in manufacturing carpet has tensile strength that is normally distributed with mean 75.5 psi and standard deviation 3.5 psi. Find the probability that a random sample of n = 6 fiber specimens will have sample.mean tensile strength that exceeds 75.75 psi. Report your answer in four significant figures. %3DA light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 769 hours. A random. sample of 29 light bulbs has a mean life of 756 hours. Assume the population is normally distributed and the population standard deviation is 64 hours. At a = 0.02, do you have enough evidence to reject the manufacturer's claim? Complete parts (a) through (e). (a) Identify the null hypothesis and alternative hypothesis. OB. Ho: H=756 OA. Ho: 769 H₂: μ#756 (claim) Ho: 2769 (claim) H₂H756 (claim)
- Let type A thread correspond to population 1 and let type B thread correspond to population 2. Identify the null and alternative hypotheses. Choose the correct answer below. O A. Ho H4- H2# 14 H1 H1 - H2 = 14 OD. Ho H-H2> 14 H, H - 12 = 14 B. Ho H - 42 = 14 OC. Ho H1 -42 = 14 H -2 14 OF. H H1-H2 = 14 H -12 > 14 OE Ho H-H2 14 H, -2=14 Identify the critical region. Select the correct choice below and fill in the answer box(es) to complete your choice. (Round to two decimal places as needed) XA. I' B. t'> 1.66 Oc. t'< Find the test statistic 2.73 (Round to two decimal places as needed)A car company says that the mean gas mileage for its luxury sedan is 21 mpg. You believe the mean gas mileage is lower than this and find that a random sample of 5 cars has a mean gas mileage of 19 mpg and a sample standard deviation of 4 mpg. Assume the gas mileage of all of the company's luxury sedans is normally distributed. At x = 0.10, use a t-test to assert the validity of the company's claim. The alternative hypothesis is: HA: μ 21 HA: H = 21 HA: μ # 21A tire manufacturer wants to get an estimate of the average length of road that can be traveled (in 100 km) by a brand new tire, until the tire breaks. The assumption is that the tires are used fairly in relatively the same road conditions. For this purpose, research has been carried out on the tire production and obtained the average road that can be traveled until the tire is damaged, which is 25,300 km, and the standard deviation is estimated at 6,100 km. - What is the probability that the tire can reach a maximum of 30,000 km.
- The owner of a coin-operated hot coffee machine has received claims that there is an error in his machine, and it is not dispensing enough hot coffee into hand-held cups. He takes a random sample of 46 “8 oz servings” from a large number of servings and finds that the mean is 7.93 fluid ounces with a standard deviation of 0.38 ounces. Is this evidence of error in the machine if ? = 0.05? Use the P-Value method.A fishing line manufacturer tests the breaking stain of his products. He has found that, for a particular ‘line weight’, the maximum breaking stain follows a normal distribution, with a mean of 21.5kg and a standard deviation of 1.5kg. If a line is selected at random, calculate the probability that it has a breaking strain of between 22kg and 23.5kg.The men body mas index (BMI) for boys of age 12 years is 23.6kg/m An investigator wants to test if the BMI is higher in 12-year-old boys living in New York CIty. How many bos are needed to ensure that a two-sided test of hypothesis has 80% power to detect a difference in BMI of 2 kg/m? Assume that the standard deviation in BMI is 5.7 kg/m.
