(d) Find the critical values. (e) Rejection region and conclusion. (f) Interpret the results.
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A dynamic cone pentameter (DCP) is used for measuring material resistance to penetration (mm/blow) as a cone is driven into pavement or subgrade. Suppose that for a particular application it is required that the true average DCP value for a certain type of pavement be less than 30. The pavement will not be used unless there is conclusive evidence that the specification has been met. Suppose that the sample mean is 28.8 and the sample standard deviation is 12.3 for the
(d) Find the critical values.
(e) Rejection region and conclusion.
(f) Interpret the results.
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- A survey found that women's heights are normally distributed with mean 63.4 in. and standard deviation 3.8 in. The survey also found that men's heights are normally distributed with mean 67.9 in. and standard deviation 3.6 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 57 in. and a maximum of 63 in. Complete parts (a) and (b) below.a) Soil has been improved to increase the strength of a ground. The average compressive strength of 61 samples before treatment is 45 kg / cm2 and the standard deviation is 6.75 kg / cm2; The average compressive strength of 56 samples after the improvement is 52.5 kg / cm2 and the standard deviation is 8 kg / cm2. Determine whether the improvement application changes the standard deviation of the soil strength or not at the 5% significance level .b) Find the confidence intervals at the 7% significance level of the mean compressive strength of the sample after improvement?The time it takes for a compact fluorescent bulb to reach full brightness is normally distributed with mean 29.9 seconds and standard deviation 4.1 seconds. Find and interpret the z-score for x = 26.4.
- Acrylic bone cement is sometimes used in hip and knee replacements to fix an artificial joint in place. The force required to break an acrylic bone cement bond was measured for six specimens under specified conditions, and the resulting mean and standard deviation were 306.03 newtons and 41.95 newtons, respectively. Assuming that it is reasonable to believe that breaking force under these conditions has a distribution that is approximately normal, estimate the mean breaking force for acrylic bone cement under the specified conditions using a 95% confidence interval. (Round your answers to three decimal places.) n USE SALTAn engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 100 engines and the mean pressure was 4.9 lbs/square inch. Assume the standard deviation is known to be 0.7. If the valve was designed to produce a mean pressure of 4.7 lbs/square inch, is there sufficient evidence at the 0.02 level that the valve performs above the specifications? State the null and alternative hypotheses for the above scenario.To compare the dry braking distances from 30 to 0 miles per hour for two makes of automobiles, a safety engineer conducts braking tests for 35 models of Make A and 35 models of Make B. The mean braking distance for Make A is 43 feet. Assume the population standard deviation is 4.6 feet. The mean braking distance for Make B is 46 feet. Assume the population standard deviation is 4.5 feet. At α=0.10, can the engineer support the claim that the mean braking distances are different for the two makes of automobiles? Assume the samples are random and independent, and the populations are normally distributed. The critical value(s) is/are Find the standardized test statistic z for μ1−μ2.
- A survey found that women's heights are normally distributed with mean 62.2 in. and standard deviation 3.9 in. The survey also found that men's heights are normally distributed with mean 67.9 in. and standard deviation 3.4 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 57 in. and a maximum of 64 in. Complete parts (a) and (b) below. ..... a. Find the percentage of men meeting the height requirement. What does the result suggest about the genders of the people who are employed as characters at the amusement park? The percentage of men who meet the height requirement is %. (Round to two decimal places as needed.) Since most men the height requirement, it is likely that most of the characters are b. If the height requirements are changed to exclude only the tallest 50% of men and the shortest 5% of men, what are the new height requirements? The new height requirements are a minimum of in. and a maximum of in. (Round to one decimal…A fiber spinning process currently produces a fiber whose strength is normally distributed with a mean of 75 Pa. The minimum acceptable strength is 65Pa. If 10% of the fiber produced by the current method fails to meet the minimum specifications, what is the standard deviation of fiber strengths in the process? If the mean remains at 75 Pa, what must the standard deviation be so that only 1% of the fiber will fail to meet the specifications? Given that the standard deviation is 5Pa, to what value must be mean be set so that only 1% of the fiber will fail to meet the specifications?An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 200 engines and the mean pressure was 4.4 lbs/square inch. Assume the standard deviation is known to be 0.9. If the valve was designed to produce a mean pressure of 4.5 lbs/square inch, is there sufficient evidence at the 0.02 level that the valve performs below the specifications? State the null and alternative hypotheses for the above scenario.
- A sample of 50 earthquakes was found to have a sample mean of x ¯ = 1.184 and a sample standard deviation of s = 0.5864. Test the claim that the population of earthquakes has a mean magnitude greater than 1.00. Use a 0.01 significance level. Find the test statistic and critical value used for this test. Round to three decimal places.A manufacturing process produces a critical part of average length 80 millimeters, with a standard deviation of 3 millimeters. All parts deviating by more than 5 millimeters from the mean must be rejected. What percentage of the parts must be rejected, on average? Assume a normal distribution.Concrete cubes are used to test the quality of mix from a concrete mixing plant. 28 day compressive strength is taken as the standard measure to test the quality of the mix. Tests show that mean compressive strength of a sample of cubes is 28.4 units with a standard deviation of 2.95 units. To assure quality, the mixing company requires that at least 95% of the samples have compressive strength greater than 24 units. Based on this information and assuming a large sample size, answer the following questions. After major improvements on the plant, the mixing company is able to make cubes more consistent (reduce SD of compressive strength but maintain the same mean). For what value of the new SD will be cube standards be just met? Based on the requirements, only about___% of the samples meet the company standards.?
