The following data represent the results from the specific gravity test performed in a soil laboratory including twenty samples of sand. * :The value of Root Mean Square is Specific Gravity 2.30-2.39 Number of Samples 1 2.40-2.49 2 2.50-2.59 3 2.60-2.69 2.70-2.79 6. 7 2.80-2.89 1 3.6-3.8 2.97-3.0 2.4-2.5 2.85-2.95 2.75-2.84 1.5-2.0 2.6-2.7 2.32-2.39
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- A 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 5 kg and standard deviation 0.2 kg. The process specifications call for applying a force between 11.2 and 12.2 kg. What percent of tablets are subject to a force that meets the specifications? The manufacturer adjusts the process so that the mean force is at the center of the specifications, μ = 11.7 kg. The standard deviation remains 0.2 kg. What percent now meets the specificationsAssume that the mean weight of 1-year-old girls in the US is normally distributed with amean of about 9.5 grams with a standard deviation of approximately 1.1 grams. Withoutusing a calculator estimate the percentage of 1-year-old girls in the US that meet thefollowing conditions. Draw a sketch and shade the proper region for each problem.Less than 8.4 kg Between 7.3 kg and 11.7 kgMore than 12.8 kgUnfortunately, arsenic occurs naturally in some ground water. † A mean arsenic level of μ = 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 31 tests gave a sample mean of x = 6.9 ppb arsenic, with s = 2.4 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use α = 0.01. USE SALT (a) What is the level of significance? State the null and alternate hypotheses. Ho: μ = 8 ppb; H₁₂: μ > 8 ppb Ho: μ = 8 ppb; H₁: μ 8 ppb; H₁: μ = 8 ppb Ho: μ 0.100 0.050 P-value < 0.100 0.010 < P-value < 0.050 0.005 P-value < 0.010 P-value < 0.005 Sketch the sampling distribution and show the area corresponding to the P-value. -2 -2 0 0 2 2 4 4 -4 -2 -2 0 0 2 2 4 4 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? At the α =…
- Unfortunately, arsenic occurs naturally in some ground water.† A mean arsenic level of μ = 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 31 tests gave a sample mean of x = 6.9 ppb arsenic, with s = 2.4 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use ? = 0.01. (a) What is the level of significance? What is the value of the sample test statistic? (Round your answer to three decimal places.)At wind speeds above 1000 centimeters per second, significant sand-moving events begin to occur sand is moved to new locations. The cyclic nature of wind and moving sand determines the shape and locations of large dunes. At a test site, the prevailing direction of wind did not change noticeably. However, the velocity did chnage. Sixty wind speed readings gave an average velocity of 1075 cm/sec (standard deviation weas 265 cm/sec). The researcher wants to determine if the wind speed is such that the sand is always moving at this site. Use alpha = 0.10.An automobile parts supplier owns a machine that produces a cylindrical engine part. This part is supposed to have an outside diameter of three inches. The technical staff feels that the mean diameter produced by the machine is off target. In order to verify this, a special study will randomly sample 40 parts produced by the machine. The 40 sampled parts will be measured, and if the results obtained cast a substantial amount of doubt on the hypothesis that the mean diameter equals the target value of three inches, the company will assign a problem-solving team to intensively search for the causes of the problem. Formula the hypotheses so that the problem-solving team will be assigned when the null hypothesis is rejected. A sample of 40 parts yields a sample mean diameter of 3.006 inches. Assume that the population standard deviation equals 0.016 inches. (1) Use the critical value approach to test H0 versus Ha when α = 0.05. (2) Use the p-value approach to test H0 versus Ha when α =…
- Unfortunately, arsenic occurs naturally in some ground water.† A mean arsenic level of μ = 8.3 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 41 tests gave a sample mean of x = 7.3 ppb arsenic, with s = 2.4 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8.3 ppb? Use ? = 0.01. (a) What is the level of significance? State the null hypotheses H0 and the alternate hypothesis H1 . H0 : μ ---Select--- < ≥ ≤ = > ≠ H1 : μ ---Select--- < > ≤ ≥ = ≠ (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since the sample size is large and σ is known.The Student's t, since the sample size is large and σ is known. The standard normal, since the sample size is large and σ is unknown. The Student's t, since the…The mean score on a driving exam for a group of drivers education students is 72 points with a standard deviation of 6 points. apply Chebyshev theorem to the data using K=2. Interpret the results. Simplify answer.The specifications for a plastic liner for concrete high-way projects calls for a thickness of 3.0 mm {.1 mm. The stand-ard deviation of the process is estimated to be .02 mm. What are the upper and lower specification limits for this product? The pro-cess is known to operate at a mean thickness of 3.0 mm. What is the Cpk for this process? About what percentage of all units of thisliner will meet specifications?
- In a herd of longhern cattle the mean horn length is 52cm and h2 is 0.2. Predict the mean horn length if cattle with horn of 61cm long are interbredOver a short period of time, a roller bearing manufacturer finds that 2% of the bearings exceed the USL diameter of 2.01 cm and 2% are less than the LSL of 1.99 cm. If the distribution ofdiameters is normal:a) What is the mean diameter?b) What is the standard deviation?c) What is Cp for the process?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 40 feet. Assume the population standard deviation is 4.9 feet. The mean braking distance for Make B is 44 feet. Assume the population standard deviation is 4.6 feet. At a = 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. Complete parts (a) through (e). Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) Identify the claim and state H, and Ha. What is the claim? A. The mean braking distance is different for the two makes of automobiles. B. The mean braking distance is less for Make A automobiles than Make B…