Here are measurements (in millimeters) ot a critical dimension on an SRS of 8 of the more than 200 auto engine crankshafts produced in one day that are known to be normally distributed 234.12 233.91 234.21 233.96 234.07 233.98 234.09 234.15 Construct a 95% confidence interval for the mean measurements of a critical dimension at the time these crankshafts were produced

Here are measurements (in millimeters) ot a critical dimension on an SRS of 8 of the more than 200 auto engine crankshafts produced in one day that are known to be normally distributed 234.12 233.91 234.21 233.96 234.07 233.98 234.09 234.15 Construct a 95% confidence interval for the mean measurements of a critical dimension at the time these crankshafts were produced

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.2: Expected Value And Variance Of Continuous Random Variables

Problem 10E

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Let us assume that the mean dissolve times of two shapes of an ibuprofen tablet are normally distributed with standard deviations of σD = 10 for disk-shaped tablets and σO = 14 seconds for oval-shaped tablets. In a study of the relationship of the shape of a tablet to its dissolution time, 6 disk-shaped ibuprofen tablets and 8 oval-shaped ibuprofen tablets were dissolved in water. The dissolve times, in seconds, were observed to be as follows: Disk: 269.0 249.3 255.2 252.7 247.0 261.6Oval: 268.8 260.0 273.5 253.9 278.5 289.4 261.6 280.2 a) Can you conclude that the mean dissolve times differ between the two shapes? Test using α = 0.05. b) What is the p-value for this test?
A regulation golf ball should weigh 45 grams. A company produces golf balls for the PGA. To help ensure a high degree of accuracy, a random sample of 23 golf balls is drawn from the production line every 30 minutes and each golf ball is measured for accuracy. If the average weight of the sample is found to be significantly different than 45 grams, then the production line is shut down for inspection. The mean weight of a recent sample of 23 golf balls was found to be 43.66 grams. Use the p-value method to test the hypothesis that the mean weight of a golf ball produced by this company is different than 45 grams, using a significance level of 0.5%. Assume that the distribution of weights of all golf balls produced by this company is known to be approximately normally distributed with a standard deviation of 5.4 grams. State the null and alternative hypothesis for this test. Ho: ? H₁: ? V Determine if this test is left-tailed, right-tailed, or two-tailed. Otwo-tailed Oright-tailed…
The level of calciumin the blood of healthy young adults follows aNormal distributionwithmean μ = 10milligrams per deciliter and standard deviation = 0.4. A clinicmeasures theblood calcium of 100 healthy pregnant young women at their first visit for prenatal care.The mean of these 100 measurements is ¯ x = 9.8. Is this evidence that the mean calciumlevel in the population of healthy pregnant young women is less than 10? To answer this,test the hypotheses H0 : μ = 10 versus Ha : μ < 10 at the 5% significance level.(a) What is the value of the P-value?(b) Determine which of the following statements is true.• H0 should be rejected.• H0 should not be rejected.• Ha should be rejected.• There is a 5% chance that the null hypothesis is true.
Suppose that a researcher is interested in estimating the mean systolic blood pressure, u, of executives of major corporations. He plans to use the blood pressures of a random sample of executives of major corporations to estimate u. Assuming that the standard deviation of the population of systolic blood pressures of executives of major corporations is 27 mm Hg, what is the minimum sample size needed for the researcher to be 95% confident that his estimate is within 5 mm Hg of u? Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements). (If necessary, consult a list of formulas.) Aa,
Unfortunately, arsenic occurs naturally in some ground watert. 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 = 7.0 ppb arsenic, with s = 2.3 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use a = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. О но: и 3 8 рb; н,: и +8 ppb O Ho: H > 8 ppb; H: µ = 8 ppb O Ho: H = 8 ppb; H: µ > 8 ppb O Ho: H = 8 ppb; H,: µ < 8 ppb O Ho: H < 8 ppb; H,: µ = 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 o is unknown. O The Student's t, since the sample size is large and o is unknown. O The standard normal, since the sample size is large and o is…
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Unfortunately, arsenic occurs naturally in some ground watert. 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 41 tests gave a sample mean of x = 6.9 ppb arsenic, with s = 2.8 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. О Но: и 8 pb О Но: и> 8 рpb; Hi: и %3D 8 рpb (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since the sample size is large and o is unknown. The standard normal, since the sample size is large and o is known. The Student's t, since the sample size is large and o is known. O The standard normal, since the sample size is large and o is unknown. What is the value of the sample test…
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