Questions and Answers of Applied Statistics and Probability

Consider the hypothesis test H0: μ1 = μ2 against H1: μ1 ≠ μ2. Suppose that sample sizes n1 = 10 and n2 = 10, that x̅1 = 7.8 and x̅2 = 5.6, and that s21 = 4 and s22 = 9. Assume that σ21 =
Consider the hypothesis test H0: μ1 = μ2 against H1: μ1 = μ2. Suppose that sample sizes n1 = 15 and n2 = 15, that x̅1 = 6.2 and x̅2 = 7.8, and that s21 = 4 and s22 = 6.25. Assume that σ21 =
Consider the hypothesis test H0: μ1 = μ2 against H1: μ1 ≠ μ2. Suppose that sample sizes are n1 = 15 and n2 = 15, that x̅1 = 4.7 and x̅2 = 7.8, and that s21 = 4 and s22 = 6.25. Assume that
Consider the computer output below.Difference = mu (1) €“ mu (2)Estimate for difference: €“3.9195% upper bound for difference: ?T-test of difference = 0(vs <): T-value =
Consider the following computer output.Difference = mu (1) €“ mu (2)Estimate for difference: €“1.21095% CI for difference: (€“2.560, 0.140)T-test of difference = 0 (vs
In their book Statistical Thinking (2nd ed.), Roger Hoerl and Ron Snee provide data on the absorbency of paper towels that were produced by two different manufacturing processes. From process 1, the
Reconsider the study described in Exercise 10-10. Suppose that you wanted to detect a true difference in mean force of 0.25 pounds on the hands for these two activities. What level of type II error
Reconsider the data from Exercise 10-10. Find a 95% confidence interval on the difference in mean force on the hands for the two activities. How would you interpret this CI? Is the value zero in the
An article in Industrial Engineer (September 2012) reported on a study of potential sources of injury to equine veterinarians conducted at a university veterinary hospital. Forces on the hand were
The concentration of active ingredient in a liquid laundry detergent is thought to be affected by the type of catalyst used in the process. The standard deviation of active concentration is known to
A polymer is manufactured in a batch chemical process. Viscosity measurements are normally made on each batch, and long experience with the process has indicated that the variability in the process
Two different formulations of an oxygenated motor fuel are being tested to study their road octane numbers. The variance of road octane number for formulation 1 is σ21 = 1.5, and for formulation, 2
Two types of plastic are suitable for an electronics component manufacturer to use. The breaking strength of this plastic is important. It is known that σ1 = σ2 = 1.0 psi. From a random sample of
Two machines are used for filling plastic bottles with a net volume of 16.0 ounces. The fill volume can be assumed to be normal with standard deviation Ïƒ1= 0.020 and Ïƒ2= 0.025
Consider the hypothesis test H0: μ1 = μ2 against H1: μ1 > μ2 with known variances σ1 = 10 and σ2 = 5. Suppose that sample sizes n1 = 10 and n2 = 15 and that x1 = 24.5 and x2 = 21.3. Use α =
Consider the hypothesis test H0: μ1 = μ2 against H1: μ1 ≠ μ2 with known variances σ1 = 10 and σ2 = 5. Suppose that sample sizes n1 = 10 and n2 = 15 and that x̅1 = 4.7 and x̅2 = 7.8. Use α
Let X1, X2, …, Xn be a sample from an exponential distribution with parameter λ. It can be shown that 2λ Σni=1 Xi has a chi-square distribution with 2n degrees of freedom. Use this fact to
When X1, X2, €¦, Xnis a random sample from a normal distribution and n is large, the sample standard deviation has approximately a normal distribution with mean Ïƒ and variance
When X1, X2, €¦, Xnare independent Poisson random variables, each with parameter Î», and n is large, the sample mean X has an approximate normal distribution with mean
Derive an expression for β for the test on the variance of a normal distribution. Assume that the two-sided alternative is specified.
Suppose that we wish to test H0: μ = μ0 versus H1: μ ≠ μ0 where the population is normal with known σ. Let 0 < e < α, and define the critical region so that we will reject H0 if z0 >
Suppose that eight sets of hypotheses of the form H0: μ = μ0 H1: μ ≠ μ0 have been tested and that the P-values for these tests are 0.15, 0.06. 0.67, 0.01, 0.04, 0.08, 0.78, and 0.13. Use
A manufacturer of a pharmaceutical product is developing a generic drug and must show its the equivalence to the current product. The variable of interest is the activity level of the active
An article in the Journal of Electronic Material [“Progress in CdZnTe Substrate Producibility and Critical Drive of IRFPA Yield Originating with CdZnTe Substrates” (1998, Vol. 27(6), pp.
An article in Experimental Brain Research [€œSynapses in the Granule Cell Layer of the Rat Dentate Gyrus: Serial- Sectionin Study€ (1996, Vol. 112(2), pp. 237€“243)]
An article in Biological Trace Element Research [€œInteraction of Dietary Calcium, Manganese, and Manganese Source (Mn Oxide or Mn Methionine Complex) or Chick Performance and Manganese
An article in Food Chemistry [€œA Study of Factors Affecting Extraction of Peanut (Arachis Hypgaea L.) Solids with Water€ (1991, Vol. 42(2), pp. 153€“165)] reported
Consider the computer output belowUsing the normal approximation:(a) Fill in the missing information.(b) What are your conclusions if Î± = 0.05?(c) The normal approximation to the
An article in Food Testing and Analysis [€œImproving Reproducibility of Refractometry Measurements of Fruit Juices€ (1999, Vol. 4(4), pp. 13€“17)] measured the sugar
Consider the situation of Exercise 9-144. After collecting a sample, we are interested in testing H0: p = 0.10 versus H1: p ≠ 0.10 with α = 0.05. For each of the following situations, compute the
An article in Fire Technology [“An Experimental Examination of Dead Air Space for Smoke Alarms” (2009, Vol. 45, pp. 97–115)] studied the performance of smoke detectors installed not less than
An article in Transfusion Science [“Early Total White Blood Cell Recovery Is a Predictor of Low Number of Apheresis and Good CD34+ Cell Yield” (2000, Vol. 23, pp. 91–100)] studied the white
Consider the following computer output.(a) How many degrees of freedom are there on the t-statistic?(b) Fill in the missing information. You may use bounds on the P-value.(c) What are your
Consider the following computer output.(a) How many degrees of freedom are there on the t-statistic?(b) Fill in the missing information. You may use bounds on the P-value.(c) What are your
Consider the following computer output.(a) Fill in the missing information.(b) Is this a one-sided or a two-sided test?(c) What are your conclusions if Î± = 0.05?(d) Find a 95% two-sided
The mean weight of a package of frozen fish must equal 22 oz. Five independent samples were selected, and the statistical hypotheses about the mean weight were tested. The P-values that resulted from
The standard deviation of fill volume of a container of a pharmaceutical product must be less than 0.2 oz to ensure that the container is accurately filled. Six independent samples were selected, and
Suppose that eight sets of hypotheses about a population proportion of the form H0: p = 0.3 H1: p > 0.3 have been tested and that the P-values for these tests are 0.15, 0.83, 0.103, 0.024, 0.03,
Suppose that 10 sets of hypotheses of the form H0: μ = μ0 H1: μ ≠ μ0 have been tested and that the P-values for these tests are 0.12, 0.08. 0.93, 0.02, 0.01, 0.05, 0.88, 0.15, 0.13, and
The mean bond strength of a cement product must be at least 1000 psi. The process by which this material is manufactured must show equivalence to this standard. If the process can manufacture cement
The mean breaking strength of a ceramic insulator must be at least 10 psi. The process by which this insulator is manufactured must show equivalence to this standard. If the process can manufacture
A chemical products manufacturer must identify a new supplier for a raw material that is an essential component of a particular product. The previous supplier was able to deliver material with a mean
In developing a generic drug, it is necessary for a manufacturer of biopharmaceutical products to show equivalence to the current product. The variable of interest is the absorption rate of the
A group of civil engineering students has tabulated the number of cars passing eastbound through the intersection of Mill and University Avenues. They obtained the data in the following table.(a)
Recall the sugar content of the syrup in canned peaches from Exercise 8-51. Suppose that the variance is thought to be σ2 = 18 (milligrams)2. Recall that a random sample of n = 10 cans yields a
Data for tire life was described in Exercise 8-29. The sample standard deviation was 3645.94 kilometers and n = 16. (a) Can you conclude, using α = 0.05, that the standard deviation of tire
Data from an Izod impact test was described in Exercise 8-30. The sample standard deviation was 0.25 and n = 20 specimens were tested.(a) Test the hypothesis that σ = 0.10 against an alternative
The data from Technometrics described in Exercise 8-56 considered the variability in repeated measurements of the weight of a sheet of paper. In summary, the sample standard deviation from 15
The data from Medicine and Science in Sports and Exercise described in Exercise 8-53 considered ice hockey player performance after electrostimulation training. In summary, there were 17 players, and
Human oral normal body temperature is believed to be 98.6° F, but there is evidence that it actually should be 98.2° F [Mackowiak, Wasserman, Steven and Levine, JAMA (1992, Vol. 268(12), pp.
Exercise 6-38 gave data on the heights of female engineering students at ASU.(a) Can you support a claim that the mean height of female engineering students at ASU is at least 65 inches? Use α =
Exercise 6-40 presented data on the concentration of suspended solids in lake water.(a) Test the hypothesis H0: μ = 55 versus H1: μ ≠ 55; use α = 0.05. Find the P-value.(b) Check the
Reconsider the data from Medicine and Science in Sports and Exercise described in Exercise 8-32. The sample size was seven and the sample mean and sample standard deviation were 315 watts and 16
Consider the dissolved oxygen concentration at TVA dams first presented in Exercise 8-105.(a) Test the hypothesis H0: μ = 4 versus H1: μ ≠ 4. Use α = 0.01. Find the P-value.(b) Check the
A primer paint can be used on aluminum panels. The primer’s drying time is an important consideration in the manufacturing process. Twenty panels are selected, and the drying times are as follows:
A new type of tip can be used in a Rockwell hardness tester. Eight coupons from test ingots of a nickel-based alloy are selected, and each coupon is tested using the new tip. The Rockwell C-scale
An inspector are measured the diameter of a ball bearing using a new type of caliper. The results were as follows (in mm): 0.265, 0.263, 0.266, 0.267, 0.267, 0.265, 0.267,0.267, 0.265, 0.268, 0.268,
An article in the British Medical Journal [“Comparison of Treatment of Renal Calculi by Operative Surgery, Percutaneous Nephrolithotomy, and Extracorporeal Shock Wave Lithotripsy” (1986, Vol.
A company operates four machines in three shifts each day. From product ion records, the following data on the number of breakdowns are collected:Test the hypothesis (using Î± = 0.05)
Did survival rate for passengers on the Titanic really depend on the type of ticket they had? Following are the data for the 2201 people on board listed by whether they survived and what type of
The Hopkins Forest is a 2600-acre forest reserve located at the intersection of three states: New York, Vermont, and Massachusetts. Researchers monitor forest resources to study long-term ecological
Reconsider Exercise 6-87. The data were the number of earthquakes per year of magnitude 7.0 and greater since 1900. (a) Use computer software to summarize these data into a frequency
Construct a 95% lower confidence interval for the proportion of patients with kidney stones successfully removed in Exercise 9-95. Does this confidence interval support the claim that at least 78% of
Construct a 90% confidence interval for the proportion of handwritten zip codes that were read correctly using the data provided in Exercise 9-103. Does this confidence interval support the claim
In a random sample of 500 handwritten zip code digits, 466 were read correctly by an optical character recognition (OCR) system operated by the U.S. Postal Service (USPS). USPS would like to know
A computer manufacturer ships laptop computers with the batteries fully charged so that customers can begin to use their purchases right out of the box. In its last model, 85% of customers received
In a random sample of 85 automobile engine crankshaft bearings, 10 have a surface finish roughness that exceeds the specifications. Do these data present strong evidence that the proportion of
An article in Fortune (September 21, 1992) claimed that nearly one-half of all engineers continue academic studies beyond the B.S. degree, ultimately receiving either an M.S. or a Ph.D. degree. Data
A researcher claims that at least 10% of all football helmets have manufacturing flaws that could potentially cause injury to the wearer. A sample of 200 helmets revealed that 16 helmets contained
An article in the British Medical Journal [“Comparison of Treatment of Renal Calculi by Operative Surgery, Percutaneous Nephrolithotomy, and Extra-Corporeal Shock Wave Lithotrips” (1986, Vol.
A random sample of 300 circuits generated 13 defectives.(a) Use the data to test H0: p = 0.05 versus H1: p ≠ 0.05. Use α = 0.05. Find the P-value for the test.(b) Explain how the question in part
Suppose that 500 parts are tested in manufacturing and 10 are rejected.(a) Test the hypothesis H0: p = 0.03 against H1: p < 0.03 at α = 0.05. Find the P-value.(b) Explain how the question in part
Suppose that of 1000 customers surveyed, 850 are satisfied or very satisfied with a corporation’s products and services.(a) Test the hypothesis H0: p = 0.9 against H1:p ≠ 0.9 at α = 0.05. Find
Consider the following computer output(a) Is this a one-sided or a two-sided test?(b) Is this a test based on the normal approximation? Is that appropriate?(c) Complete the missing items.(d) Suppose
Consider the following computer outputUsing the normal approximation.(a) Is this a one-sided or a two-sided test?(b) Complete the missing items.(c) The normal approximation was used in the problem.
If the standard deviation of hole diameter exceeds 0.01 millimeters, there is an unacceptably high probability that the rivet will not fit. Suppose that n = 15 and s = 0.008 millimeter.(a) Is there
Consider the hypothesis test of H0: σ2 = 10 against H1: σ2 > 10. Approximate the P-value for each of the following test statistics.(a) x20 = 25.2 and n = 20 (b) x20 = 15.2 and n = 12(c) x20
Consider the test of H0: σ2 = 5 against : σ2 < 5. Approximate the P-value for each of the following test statistics.(a) x20 = 25.2 and n = 20 (b) x20 = 15.2 and n = 12(c) x20 = 4.2 and n =
Consider the hypothesis test of H0: σ2 = 7 against H1: σ2 ≠ 7. Approximate the P-value for each of the following test statistics.(a) x20 = 25.2 and n = 20(b) x20 = 15.2 and n = 12(c) x20 = 23.0
Consider the test of H0: σ2 = 5 against H1: σ2 < 5. What are the critical values for the test statistic χ20 for the following significance levels and sample sizes?(a) α = 0.01 and n =
Consider the test of H0: σ2 = 10 against H1: σ2 10. What are the critical values for the test statistic χ20 for the following significance levels and sample sizes?(a) α = 0.01 and n = 20 (b)
Consider the test of H0: σ2 = 7 against H1: σ2 ≠ 7. What are the critical values for the test statistic χ20 for the following significance levels and sample sizes?(a) α = 0.01 and n = 20(b) α
In a little over a month, from June 5, 1879, to July 2, 1879, Albert Michelson measured the velocity of light in air 100 times (Stigler, Annals of Statistics, 1977). Today we know that the true value
Consider the baseball coefficient of restitution data first presented in Exercise 8-103.(a) Do the data support the claim that the mean coefficient of restitution of baseballs exceeds 0.635? Use α =
An article in Growth: A Journal Devoted to Problems of Normal and Abnormal Growth [€œComparison of Measured and Estimated Fat-Free Weight, Fat, Potassium and Nitrogen of Growing Guinea
Consider the following computer output.(a) How many degrees of freedom are there on the t-test statistic?(b) Fill in the missing quantities.(c) At what level of significance can the null hypothesis
Consider the following computer output.(a) How many degrees of freedom are there on the t-test statistic?(b) Fill in the missing values. You may calculate bounds on the P-value. What conclusions
For the hypothesis test H0: μ = 5 against H1: μ < 5 with variance unknown and n = 12, approximate the P-value for each of the following test statistics.(a) t0 = 2.05 (b) t0 = −
For the hypothesis test H0: μ = 10 against H1: μ >10 with variance unknown and n = 15, approximate the P-value for each of the following test statistics.(a) t0 = 2.05 (b) t0 = −
For the hypothesis test H0: μ = 7 against H1: μ ≠ 7 with variance unknown and n = 20, approximate the P-value for each of the following test statistics.(a) t0 = 2.05 (b) t0 = −
A hypothesis will be used to test that a population mean equals 5 against the alternative that the population mean is less than 5 with unknown variance. What is the critical value for the test
A hypothesis will be used to test that a population mean equals 10 against the alternative that the population mean is greater than 10 with unknown variance. What is the critical value for the test
A hypothesis will be used to test that a population mean equals 7 against the alternative that the population mean does not equal 7 with unknown variance. What are the critical values for the test
The bacterial strain Acinetobacter has been tested for its adhesion properties. A sample of five measurements gave readings of 2.69, 5.76, 2.67, 1.62 and 4.12 dyne-cm2. Assume that the standard
Humans are known to have a mean gestation period of 280 days (from last menstruation) with a standard deviation of about 9 days. A hospital wondered whether there was any evidence that their patients
Supercavitation is a propulsion technology for undersea vehicles that can greatly increase their speed. It occurs above approximately 50 meters per second when pressure drops sufficiently to allow
Output from a software package follows:(a) Fill in the missing items. What conclusions would you draw?(b) Is this a one-sided or a two-sided test?(c) If the hypothesis had been H0: Î¼=
Output from a software package follows:(a) Fill in the missing items. What conclusions would you draw?(b) Is this a one-sided or a two-sided test?(c) Use the normal table and the preceding data to
Output from a software package follows:(a) Fill in the missing items. What conclusions would you draw?(b) Is this a one-sided or a two-sided test?(c) Use the normal table and the preceding data to
Output from a software package follows:(a) Fill in the missing items. What conclusions would you draw?(b) Is this a one-sided or a two-sided test?(c) Use the normal table and the preceding data to

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