Questions and Answers of Applied Statistics and Probability

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
For the hypothesis test H0: μ = 5 against H1: μ < 5 and variance known, calculate the P-value for each of the following test statistics.(a) z0 = 2.05 (b) z0 = −1.84 (c) z0 = 0.4
For the hypothesis test H0: μ = 10 against H1:μ >10 and variance known, calculate the P-value for each of the following test statistics.(a) z0 = 2.05 (b) z0 = −1.84 (c) z0 = 0.4
For the hypothesis test H0: μ = 7 against H1: μ ≠ 7 and variance known, calculate the P-value for each of the following test statistics.(a) z0 = 2.05 (b) z0 =−1.84 (c) z0 = 0.4
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 known variance σ. 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 more than 10 with known variance σ. 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 known variance σ. What are the critical values for the test
State the null and alternative hypothesis in each case.(a) A hypothesis test will be used to potentially provide evidence that the population mean is more than 10.(b) A hypothesis test will be used
In the quality-control example of Exercise 9-29, the manager says that the probability of a type I error is too large and that it must be no larger than 0.01.(a) How does this change the rule for
A quality-control inspector is testing a batch of printed circuit boards to see whether they are capable of performing in a high temperature environment. He knows that the boards that will survive
If we plot the probability of accepting H0: μ = μ0 versus various values of μ and connect the points with a smooth curve, we obtain the operating characteristic curve (or the OC curve) of the test
In Exercise 9-20, calculate the probability of a type II error if the true mean output is 5.05 volts and(a) α = 0.05 and n = 10 (b) α = 0.05 and n = 16(c) Compare the values of β calculated
In Exercise 9-20, calculate the P-value if the observed statistic is(a) x̅ = 5.2 (b) x̅ = 4.7 (c) x̅ = 5.1
In Exercise 9-20, find the boundary of the critical region if the type I error probability is(a) α = 0.01 and n = 8(b) α = 0.05 and n = 8 (c) α = 0.01 and n = 16(d) α = 0.05 and n = 16
In Exercise 9-15, calculate the P-value if the observed statistic is(a) x̅ = 180 (b) x̅ = 190 (c) x̅ = 170
In Exercise 9-15, calculate the probability of a type II error if the true mean foam height is 185 millimeters and(a) α = 0.05 and n = 10 (b) α = 0.05 and n = 16(c) Compare the values of β
In Exercise 9-15, find the boundary of the critical region if the type I error probability is(a) α = 0.01 and n = 10(b) α = 0.05 and n = 10 (c) α = 0.01 and n = 16(d) α = 0.05 and n = 16
A consumer products company is formulating a new shampoo and is interested in foam height (in millimeters). Foam height is approximately normally distributed and has a standard deviation of 20
In Exercise 9-10, calculate the P-value if the observed statistic is(a) x̅ = 98 (b) x̅ = 101 (c) x̅ = 102
In Exercise 9-10, calculate the probability of a type II error if the true mean heat evolved is 103 and(a) α = 0.05 and n = 9 (b) α = 0.05 and n = 5(c) Compare the values of β calculated in
In Exercise 9-10, find the boundary of the critical region if the type I error probability is(a) α = 0.01 and n = 9 (b) α = 0.05 and n = 9(c) α = 0.01 and n = 5(d) α = 0.05 and n = 5
Repeat Exercise 9-10 using a sample size of n = 5 and the same acceptance region.Exercise 9-10The heat evolved in calories per gram of a cement mixture is approximately normally distributed. The mean
In Exercise 9-5, calculate the P-value if the observed statistic is(a) x̅ = 11.25 (b) x̅ = 11.0 (c) x̅ = 11.75
In Exercise 9-5, calculate the probability of a type II error if the true mean elongation is 11.5 kilograms and(a) α = 0.05 and n = 4(b) α = 0.05 and n = 16(c) Compare the values of β calculated
In Exercise 9-5, find the boundary of the critical region if the type I error probability is(a) α = 0.01 and n = 4(b) α = 0.05 and n = 4(c) α = 0.01 and n = 16(d) α = 0.05 and n = 16
The mean pull-off force of a connector depends on cure time.(a) State the null and alternative hypotheses used to demonstrate that the pull-off force is below 25 newtons.(b) Assume that the previous
The standard deviation of critical dimension thickness in semiconductor manufacturing is σ = 20 nm. (a) State the null and alternative hypotheses used to demonstrate that the standard deviation
A semiconductor manufacturer collects data from a new tool and conducts a hypothesis test with the null hypothesis that a critical dimension mean width equals 100 nm. The conclusion is to not reject
A biology student finds that of 35 males with Drosophila melanogaster, 2 have Adh genotypes with a male mating advantage.(a) Using the standard methods, find a 95% confidence interval for the true
The confidence interval for a population proportion depends on the central limit theorem. A common rule of thumb is that to use the normal approximation for the sampling distribution for ˆp, you
An article in the Journal of Human Nutrition and Dietetics [€œThe Validation of Energy and Protein Intakes by Doubly Labeled Water and 24-Hour Urinary Nitrogen Excretion in Post-Obese
An article in the Journal of Applied Physiology [€œHumidity Does Not Affect Central Nervous System Oxygen Toxicity€ (2001, Vol. 91, pp. 1327€“1333)] reported that
Consider the bottle-wall thickness measurements described in Exercise 8-42.(a) Compute a 90% tolerance interval on bottle-wall thickness that has confidence level 90%.(b) Compute a 90% lower
Consider the strength-of-concrete data in Exercise 8-39. Compute a 90% tolerance interval on the compressive strength of the concrete that has 90% confidence.
Consider the rainfall in Exercise 8-35. Compute a 95% prediction interval on the rainfall for the next year. Compare the length of the prediction interval with the length of the 95% CI on the
Consider the natural frequency of beams described in Exercise 8-34. Compute a 90% prediction interval on the diameter of the natural frequency of the next beam of this type that will be tested.
Use the data from Exercise 8-66 to compute a two-sided Agresti-Coull CI on the proportion of correct digits that can be automatically read. Compare and discuss the CI to the one computed in Exercise
Use the data from Exercise 8-60 to compute a two-sided Agresti-Coull CI on the proportion of tears that will heal. Compare and discuss the CI to the one computed in Exercise 8-60.Exercise-60An
Use the data from Exercise 8-68 to compute a two-sided Agresti-Coull CI on the proportion of seeds that germinate. Compare and discuss the CI to the one computed in Exercise 8-68.

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