Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.75. (a) Compute a 99% two-sided confidence interval for the true average porosity of a certain seam if the average porosity for 36 specimens from the seam was 4.85. (Give your answers to 2 decimal places) Answer. ( (b) Compute a 95% two-sided confidence interval for true average porosity of another seam based on 45 specimens with a sample average porosity of 4.56. (Give your answers to 2 decimal places) Answer: ( (c) What is the smallest sample size n necessary if,the width of the 90% two-sided confidence interval is to be 0.2? Round your answer up to the nearest whole number. n=

Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.75. (a) Compute a 99% two-sided confidence interval for the true average porosity of a certain seam if the average porosity for 36 specimens from the seam was 4.85. (Give your answers to 2 decimal places) Answer. ( (b) Compute a 95% two-sided confidence interval for true average porosity of another seam based on 45 specimens with a sample average porosity of 4.56. (Give your answers to 2 decimal places) Answer: ( (c) What is the smallest sample size n necessary if,the width of the 90% two-sided confidence interval is to be 0.2? Round your answer up to the nearest whole number. n=

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: the past, a chemical company produced a certain type of plastic. Now, using a newly developed and…

Q: A shipment of 1000 small lab mice arrives at the animal care facility with a nominal weight of 12 g…

A: Obtain the number of mice need to be sampled to ensure that the 95%confidence interval has a margin…

Q: A sample of 55 night-school students' ages is obtained in order to estimate the mean age of…

A: Given information Sample size(n) = 55 Sample mean = 25.8 Population variance = 30 Population…

Q: A researcher wishes to estimate the mean length of North American adult bullfrogs. To do so, a…

A: Solution-: Given: x¯=130.1cm,n=69,σ=24.2,α=0.01 We find, Intermediate values: Z_{tab}=? SE=? Maximum…

Q: A sample of only 8 adult rhinos had an average weight of 2,500 pounds. The standard deviation for…

Q: The weekly expenditures of all students of SQU are believed to have standard deviation of 15 RO.…

A: From the provided information, Standard deviation (σ) = 15 The confidence level = 99% The Z value at…

Q: Lian wants to advertise how many chocolate chips are in each Big Chip cookie at her bakery. She…

A: Given,sample size(n)=53mean(x)=11.4standard deviation(s)=1.8degrees of…

Q: random sample of 68 SAT scores of students applying for merit scholarships showed an average of 1400…

Q: A student repeated seven measurements of sulfur content in a lab sample giving the following…

A: The null and alternative hypothesis is; H0: μ=1.45H1: μ≠1.45The given level of significance…

Q: An article reports that in a sample of 7 men, the average volume of femoral cartilage (located in…

Q: 1. The burning rate of solid propellant used to power aircrew escape systems is normally distributed…

Q: A sample of 23 pomegranates found they had a mean weight of 12.7ounces and a standard deviation of…

A: A sample of 23 pomegranates is selected which have a mean weight of 12.7ounces and a standard…

Q: What is tα/2,df for a 95% confidence interval of the population mean based on a sample of 15…

A: Solution: We have to find the t-critical value (tα/2) at the given significance level 1- 0.95=0.05…

Q: A biology student measured the ear lengths of an SRS of 10 Mountain cottontail rabbits, and an SRS…

A: Given data: Mountain cotton tail 5.4 5.5 6.0 5.6 4.9 5.0 5.1 5.9 6.2 5.5 Holland Lop 12.1 12.0…

Q: (a) Compute a 90% confidence interval for the true average porosity of a certain seam if the average…

A: Given that True population standard deviation =0.75 Sample size =20 Sample mean =4.85 Then we…

Q: Suppose we want a 95% confidence interval for the average amount spent on books by freshmen in their…

A: We have given that Margin of error =E = 2 Population standard deviation =22 95% confidence…

Q: The waiting time for patients at a health clinic follows a normal distribution with a mean of 15…

A: We have to perform Z test for mean.

Q: find a 95% confidence interval for the true unknown mean.

A: here given, A sample of 25 pieces of laminate used in the manufacture of circuit boards was chosen,…

Q: (a) Calculate a 90% confidence interval for the average difference between the temperature…

A: (a) The degrees of freedom is, Computation of critical value: The critical value of t-distribution…

Q: 2. It is known that the amount of time needed to change the oil on a car is normally distributed…

A: Solution : Given : σ = 5 minutes n = 14 α = 0.01 confidence level = 99%…

Q: In the past, a chemical company produced a certain type of plastic. Now, using a newly developed…

A: Confidence Level = 90 Significance Level = α = (100-90)% = 0.1

Q: The quality control manager at a light bulb factory needs to estimate the mean life of a large…

A: Hey there! As per our policy we can answer only 3 sub-parts at a time. Please make a new request for…

Q: A shipment of 900 small lab mic arrives at the animal care facility with a nominal weight of 10 g…

Q: Lifetimes of AAA batteries are approximately normally distributed. A manufacturer wants to estimate…

Q: An SRS of 450 high school seniors gained an average of x = 20.80 points in their second attempt at…

A: The sample size is defined as: n=450. The sample average change in SAT score, x¯=20.80 And the…

Q: A laboratory tested 60 compact fluorescent bulbs for mercury content and found that the mean amount…

A: Given that Sample size n =60 Sample mean =5.33 Standard deviation =1.1

Q: We want to estimate the number of pounds of ground beef produced during a month. The firm processes…

A: Given, From the sample of 500 cows, it is found that the mean, or average, pounds of ground beef…

Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

Assume that the helium porosity (in percentage) of coal samples taken from any particular
seam is normally distributed with true standard deviation 0.75.
(a) Compute a 99% two-sided confidence interval for the true average porosity of a
certain seam if the average porosity for 36 specimens from the seam was 4.85.
(Give your answers to 2 decimal places)
Answer:
(b) Compute a 95% two-sided confidence interval for true average porosity of
another seam based on 45 specimens with a sample average porosity of 4.56.
(Give your answers to 2 decimal places)
Answer: (
(c) What is the smallest sample size n necessary if,the width of the 90% two-sided
confidence interval is to be 0.2? Round your answer up to the nearest whole number.
n=

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2: (a)

Step 3: (b)

Step 4: (c)

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions

The viscosity of a liquid detergent is supposed to average 800 centistokes at 25°C. A random sample of 16 batches of detergent is collected, and the average viscosity is 812. Suppose we know that the standard deviation of viscosity is σ = 25 centistokes. (a) What is the P-value for the test? (b) Find a 95 percent confidence interval on the mean.
A construction company is developing a machine to make bricks. A sample of 65 bricks made by the machine was weighed with sample mean 5.6 lbs, where ”lbs” is pounds. Assume that the weight of bricks has a distribution with standard deviation σ = 0.5 lbs. (i) Find the 95% confidence interval for the true mean weight of bricks made by the machine. (ii) To satisfy building standards, bricks must have error in weight of ±0.05 lbs from the mean weight. At 95% confidence level, what is the minimum number of bricks which must be weighed to make sure that the machine is making bricks satisfying building standards?
If the standard deviation of hole diameter significantly exceeds 0.011 mm, there is an unacceptably high probability that a rivet designed to be placed in the hole will not fit. After drilling 30 of these holes, a sample standard deviation in hole diameter was calculated as 0.012 mm. Construct a 95% interval estimate for the true deviation of the hole diameters and discuss the likelihood of the standard deviation exceeding our target.
You want to estimate the mean weight of quarters in circulation. A sample of 40 quarters has a mean weight of 5.629 grams and a standard deviation of 0.063 gram. Use a single value to estimate the mean weight of all quarters. Also, find the95% confidence interval for the average weight of all quarters. The estimate for the mean weight of all quarters is 5.6295.629 grams. (Round to three decimal places as needed.) Find the 95% confidence interval for the mean weight of all quarters. nothing grams<μ<nothing grams
A laboratory in California is interested in finding the mean chloride level for a healthy resident in the state. A random sample of 70 healthy residents has a mean chloride level of 103 mEq/L. If it is known that the chloride levels in healthy individuals residing in California have a standard deviation of 44 mEq/L, find a 90% confidence interval for the true mean chloride level of all healthy California residents. Then complete the table below. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. What is the lower limit of the 90% confidence interval? What is the upper limit of the 90% confidence interval?
An SRS of 400 high school seniors gained an average of x = 21.87 points in their second attempt at the SAT Mathematics exam. Assume that the change in score has a Normal distribution with standard deviation o = 48.66. We want to estimate the mean change in score µ in the population of all high school seniors. (a) Using the 68-95-99.7 Rule or the z-table (Table A), give a 95% confidence interval (a, b) for u based on this sample. (Enter your answers rounded to three decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.) a: b: (b) Based on your confidence interval in part (a), how certain are you that the mean change in score u in the population of all high school seniors is greater than 0? O The upper endpoint of the interval is larger than 0, so we are 95% certain that the mean change in score in the population of all high school seniors is greater than 0. O We cannot be…
A patient with suspected high blood pressure measures his bloodpressure using an automated test at a pharmacy every day for 30 days.The results of the blood pressure samples reveal a sample meansystolic blood pressure of 128.3mmHg.If it is known that the standard deviation between systolic bloodpressure measurements for the average person is 15.2mmHg, calculatethe margin of error and construct the 95% confidence interval for thepopulation mean systolic blood pressure for this patient.
The level of lead in the blood was determined for a sample of 152 male hazardous-waste workers age 20-30 and also for a sample of 86 female workers, resulting in a mean + standard error of 5.3 ± 0.3 for the men and 3.6 t 0.2 for the women. Calculate an estimate of the difference between true average blood lead levels for male and female workers in a way that provides information about reliability and precision. (Use a 95% confidence interval. Round your answers to two decimal places.) Interpret the interval. O we are 95% confident that the true average blood lead level for male workers is less than that of female workers by an amount within the confidence interval. O we are 95% confident that the true average blood lead level for male workers is greater than that of female workers by an amount outside the confidence interval. O we cannot draw a conclusion from the given information. O we are 95% confident that the true average blood lead level for male workers is greater than that of…
A warehouse owner wants to know the average weight of books at his facility. He weighs 18 books and finds that the sample has a mean weight of 9.41 pounds and standard deviation of 2.89 pounds. Construct a 99%confidence interval for the population mean of book weights. Assume the population is normally distributed.Choose the correct confidence interval and critical value used in the calculation. (7.46,11.36)(tc=2.8609) (7.83,10.99)(Zc=2.326) (7.44,11.38) (tc=2.8982) (7.45,11.37) (tc=2.8784) (7.66,11.16)(Zc=2.576)
The adhesive strength of medical monitoring device has a known standard deviation of 0.55 dyne cm. Tests on the first five prototypes of a new model yielded the following values of adhesive strength: 2.96, 5.67, 2.76, 1.26 and 4.21 dyne-cm'. a. What is the 95% confidence interval for the mean adhesion? b. If the manufacturer wants the confidence interval to be no wider than 0.62 dyne-cm2, how many 1. observations should they take?
An article reports that in a sample of 9 men, the average volume of femoral cartilage (located in the knee) was 18.7 cm3 with a standard deviation of 3.3 cm3 and the average volume in a sample of 9 women was 11.2 cm3 with a standard deviation of 2.4 cm2. Let μXμX represent the population mean for men and let μYμY represent the population mean for women. Find a 95% confidence interval for the difference μX−μYμX−μY . Round down the degrees of freedom to the nearest integer and round the answers to three decimal places. The 95% confidence interval is
From the past experience, it is known that the math score of graduates of an engineering college approximately follows a normal distribution with a standard deviation sigma = 21 When trying to find a 95% confidence interval for the mean math score using the sample mean, What is the size of the sample required to ensure that the error does not exceed 0.5 ?