An Introduction to Statistical Methods and Data Analysis
7th Edition
ISBN: 9781305269477
Author: R. Lyman Ott, Micheal T. Longnecker
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Textbook Question
Chapter 5.12, Problem 5E
A company that manufacturers coffee for use in commercial machines monitors the caffeine content in its coffee. The company selects 50 samples of coffee every hour from its production line and determines the caffeine content. From historical data, the caffeine content (in milligrams, mg) is known to have a
- a. Identify the population about which inferences can be made from the sample data.
- b. Calculate a 95% confidence interval for the mean caffeine content μ of the coffee produced during the hour in which the 50 samples were selected.
- c. Explain to the CEO of the company in nonstatistical language the interpretation of the constructed confidence interval.
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
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…
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…
Unfortunately, arsenic occurs naturally in some ground water. A mean arsenic level of m= 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 37 tests gave a sample mean of xbar= 7.2 ppb arsenic, with s= 1.9 ppb. Does this info indicate that the mean level of arsenic in this well is less than 8ppb? Use a= 0.01. Show full detail.
Chapter 5 Solutions
An Introduction to Statistical Methods and Data Analysis
Ch. 5.12 - The county government in a city that is dominated...Ch. 5.12 - In the research study on percentage of calories...Ch. 5.12 - Face masks used by firefighters often fail by...Ch. 5.12 - Refer to Exercise 5.3. Describe a process to...Ch. 5.12 - A company that manufacturers coffee for use in...Ch. 5.12 - Refer to Exercise 5.5. The engineer in charge of...Ch. 5.12 - Refer to Exercise 5.5. Because the company is...Ch. 5.12 - As part of the recruitment of new businesses, the...Ch. 5.12 - A program to reduce recidivism has been in effect...Ch. 5.12 - The susceptibility of the root stocks of a variety...
Ch. 5.12 - Prob. 11ECh. 5.12 - In any given situation, if the level of confidence...Ch. 5.12 - A biologist wishes to estimate the effect of an...Ch. 5.12 - Refer to Exercise 5.14. Suppose the mayors staff...Ch. 5.12 - Refer to Exercise 5.14. Suppose the mayors staff...Ch. 5.12 - A study is designed to test the hypotheses H0: ...Ch. 5.12 - Refer to Exercise 5.16. Graph the power curve for...Ch. 5.12 - A study was conducted of 90 adult male patients...Ch. 5.12 - Prob. 22ECh. 5.12 - A national agency sets recommended daily dietary...Ch. 5.12 - To evaluate the success of a 1-year experimental...Ch. 5.12 - Refer to Exercise 5.24. Suppose a random sample of...Ch. 5.12 - The administrator of a nursing home would like to...Ch. 5.12 - The vulnerability of inshore environments to...Ch. 5.12 - The RD department of a paint company has developed...Ch. 5.12 - Prob. 29ECh. 5.12 - A concern to public health officials is whether a...Ch. 5.12 - Prob. 31ECh. 5.12 - Prob. 32ECh. 5.12 - Prob. 33ECh. 5.12 - Provide the rejection region based on a t-test...Ch. 5.12 - A study was designed to evaluate whether the...Ch. 5.12 -
The ability to read rapidly and simultaneously...Ch. 5.12 - Refer to Exercise 5.36. Using the reading...Ch. 5.12 -
Refer to Exercise 5.36.
Does there appear to be a...Ch. 5.12 - A consumer testing agency wants to evaluate the...Ch. 5.12 -
Refer to Exercise 5.39.
Does the normality of the...Ch. 5.12 - The amount of sewage and industrial pollutants...Ch. 5.12 - A dealer in recycled paper places empty trailers...Ch. 5.12 - Prob. 47ECh. 5.12 - Prob. 48ECh. 5.12 - Prob. 49ECh. 5.12 - Prob. 50ECh. 5.12 - Prob. 51ECh. 5.12 - Prob. 52ECh. 5.12 - Prob. 53ECh. 5.12 - Prob. 54ECh. 5.12 - Prob. 55ECh. 5.12 - Prob. 56ECh. 5.12 - Prob. 57SECh. 5.12 - The concentration of mercury in a lake has been...Ch. 5.12 -
In a standard dissolution test for tablets of a...Ch. 5.12 - Prob. 60SECh. 5.12 -
Over the past 5 years, the mean time for a...Ch. 5.12 - If a new process for mining copper is to be put...Ch. 5.12 - Prob. 63SECh. 5.12 - Prob. 64SECh. 5.12 - Prob. 65SECh. 5.12 - Prob. 66SECh. 5.12 - Prob. 67SECh. 5.12 - Prob. 68SECh. 5.12 - Prob. 69SECh. 5.12 - Prob. 70SECh. 5.12 - Prob. 71SECh. 5.12 - Prob. 73SECh. 5.12 - Prob. 74SECh. 5.12 - Prob. 75SECh. 5.12 - Prob. 76SE
Knowledge Booster
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
- A researcher studying stress is interested in the blood pressure measurements of chief executive officers (CEOS) of major corporations. He believes that the mean systolic blood pressure, u, of CEOS of major corporations is more than 136 mm Hg, which is the value reported in a possibly outdated journal article. He plans to perform a statistical test and measures the systolic blood pressures of a random sample of 150 CEOS of major corporations. Suppose that the population of systolic blood pressures among CEOS of major corporations has a standard deviation of 16 mm Hg and that the researcher performs his hypothesis test using the 0.01 level of significance. Based on this information, answer the questions below. Carry your intermediate computations to at least four decimal places, and round your responses as indicated. (If necessary, consult a list of formulas.)arrow_forwardA researcher studying stress is interested in the blood pressure measurements of chief executive officers (CEOS) of major corporations. He believes that the mean systolic blood pressure, u, of CEOS of major corporations is more than 136 mm Hg, which is the value reported in a possibly outdated journal article. He plans to perform a statistical test and measures the systolic blood pressures of a random sample of 100 CEOS of major corporations. Suppose that the population of systolic blood pressures among CEOS of major corporations has a standard deviation of 15 mm Hg and that the researcher performs his hypothesis test using the 0.1 level of significance. Based on this information, answer the questions below. Carry your intermediate computations to at least four decimal places, and round your responses as indicated. (If necessary, consult a list of formulas.) Н : μ is What are the null and alternative hypotheses that the researcher should use for the test? Н : μ is Assuming that the…arrow_forwardUnfortunately, arsenic occurs naturally in some ground water. A mean arsenic level of mu equals 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 test gave a sample mean of x-bar = 6.9 ppb arsenic, with s = 2.6 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Alpha = 0.01. a) What is the level of significance? b) What is the value of the sample test statistic? Round answer to 3 decimal places. c) estimate the p-value?arrow_forward
- Tire pressure (psi) and mileage (mpg) were recorded for a random sample of seven cars of thesame make and model. The extended data table (left) and fit model report (right) are based on aquadratic model What is the predicted average mileage at tire pressure x = 31?arrow_forwardA researcher studying stress is interested in the blood pressure measurements of chief executive officers (CEOs) of major corporations. He believes that the mean systolic blood pressure, μ , of CEOs of major corporations is less than 130 mm Hg, which is the value reported in a possibly outdated journal article. He plans to perform a statistical test and measures the systolic blood pressures of a random sample of 100 CEOs of major corporations. Suppose that the population of systolic blood pressures among CEOs of major corporations has a standard deviation of 18 mm Hg and that the researcher performs his hypothesis test using the 0.05 level of significance. Based on this information, answer the questions below.arrow_forwardIn 2017, the entire fleet of light‑duty vehicles sold in the United States by each manufacturer must emit an average of no more than 9090 milligrams per mile (mg/mi) of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) over the useful life (150,000150,000 miles of driving) of the vehicle. NOX ++ NMOG emissions over the useful life for one car model vary Normally with mean 8484 mg/mi and standard deviation 66 mg/mi. (a) What is the probability that a single car of this model emits more than 9090 mg/mi of NOX ++ NMOG? (Enter your answer rounded to four decimal places.) (b) A company has 1616 cars of this model in its fleet. What is the probability that the average NOX ++ NMOG level ?¯x¯ of these cars is above 9090 mg/mi? (Enter your answer rounded to four decimal places.)arrow_forward
- Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma. Over a period of months, anadult male patient has taken eight blood tests for uric acid. The mean concentration was ?̅= 5.35mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal, withσ = 1.85 mg/dl.a. Find a 90% confidence interval for the population mean concentration of uric acid in thispatient’s blood. What is the margin of error?b. Find a 99% confidence interval for the population mean concentration of uric acid in thispatient’s blood. What is the margin of error?c. Compare the margins of error for parts (a) and (b). As confidence levels increase, do marginsof error increase?arrow_forwardSpray drift is a constant concern for pesticide applicators and agricultural producers. The inverse relationship between droplet size and drift potential is well known. The paper "Effects of 2,4-D Formulation and Quinclorac on Spray Droplet Size and Deposition"† investigated the effects of herbicide formulation on spray atomization. A figure in a paper suggested the normal distribution with mean 1050 µm and standard deviation 150 µm was a reasonable model for droplet size for water (the "control treatment") sprayed through a 760 ml/min nozzle. (a) What is the probability that the size of a single droplet is less than 1455 µm? At least 900 µm? (Round your answers to four decimal places.) less than 1455 µm at least 900 µm (b) What is the probability that the size of a single droplet is between 900 and 1455 µm? (Round your answer to four decimal places.)(c) How would you characterize the smallest 2% of all droplets? (Round your answer to two decimal places.) The…arrow_forwardUnfortunately, arsenic occurs naturally in some ground water. A mean arsenic level of u = 8 parts per billion (ppb) is considered safe for agricultural use. A well in Los Banos is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 37 tests gave a sample mean of - = 7.3 ppb arsenic. It is known that o = this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use the classical approach. Use a = 0.01 1.9 ppb for this type of data. Does What is the hypotheses for this problem? A: H, µ = 7.3 ppb vs HA µ 7.3 ppb С: Н. и %3D8.0 рpb us HA И < 8.0 ppb D : H, μ< 8.0 ppb us H μΣ8.0 ppb O A OBarrow_forward
- 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…arrow_forwardThe company selects 50 samples of coffee every hour from its pro-duction line and determines the caffeine content. From historical data, the caffeine content (in milligrams, mg) is known to have a normal distribution with s^ 5 7.1 m.gDuring a 1-hour time period, the 50 samples yielded a mean caffeine content of y 5 110 mg. a. Identify the population about which inferences can be made from the sample data. b. Calculate a 95% confidence interval for the mean caffeine content m of the coffee produced during the hour in which the 50 samples were selected. c. Explain to the CEO of the company in nonstatistical language the interpretation of the constructed confidence interval.arrow_forwardUnfortunately, 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 =…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Hypothesis Testing using Confidence Interval Approach; Author: BUM2413 Applied Statistics UMP;https://www.youtube.com/watch?v=Hq1l3e9pLyY;License: Standard YouTube License, CC-BY
Hypothesis Testing - Difference of Two Means - Student's -Distribution & Normal Distribution; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=UcZwyzwWU7o;License: Standard Youtube License