### Statistics Question: Sulfur Dioxide in U.S. Cities#### Problem Statement:An environmental researcher claims that the mean amount of sulfur dioxide in the air in U.S. cities is 1.15 parts per billion. In a random sample of 134 U.S. cities, the mean amount of sulfur dioxide in the air is 0.93 parts per billion. Assume the population standard deviation is 2.62 parts per billion. At \( \alpha = 0.01 \), is there enough evidence to reject the claim?#### Step-by-Step Solution:1. **Null and Alternative Hypothesis**: - Null Hypothesis (\(H_0\)): The mean amount of sulfur dioxide in the air in U.S. cities is 1.15 parts per billion. \[ H_0: \mu = 1.15 \, \text{parts per billion} \] - Alternative Hypothesis (\(H_A\)): The mean amount of sulfur dioxide in the air in U.S. cities is not 1.15 parts per billion. \[ H_A: \mu \ne 1.15 \, \text{parts per billion} \]2. **Significance Level**: \[ \alpha = 0.01 \]3. **Sample Statistics**: - Sample size (\(n\)): 134 - Sample mean (\(\bar{x}\)): 0.93 parts per billion - Population standard deviation (\(\sigma\)): 2.62 parts per billion4. **Test Statistic**: Since the sample size is large (\(n > 30\)), we use the Z-test for the population mean. \[ Z = \frac{\bar{x} - \mu_0}{\frac{\sigma}{\sqrt{n}}} \] Plug in the values: \[ Z = \frac{0.93 - 1.15}{\frac{2.62}{\sqrt{134}}} = \frac{-0.22}{\frac{2.62}{11.57}} = \frac{-0.22}{0.2264} \approx -0.97 \]5. **Critical Value**: For a two-tailed test with \( \alpha = 0.01 \), the critical z-values

Name: ### Statistics Question: Sulfur Dioxide in U.S. Cities#### Problem St
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: ### Statistics Question: Sulfur Dioxide in U.S. Cities#### Problem Statement:An environmental researcher claims that the mean amount of sulfur dioxide in the air in U.S. cities is 1.15 parts per billion. In a random sample of 134 U.S. cities, the me

Answered: Image /qna-images/answer/946fc695-d392-418e-ae5b-708a440e19c6.jpg

Math

Statistics

An environmental researcher claims that the mean amount of sulfur dioxide in the air in U.S. cities is 1.15 parts per billion. In a random sample of 134 U.S. cities, the mean amount of sulfur dioxide in the air is 0.93 parts per billion. Assume the population standard deviation is 2.62 parts per billion. At a = 0.01, is there enough evidence to reject the claim? %3D

An environmental researcher claims that the mean amount of sulfur dioxide in the air in U.S. cities is 1.15 parts per billion. In a random sample of 134 U.S. cities, the mean amount of sulfur dioxide in the air is 0.93 parts per billion. Assume the population standard deviation is 2.62 parts per billion. At a = 0.01, is there enough evidence to reject the claim? %3D

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

Similar questions

A test was administered for a group of 400 students and scores were obtained. The scores are approximately normally distributed with a mean of 65 and standard deviation of 4.5. What are the scores within which approximately 95% of the total test scores fall?
One of the measurements used to determine the health of a person's lungs is the amount of air a person can exhale under force in one second. This is called forced expiratory volume in one second, and is abbreviated FEV,. Assume the mean FEV, for 10-year-old boys is 2.1 liters that the population standard deviation is o =0.2. A random sample of 53 10-year-old boys live in a community with high levels of ozone pollution are found to have a sample mean FEV, of 2.09 liters. Can you conclude that the mean FEV, in the high-pollution community differs from 2.1 liters? (A) Yes (B) No
The birth weight of newborn babes (measured by O'Cathain et al, 2002 n = 3226) is approximately normally distributed with a mean of 3.39kg and standard deviation of 0.55kg. Rounded to three decimals, What weight does a baby have to have to be in the 97%?
A certain grade egg must weigh at least 2.0 Oz. If the weights of eggs are normally distributed with a mean of 1.5oz. And a standard deviation of 0.4oz, approximately how many eggs would you expect to weigh more than 2oz?
To compare the dry braking distances from 30 to 0 miles per hour for two makes of automobiles, a safety engineer conducts braking tests for 35 models of Make A and 35 models of Make B. The mean braking distance for Make A is 42 feet. Assume the population standard deviation is 4.7 feet. The mean braking distance for Make B is 45 feet. Assume the population standard deviation is 4.4 feet. At a = 0.10, can the engineer support the claim that the mean braking distances are different for the two makes of automobiles? Assume the samples are random and independent, and the populations are normally distributed. Complete parts (a) rari rz (b) Find the critical value(s) and identify the rejection region(s). The critical value(s) is/are (Round to three decimal places as needed. Use a comma to separate answers as needed.)
Suppose a researcher wants to test if the average diastolic blood pressure in Irish-Americans is different than the average diastolic blood pressure in the general population. Note that the average diastolic blood pressure in the general population is 70 mmHG. The researcher recruits 30 Irish-Americans into this particular study and then measures each of their diastolic blood pressures (mmHG). The population of this sample has a standard deviation equal to 3.0. What is the two-sided alternative hypothesis? (in words) Group of answer choices The mean is different than 70 The mean is different than 73 The mean is greater than 70 The mean is greater than 73
Consider a normally distributed population with a mean of 196 and a standard deviation of 20. Find the value from this population that gives the 0.195 percentile. (Please round your answer to one decimal place, e.g. 0.6.)
Records indicate that the mean weight of mature rainbow trout in Eagle Creek is 1.75 kg with a standard deviation of 0.33 kg. After years of marked oxygen depletion from pollutants in the creek, a biologist wants to see if the standard deviation, o, of weights has changed. The biologist measures the weights of 20 randomly chosen mature rainbow trout from the creek and finds that the sample standard deviation is 0.38 kg. Assume the current weights of mature rainbow trout in the creek follow a normal distribution. Does the biologist have sufficient evidence to conclude that the population standard deviation, o, differs from 0.33 kg? To answer, complete the parts below to perform a hypothesis test. Use the 0.10 level of significance.
What happens to the standard deviation if the differences between the mean and data values are small? A SD is large. B SD is small. © SD is undetermined. D SD is zero.
The mean weight of a Great Dane is 63.0 kg with a standard deviation of 2.3 kg. Suppose a researcher randomly samples 61 Great Danes and records the weights of the sampled dogs. Calculate the standard deviation of the mean, rounded to 2 decimal places
According to Current Population Reports, the population distribution of number of years of education for self-employed individuals in the United States has a mean of 13.6 and a standard deviation of 3.0. Find the mean and standard error of the sampling distribution of ȳ for a random sample of 9 residents.
Suppose the length of human pregnancies from conception to birth varies according to a distribution that is normal with mean of 266 days and standard deviation of “alpha”. 11.7% of pregnancies last 284 days or more, find the variance of the distribution .