a. Suppose that a random sample of 41 state college students is asked to measure the length of their right foot in centimeters. A 95% confidence interval for the mean foot length for students at this university turns out to be (21.709, 25.091). If we now calculated a 90% confidence interval, would the new confidence interval be wider than or narrower than or the same as the original? b. Suppose two researchers want to estimate the proportion of American college students who favor abolishing the penny. They both want to have about the same margin of error to estimate this proportion. However, Researcher 1 wants to estimate with 95% confidence and Researcher 2 wants to estimate with 99% confidence. Which researcher would need fewer students for her study in order to obtain the desired margin of error? The answer is Researcher c. A 95% confidence interval for the mean reading achievement score for a population of third grade students is (55, 65). The margin of error of this interval is what whole number?

a. Suppose that a random sample of 41 state college students is asked to measure the length of their right foot in centimeters. A 95% confidence interval for the mean foot length for students at this university turns out to be (21.709, 25.091). If we now calculated a 90% confidence interval, would the new confidence interval be wider than or narrower than or the same as the original? b. Suppose two researchers want to estimate the proportion of American college students who favor abolishing the penny. They both want to have about the same margin of error to estimate this proportion. However, Researcher 1 wants to estimate with 95% confidence and Researcher 2 wants to estimate with 99% confidence. Which researcher would need fewer students for her study in order to obtain the desired margin of error? The answer is Researcher c. A 95% confidence interval for the mean reading achievement score for a population of third grade students is (55, 65). The margin of error of this interval is what whole number?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: If n 20, 40, and s 20, construct a confidence interval at a 90% confidence level. Assume the data…

Q: If n = 15, 43, and s = 9, construct a confidence interval at a 98 % confidence level. Assume the…

Q: If n=16, ¯xx¯(x-bar)=46, and s=12, construct a confidence interval at a 95% confidence level. Assume…

A: Given n=16 x=46 s=12 CL=95% Data is normally distributed

Q: Suppose we wanted to estimate the average amount of sleep (in hours) a college student gets a night.…

A: Confidence interval : Confidence interval is a range of values it contains the true population…

Q: If n=22, ¯xx¯(x-bar)=45, and s=4, construct a confidence interval at a 90% confidence level. Assume…

A: Ans - Given the level of confidence interval 90 % Then α = 1 - 0.90 =…

Q: A random sample of size n₁ = 23, taken from a normal population with a standard deviation 01 = 6,…

A: Hey there! Thank you for posting the question. Since there are multiple questions posted, we will…

Q: If n = 28, ¯xx¯ = 49, and s = 19, construct a confidence interval at a 90% confidence level. Assume…

A: Given information- Sample size, n = 28 Sample mean, x-bar = 49 Sample standard deviation, s = 19…

Q: Suppose that the a college wants to have an idea of the average SAT score of the incoming freshman…

A: The confidence level is 0.90, the standard deviation is 310 and margin of error E is 50.

Q: 1. Your colleague collected a sample of data regarding the mean length of a movie and they computed…

A: It has been given that the confidence interval of the mean length of a movie has been computed on a…

Q: What is the value of the point estimate for our 90% confidence interval? Round your answer to three…

Q: If n=19, ¯xx¯(x-bar)=37, and s=13, construct a confidence interval at a 99% confidence level. Assume…

Q: Suppose you are interested in the rate of autism among current school-aged children in Utah. You…

A: Given Information: Sample size n=400 Out of which 2 have had a previous diagnosis of an autism…

Q: If n=41n=41, ¯xx¯=36, and s=9s=9, find the margin of error for a 80% confidence level.

A: Answer - Given, Sample size n = 41, x = 36 and s = 9 80% confidence interval…

Q: n=31, ¯xx¯(x-bar)=30, and s=5, construct a confidence interval at a 98% confidence level. Assume the…

Q: All residents of Homer Glen, IL (N = 21,000). You want to estimate the mean age of each population…

A: Sample size n=7595% confidence level.

Q: A sample of 23 plants was taken and the mean height was 27 cm. A 95% confidence interval for the…

A: From the given information, The 95% confidence interval for the true mean height of plants of that…

Q: If n=24, ¯xx¯(x-bar)=49, and s=9, construct a confidence interval at a 80% confidence level. Assume…

Q: one with a 95% confidence level and the other with a 99.7% confidence level. Which interval is…

A: Confidence interval is probability, which refers that population parameter will fall within set of…

Q: If X 121, o =27, and n 38, construct a 95% confidence interval estimate of the population mean, u.…

Q: Suppose you want to estimate the weight of infants age 6 - 12 mos. A sample of 50 infants was…

A: Given Sample of 50 infants was obtained and the 95 % confidence interval was found to be…

Q: The US Treasury found that a random sample of 1309 $20 bills found that 837 of them had trace…

Q: An economist at the Florida Department of Labor and Employment needs to estimate the unemployment…

A: An economist at the Florida Department of Labor and Employment needs to estimate the unemployment…

Q: Suppose that a 95% confidence interval for a population p = the population proportion of men who…

Q: Free of CVD Prevalent CVD Total Men 1548 244 1792…

A: Given The tota number of men with CVD =244The tota number of women with CVD =135The tota number of…

Q: If n=19, ¯xx¯=40, and s=7, construct a confidence interval at a 99% confidence level. Assume the…

Q: 2. In a random sample of 150 drivers arrested for DUI (drunk driving), 90% were males. The 99%…

A: According to the given information, we have Total number of drivers arrested for DUI = 150 90% were…

Q: What proportion of Law School applicants are accepted into Law School? In a survey of a random…

A: According to the given information in this question We can say that the We are 95% confident the…

Q: In a random sample of 80 teenagers, the average number of texts handled in a day is 50. The 96%…

A: Given information: n = 80 μ=50 96% confidence interval for the mean number of texts handled by teens…

Q: Which of the following would result in the narrower confidence interval?

A: Note: The confidence interval with small confidence level has the narrower confidence interval. The…

Q: What proportion of OSU students earn their undergraduate degrees in four years? A college…

Q: 4. Two groups of drivers are surveyed to see how many miles per week they drive for pleasure trips.…

A: Given the data on the drivers (single and married).want to test whether single drivers do more…

Q: Which type of confidence interval should you use in this situation? A sample of 6 adult elephants…

A: It is given that Mean = 12200Sample std. deviation = 200Sample size = 6Confidence level = 95%

Q: If n=41, ¯x=39, and s=16, construct a confidence interval at a 99% confidence level. Assume the data…

A: Given that Sample size (n) = 41 Sample mean (x¯) = 39 Sample standard deviation (s) = 16 Confidence…

Q: Suppose that you will be taking a random sample from a population and that you intend to find a 95%…

A: If the sample size increases, then the standard error of statistic decreases. The margin of error is…

Q: If n=28, ¯x(x-bar)=32, and s=11, construct a confidence interval at a 95% confidence level. Assume…

Concept explainers

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.

Question

a. Suppose that a random sample of 41 state college students is asked to measure the length of their right foot in centimeters. A 95% confidence interval for the mean foot length for students at this
university turns out to be (21.709, 25.091). If we now calculated a 90% confidence interval, would the new confidence interval be wider than or narrower than or the same as the original?
b. Suppose two researchers want to estimate the proportion of American college students who favor abolishing the penny. They both want to have about the same margin of error to estimate this proportion.
However, Researcher 1 wants to estimate with 95% confidence and Researcher 2 wants to estimate with 99% confidence. Which researcher would need fewer students for her study in order to obtain the
desired margin of error? The answer is Researcher
c. A 95% confidence interval for the mean reading achievement score for a population of third grade students is (55, 65). The margin of error of this interval is what whole number?
d. Two different samples will be taken from the same population of test scores where the population mean and standard deviation are unknown. The first sample will have 25 data values, and the second
sample will have 64 data values. A 95% confidence interval will be constructed for each sample to estimate the population mean. Which number of data values would you expect to give a greater precision
(a smaller width) for estimating the population mean? The answer is the sample with
data values.
e. Each of the 110 students in a statistics class selects a different random sample of 35 quiz scores from a population of 5000 quiz scores they are given. Using their data, each student constructs a 90%
confidence interval for mu, the average quiz score of the 5000 students. Is the following statement correct, yes or no?
About 10% of the raw scores in the samples will not be found in these confidence intervals.

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

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Basics of Inferential Statistics$

Learn more about

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

Similar questions

If n=29, x¯(x-bar)=31, and s=8, construct a confidence interval at a 90% confidence level. Assume the data came from a normally distributed population.Give your answers to one decimal place.
When a population has less variability, for the same margin of error and confidence level, the confidence interval becomes a. larger b. smaller c. of unchanged size
if n=20, x=43, and s=9, construct a confidence interval at a 98% confidence level, the data came from a normally distributed population.
If n=14, ¯xx¯(x-bar)=34, and s=4, construct a confidence interval at a 80% confidence level. Assume the data came from a normally distributed population.
A survey is taken of 250 students, and a P of 0.45 is found. The same survey is repeated with 1,000 students, and the same value is found. Compare the two 95% confidence intervals. What is the relationship? Is the margin of error for the second one four times smaller? How much smaller is it?
If n=�=25, ¯x=�¯=45, and s=�=6, find the margin of error E� at a 95% confidence level. Give your answer to at least two decimal places.
you conducted additional studies with these men and found the following: a. The RR for those who drank one drink per day was 1.50 (95% CI:1.32-1.67) in comparison to the abstainers. b. For those men who drank three or more drinks per day the RR compared to the abstainers was 4.20 (95% CI 2.68-5.85). Question: We can tell from the Confidence Intervals provided in #7 whether there are likely more people in the “one drink a day” group or the “3+ drinks per day” group. Which one likely has more people and how can we tell?
Suppose a sample of 9 customers spends an average of $200 with a standard deviation $20 what is a 95% confidence interval for the sample mean. Use the fact that 95% of sample means are within 2.306 standard errors of the sample mean.
If n=17, ¯xx¯(x-bar)=50, and s=20, construct a confidence interval at a 98% confidence level. Assume the data came from a normally distributed population.
Days before a presidential election, an article based on a nationwide random sample of registered voters reported the following statistic, "52% (±3%) of registered voters will vote for Robert Smith." What is the "±3%" called? The "±3%" is called the confidence interval for a proportion. margin of error. sample proportion. standard error.