**Understanding Confidence Intervals in Novel Lengths**Dr. Higney, an academic researcher in an English department, aims to study the average length of a novel. To achieve this, Dr. Higney collects data on the word counts of 200 randomly selected novels. Here's a summary of the data collected:- **Sample Size (n):** 200 novels- **Sample Mean (x̄):** 85,252 words- **Sample Standard Deviation (s):** 8,413 words**Task:**Using this data, construct a 90% confidence interval for the true mean length of novels.**Options for the 90% Confidence Interval:**1. (84,273.50, 86,230.51)2. (82,719.67, 89,784.33)3. (94,086.04, 96,417.96)4. (80,937.53, 90,566.47)When constructing a confidence interval, it is essential to determine the range within which the true mean of the population is expected to fall, given a certain level of confidence (in this case, 90%).To calculate the confidence interval, we use the formula:\[ CI = x̄ \pm (z* \cdot \frac{s}{\sqrt{n}}) \]Where:- \( x̄ \) is the sample mean.- \( z* \) is the z-value corresponding to the desired confidence level (for 90%, \( z* = 1.645 \)).- \( s \) is the sample standard deviation.- \( n \) is the sample size.**Note:** The correct confidence interval should reflect these calculations.

Solution-:Given: We want to find 90% C.I. for the true mean length of novels.

Answered: Dr. Higney, an academic researcher in…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Fran is training for her first marathon, and she wants to know if there is a significant difference between the mean number of miles run each week by group runners and individual runners who are training for marathons. She interviews 37 randomly selected people who train in groups, and finds that they run a mean of 47.7 miles per week. Assume that the population standard deviation for group runners is known to be 3.3 miles per week. She also interviews a random sample of 49 people who train on their own and finds that they run a mean of 49.4 miles per week. Assume that the population standard deviation for people who run by themselves is 4.4 miles per week. Test the claim at the 0.10 level of significance. Let group runners training for marathons be Population 1 and let individual runners training for marathons be Population 2. Step 2 of 3 : Compute the value of the test statistic. Round your answer to two decimal places.
In preparation for the upcoming school year, a teacher looks at raw test scores on the statewide standardized test for the students in her class. Instead of looking at the scores relative to the norms in the state, the teacher wants to understand the scores relative to the students who will be in the class. To do so, she decides to convert the test scores into z-scores relative to the mean and standard deviation of the students in the class. The mean test score in her upcoming class is 49, and the standard deviation is 20.7. The teacher now wants to identify those students who may need extra help. She decides to look at students who have z-scores below z = -2.00 Identify the test score corresponding to a z-score of below z = -2.00. Round to the nearest whole number.
4. At private college the achievement test is used for advanced study placement. Counselors selected a random sample of 144 students from the college and scored their tests by hand before sending them in for computer processing. For this sample, the mean was 450 and s = 29. Construct a 98% confidence interval for the mean.
Please help me with this question.
Fran is training for her first marathon, and she wants to know if there is a significant difference between the mean number of miles run each week by group runners and individual runners who are training for marathons. She interviews 42 randomly selected people who train in groups and finds that they run a mean of 47.1 miles per week. Assume that the population standard deviation for group runners is known to be 4.4 miles per week. She also interviews a random sample of 47 people who train on their own and finds that they run a mean of 48.5 miles per week. Assume that the population standard deviation for people who run by themselves is 1.8 miles per week. Test the claim at the 0.01 level of significance. Let group runners training for marathons be Population 1 and let individual runners training for marathons be Population 2. Step 2 of 3 : Compute the value of the test statistic. Round your answer to two decimal places.
4. on paper. random sample of 130 human body temperatures had a mean 98.25 degree and astandard deviation of 0.73 degree. Construct a 99% confidence interval for the average body temperature ofhealthy people.
do B AND C
Suppose we have only ten scores representing the ages (in years) of randomly selected U.S. commercial aircraft. The average age of the ten aircraft is 14.25 years and the sample standard deviation is 9.349 years. Construct a 95% confidence interval for the mean age of all U.S. commercial aircraft. I would appreciate to see what formulas you use and the work through because I messed up.
There are many ways to measure the reading ability of children. One frequently used test is the DRP or Degree of Reading Power. The national average score in DRP test is 32. We want to determine if there is sufficient evidence at the 5% level to suggest that the mean score of all third graders in YOUR district is higher than the national mean. The DRP scores for a simple random sample of 41 third graders in that suburban school in YOUR district yielded a mean of 35.2. Assume that the population of DRP scores of third graders in that suburban school district are normally distributed with a population std.dev of 11.
We asked 41 people to report the number of cars they've ever owned. The results are a mean of 4.6 and a standard deviation of 1.3. Construct a 80% confidence interval.
The following is the number of hours of sleep obtained by eight college freshmen. Use the data to find a 92% confidence interval for the true mean number of hours of sleep by college freshmen. 7.5 8.0 6.5 24 8.5 6.5 7.0 7.5
A simple random sample of 1000 observations is taken from a population of 10,000. What is the standard error of the sample mean?

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