A random sample of 425 JAC students found that the average number of caffeinated drinksconsumed per day was 2.8 with s=0.3. a. Calculate a 95% confidence interval.b. Interpret. **Question 8: Statistical Analysis of Caffeinated Drink Consumption**A study involving a random sample of 425 JAC students revealed that the average number of caffeinated drinks consumed per day was 2.8, with a standard deviation (s) of 0.32.**a. Calculate a 95% Confidence Interval**- To calculate a 95% confidence interval for the average number of caffeinated drinks consumed per day, use the formula for the confidence interval of the mean: \[ \text{CI} = \bar{x} \pm z\left(\frac{s}{\sqrt{n}}\right) \] where: - $\bar{x} = 2.8$ (sample mean) - $z$ is the z-value for a 95% confidence level (typically 1.96) - $s = 0.32$ (standard deviation) - $n = 425$ (sample size)**b. Interpret**- Explain the meaning of the calculated confidence interval in the context of the study and what it implies about the population mean. The interval gives a range within which we can be 95% confident that the true average number of caffeinated drinks consumed per day by all JAC students falls.

Answered: Image /qna-images/answer/24daebe0-a0db-4196-a7dc-865e0e2811ad.jpg

Answered: 8. A random sample of 425 JAC students…

8. A random sample of 425 JAC students found that the average number of caffeinated drinks consumed per day was 2.8 with s=0.32. a. Calculate a 95% confidence interval. b. Interpret.

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: How many more Tweets are students at Hempstead High School sending in 2017 than in 2012? The table…

A: If an interval is proposed as an estimate of the unknown parameter, then it is interval estimation.…

Q: The correct value of Z to use for an 80% confidence interval for is: O A. 1.96 О В. 1.28 O C. 2.33 O…

Q: The following table illustrates the BMI for a number of patients recently enrolled in a study…

A: Note: Hey, there! Thank you for the question. Since the sample size is small and population standard…

Q: A researcher hypothesizes that the average number of sports colleges offer for males is greater than…

A: To test whether the average number of sports colleges offer for males is greater than the average…

Q: d. FIND t a n = 10 for the 90% confidence interval for the mean. %3D

A: d. Given: n=10 α=0.1 The degrees of freedom is obtained as below: df=n-1=10-1=9 Critical value: The…

Q: Find z, for the 84% confidence interval for the population mean. O a. 0.7955 O b. 1.44 O c. None O…

Q: A researcher is interested in finding a 98% confidence interval for the mean number of times per day…

A: Given Mean =X-bar=26.5 Standard deviations=S=19.7 n=97

Q: Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.10…

A: We have given that the average x-bar 3.15, population standard deviation 0.24 and margin of error is…

Q: Find a 95% confidence interval for a mean, µ, where n = 324, x̄ = 2.7, s = .91, and se = .06.

A: Given: n = 324, x̄ = 2.7, s = .91, se = .06.

Q: A mathematics teacher recently graded a chapter test for students in his abstract algebra course. In…

A: Given that, A mathematics teacher recently graded a chapter test for students in his abstract…

Q: 95% confidence interval for the true percent of workers in this city who have full health insurance…

A: The question is about confidence interval.Given :Randomly selected no. of workers ( n ) = 1700No. of…

Q: b. A group of parents want to look at the cost of college education. They took a random sample on…

A: Given : A random sample of the cost of textbooks is taken by a group pf parents to know the cost of…

Q: In terms of z scores, a 95% confidence interval consists of which of the following ranges? 1. ±1 z

A: Given, Z=x-μσ where, x= observed value μ=mean of the sample σ=standard deviation

Q: Please answer number 11.

A: Sample mean =40(using the formula ‘=AVERAGE (A1:A8).Sample standard deviation, s = 5.5549(using the…

Q: Identify the t-score for a 90% confidence interval if the sample size is 25. t = The answer isnt…

A: We have given that Confidence level (c) = 90% = 0.90 Significance level (α) = 1 - c = 1 - 0.90 =…

Q: Construct the confidence interval for the population mean y. C= 0.90, x=16.6, o= 10.0, and n= 80

A: Here, C=0.90, x=16.6, σ=10.0, and n=80.

Q: sample of 16 students was taken from university. These students spent an average of $170 on books…

Q: In a manufacturing process, a random sample of 19 manufactured bolts has a mean length of 3.2 inches…

Q: 9. 9. In a survey, 25 people were asked how much they spent on their child's last birthday gift.…

Q: A marketing researcher wants to estimate the mean savings ($) realized by shoppers who showroom.…

A: Sample size Sample mean Sample standard deviation

Q: The baseball coach tracked how long it took 8 of his players to do a series of drills. The times…

A: We have given the times recorded (in minutes) of 8 players.

Q: A human resource manager wants to see if there is a difference in the proportion of minority…

A: Confidence Interval: Confidence interval is the interval estimate of the population parameter. It is…

Q: “Over 24 weeks, systolic blood pressure in the low-carbohydrate diet group decreased by 9.6 mm Hg…

A: Confidence interval is an estimation technique is statistics.

Q: April took a sample of 10 statistics students and found the mean of their scores on an exam to be…

A: Sample mean = x̅ = 71.1 Sample size = n = 10 Sample S.D = s = 11.58 Standard Error = s/√n =…

Q: A survey was conducted that asked 1019 people how many books they had read in the past year. Results…

Q: The mean time taken to design a house plan by 40 architects was found to be 19 hours with a standard…

A: Step 1:Given data :Sample size n=40degrees of freedom df=40−1=39Sample mean xˉ=19Sample standard…

Q: A researcher is interested in fınding a 95% confidence interval for the mean number of times per day…

A: Given,Sample size(n)=97sample mean(x¯)=39.8standard deviation(s)=18.5degrees of…

Q: The data below is a list of how many people are working at your job per week. Construct the 98%…

A: Given: Enter the give data in to excel sheet

Q: . Estimate the mean with an approximate 95% confidence interval. The magazine estimates the true…

A: Let X be the random variable such that salary of the magazine's subscriber x̅ : Sample mean of…

Q: A researcher is interested in finding a 90% confidence interval for the mean number of times per day…

A: Given data A researcher is interested in finding a 90% confidence interval for the mean number of…

Q: Assume that the following samples are independent. In a random sample of 400 women, 47% favored…

A: Obtain the 98% confidence interval for the difference between the population proportions. The 98%…

Q: A teacher administers a standardized math .4 test to his class of 75 students. the mean score (out…

A: Here's, mean is 235 and standard deviation is 28. Sample number is 75. We will use one sample…

Q: A researcher is interested in finding a 95% confidence interval for the mean number of times per day…

A: Given Information: Confidence level = 95% = 0.95 Sample size (n) = 104 Sample mean (x¯) = 45.1…

Q: A random sample of high school students

A: Here it is given that, A 99% confidence interval based on this sample is 1.7 hours to 3.1 hours

Q: Let X1, X2, ..., X, be a random sample from the population N(µz,0²) and Y1, Y2,...,Ym a random…

A: Given information: Given that X1, X2, … , Xn be a random sample from the population N(µx, σ2) and…

Q: The EPA tests cars for city miles per gallon (mpg). For one model, a sample of 16 cars were tested…

Q: a. interpret the corresponding 95% confidence intervals for both Birth weight and Age. b. What is…

A: Given data: x1 x2 y 135 3 89 120 4 90 100 3 83 105 2 77 130 4 92 125 5 98 125 2 82…

Q: Tina catches a 14-pound bass. She does not know the population mean or standard deviation. So she…

A: From the provided information, The data values are as follow: 9, 12, 13, 10 and 10 Sample size (n) =…

Q: Exercise has an impact on anxiety, but a team of researchers wanted to see if where people run makes…

A: Given : Exercise has an impact on anxiety, but a team of researchers wanted to see if where people…

Question

A random sample of 425 JAC students found that the average number of caffeinated drinks
consumed per day was 2.8 with s=0.3.

a. Calculate a 95% confidence interval.

b. Interpret.

**Question 8: Statistical Analysis of Caffeinated Drink Consumption**

A study involving a random sample of 425 JAC students revealed that the average number of caffeinated drinks consumed per day was 2.8, with a standard deviation (s) of 0.32.

**a. Calculate a 95% Confidence Interval**

- To calculate a 95% confidence interval for the average number of caffeinated drinks consumed per day, use the formula for the confidence interval of the mean:
\[
\text{CI} = \bar{x} \pm z\left(\frac{s}{\sqrt{n}}\right)
\]
where:
- $\bar{x} = 2.8$ (sample mean)
- $z$ is the z-value for a 95% confidence level (typically 1.96)
- $s = 0.32$ (standard deviation)
- $n = 425$ (sample size)

**b. Interpret**

- Explain the meaning of the calculated confidence interval in the context of the study and what it implies about the population mean. The interval gives a range within which we can be 95% confident that the true average number of caffeinated drinks consumed per day by all JAC students falls.

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Which of the following t values would be used to construct a 99% confidence interval for the mean with a sample of size n=17?
A poll was conducted that asked 1010 people how many books they had read in the past year. Results indicated that x= 10.5 books and s= 16.6 books. Construct a 99% confidence interval for the mean number of books people read. Click the icon to view the table of areas under the t-distribution. Construct a 99% confidence interval for the mean number of books people read. (Use ascending order. Round to two decimal places as needed.)
Find the following. Enter your answer rounded to at least two decimals. z a/2 for the 97% confidence interval
About 25 randomly selected people were asked how long they slept at night. The mean time was 6 hours, and the standard deviation was 1 hour. Calculate the 98% confidence interval of the mean time by assuming that the variable is normally distributed. Provide only the value required below. Express your answer in 3 decimal places. a. tą (positive value only):
A developmental psychologist believes that children’s self-esteem scores change with age. She measures N=8 children’s self-esteem in 3rd grade and again in 6th. Evaluate the results of her data using α = .052tail. **Attached Image** a. Show how the 95% confidence interval was calculated. b. State the conclusion in APA format. c. What is Cohen’s d?
In a sample of seven cars, each car was tested for nitrogen oxide emissions (in grams per mile). The results appear below. Assuming that nitrogen oxide emissions are normally distributed, 4. Car 1 2 3 4 5 6 7 Nitrogen oxide emission (g/mi) 0.13 0.18 0.15 0.09 0.12 0.18 0.08 a. Construct a 95% confidence interval for the mean amount of nitrogen oxide emissions for all cars. b. What effect would increasing the level of confidence have on the length of the interval?
A study of 4 bolts of carpet showed that their average length was 76.2 yards and the sample standard deviation was 5.6 yards. Which of the following is the 80% confidence interval for the mean length per bolt of carpet? O A. 75.8 to 76.6 O B. 72.62 to 79.78 O C. 71.61 to 80.79 D. 75.40 to 77.00
A professor was curious about her students' grade point averages. She took a random sample of 15 students and found a mean GPA of 3.01 with a standard deviation of 0.534. Which of the following formulas gives a 99% confidence interval for the mean GPA of the professor's students?
The following data represent a random sample of five measurements from a normally distributed population: 7,4,2,5,7 a. Find 90% confidence interval for u. b. Find a 99% confidence interval for u.
10
Researchers studied the mean egg length (in millimeters) for a bird population. After taking a random sample of eggs, they obtained a 95% confidence interval of (45,60). What is the value of the margin of error? Choose the correct answer below. A. 15 mm B. 52.5 mm O c. 7.5 mm O D. 1.96
A poll was conducted that asked 1015 people how many books they had read in the past year. Results indicated that x= 14.3 books and s= 16.6 books. Construct a 90% confidence interval for the mean number of books people read. E Click the icon to view the table of areas under the t-distribution, Construct a 90% confidence interval for the mean number of books people read. ) (Use ascending order. Round to two decimal places as needed.)