1. Jarrid Medical, Inc., is developing a compact kidney dialysis machine, but the company's chief engineer, Mike Crowe, is having trouble controlling the variability in how fast the fluid moves through the kidney. the device. Medical standards require the flow per hour to be 4.25 liters, 98% of the time. Mr. Crowe performs tests on the prototype with the following results for each hourly flow test performed: 4.17 4.32 4.21 4.22 4.29 4.19 4.29 4.34 4.33 4.22 4.28 4.33 4.52 4.29 4.43 4.39 4.44 4.34 4.3 4.41 With the information obtained from the sample, it is necessary to find the confidence interval that reflects the expected flow per hour in 98% of the time of the developed compact machine and determine if it is satisfying the medical standards. Does the prototype satisfy medical standards? Present all the steps required to construct your confidence interval and an analysis that justifies your answer to the established question.

Brand: MathMaster
Rating: 4.9 (163 reviews)

163

likes

814 views

Answer to a math question 1. Jarrid Medical, Inc., is developing a compact kidney dialysis machine, but the company's chief engineer, Mike Crowe, is having trouble controlling the variability in how fast the fluid moves through the kidney. the device. Medical standards require the flow per hour to be 4.25 liters, 98% of the time. Mr. Crowe performs tests on the prototype with the following results for each hourly flow test performed: 4.17 4.32 4.21 4.22 4.29 4.19 4.29 4.34 4.33 4.22 4.28 4.33 4.52 4.29 4.43 4.39 4.44 4.34 4.3 4.41 With the information obtained from the sample, it is necessary to find the confidence interval that reflects the expected flow per hour in 98% of the time of the developed compact machine and determine if it is satisfying the medical standards. Does the prototype satisfy medical standards? Present all the steps required to construct your confidence interval and an analysis that justifies your answer to the established question.

$Expert avatar$

Santino

4.5

112 Answers

Step 1: Calculate the sample mean (

\bar{x}

) and the sample standard deviation (

).

Given sample data:

4.17, 4.32, 4.21, 4.22, 4.29, 4.19, 4.29, 4.34, 4.33, 4.22, 4.28, 4.33, 4.52, 4.29, 4.43, 4.39, 4.44, 4.34, 4.3, 4.41

\bar{x} = \frac{4.17 + 4.32 + 4.21 + 4.22 + 4.29 + 4.19 + 4.29 + 4.34 + 4.33 + 4.22 + 4.28 + 4.33 + 4.52 + 4.29 + 4.43 + 4.39 + 4.44 + 4.34 + 4.3 + 4.41}{20} = 4.281

s = \sqrt{\frac{\sum(x_i - \bar{x})^2}{n-1}} = \sqrt{\frac{(4.17-4.281)^2 + (4.32-4.281)^2 + \cdots + (4.41-4.281)^2}{19}} = 0.086

Step 2: Determine the t-score for a 98% confidence level with

n-1 = 19

degrees of freedom. From the t-distribution table:

t_{\alpha/2,19} \approx 2.539

Step 3: Calculate the margin of error (ME).

ME = t_{\alpha/2,19} \cdot \frac{s}{\sqrt{n}} = 2.539 \cdot \frac{0.086}{\sqrt{20}} = 0.049

Step 4: Construct the confidence interval.

\bar{x} \pm ME = 4.281 \pm 0.049 \Rightarrow (4.244, 4.319)

Step 5: Analyze if the mean flow rate meets the medical standards.

The required mean flow rate is 4.25 liters. The confidence interval (4.244, 4.319) includes 4.25, thus the prototype does satisfy the medical standards for the mean flow rate 98% of the time.

\text{Confidence interval: } (4.244, 4.319)

\text{Satisfies medical standards: Yes}

Frequently asked questions (FAQs)

How many ways can 6 people be arranged in a line?

What is the formula to find the integral of a function f(x) over an interval [a, b]?

Question: Plot the graph of the logarithmic function f(x) = log(x) with a horizontal shift of 2 units to the right.

New questions in Mathematics

How to find the value of x and y which satisfy both equations x-2y=24 and 8x-y=117

Let f(x)=||x|−6|+|15−|x|| . Then f(6)+f(15) is equal to:

𝑦 = ( 𝑥2 − 3) (𝑥3 + 2 𝑥 + 1)

a ferry travels 1/6 of the distance between two ports in 3/7 hour. the ferry travels at a constant rate. at this rate, what fraction of the distance between the two ports can the ferry travel in one hour?

431414-1*(11111-1)-4*(5*3)