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.

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)

Question: Find the derivative of f(x) = 4x^3 + 2x^2 - 5x + 1.

Math Question: What is the smallest value of n that satisfies Fermat's theorem, specifically a^n + b^n = c^n for positive integers a, b, c, and n greater than 2?

What is the number of degrees in the largest angle of a triangle if the other two angles measure 50° and 70°?

New questions in Mathematics

A circular park has a diameter of 150ft. A circular fence is to be placed on the edge of this park. Calculate the cost of fencing this park if the rate charged is $7 per foot. Use π = 3.14.

2x-y=5 x-y=4

X^2 = 25

By differentiating the function f(x)=(x³−6x)⁷ we will obtain

3x+5y=11 2x-3y=1

Perpetual annuities are a series of payments whose duration has no end. Explain how can we calculate them, if they have no end?

In a store, a person carries 14 kilos of rice and 28 kilos of flour. In what ratio are the kilos found? (Remember to simplify until you reach an irreducible fraction)

How many anagrams of the word SROMEC there that do not contain STROM, MOST, MOC or CEST as a subword? By subword is meant anything that is created by omitting some letters - for example, the word EMROSCT contains both MOC and MOST as subwords.

Solve the equation: sin(2x) = 0.35 Where 0° ≤ x ≤ 360°. Give your answers to 1 d.p.

A recurring sequence is one where elements repeat after completing one standard. If the sequence AB8C14D96AB8C1... is recurring its twentieth term is equal to: (A) B. (B) 8. (C) A. (D) 6. (E) D.