Answered: A pharmaceutical company would like to…

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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Question

A pharmaceutical company would like to investigate the response time of a COVID-19 rapid test. The company claims that the response time is 16 minutes. To investigate this claim, the company decided to consider the response time of a random sample of 28 tests.

Given:

The response times has a normal distribution with a standard deviation of σ=2.
The company wishes to test this claim at α=0.01 level of significance.
The value of the test statistic is z=−2.14.

1.1 The sample mean is x¯=15.19. Construct a 99% confidence interval for the mean response time of a COVID-19 rapid test, by answering the following questions:

The margin of error is:
The confidence interval is:

1.2 Calculate the p-value.

1.3 The company may conclude that the response time - from 16 minutes at α=0.01 level of significance. (please fill in dash)

1.4

The company would like to increase the sample size so that the sample mean is within 0.7 minutes of the true mean with 99% confidence. The new required sample size is -

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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