A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time they last is approximately normal. Researchers in a hospital used the drug on a random sample of 9 patients. The effective period of the tranquilizer for each patient (in hours) was as follows: 2.6; 2.8; 3.1; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part (a) (i) Round your answer to two decimal places. x = (rounded to two decimal places) (ii) Round your answer to two decimal places. sx = \\\ (rounded to two decimal places) (iii) Enter an exact number as an integer, fraction, or decimal. n = (iv) Enter an exact number as an integer, fraction, or decimal. n − 1 = Part (b) In words, define the random variable X. time, in minutes, of the effectiveness of a tranquilizer number of tranquilizers the hospital used for each patient the number of patients that were given a tranquilizer time, in hours, of the effectiveness of a tranquilizer Part (c) In words, define the random variable X. the average length, in minutes, of the effectiveness period of tranquilizers the average number of tranquilizers the pharmaceutical company dispenses to hospitals the average length, in hours, of the effectiveness period of tranquilizers the average number of tranquilizers used for each patient

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 makes tranquilizers. It is assumed that the distribution for the length of time they last is approximately normal. Researchers in a hospital used the drug on a random sample of 9 patients. The effective period of the tranquilizer for each patient (in hours) was as follows: 2.6; 2.8; 3.1; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4.

NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

Part (a)

(i) Round your answer to two decimal places.

x =

(rounded to two decimal places)

(ii) Round your answer to two decimal places.

s_x =

\\\ (rounded to two decimal places)

(iii) Enter an exact number as an integer, fraction, or decimal.

n =

(iv) Enter an exact number as an integer, fraction, or decimal.

n − 1 =
Part (b)

In words, define the random variable X.

time, in minutes, of the effectiveness of a tranquilizer

number of tranquilizers the hospital used for each patient

the number of patients that were given a tranquilizer

time, in hours, of the effectiveness of a tranquilizer

Part (c)
In words, define the random variable
X.

the average length, in minutes, of the effectiveness period of tranquilizers

the average number of tranquilizers the pharmaceutical company dispenses to hospitals

the average length, in hours, of the effectiveness period of tranquilizers

the average number of tranquilizers used for each patient

Part (d)
Which distribution should you use for this problem? (Enter your answer in the form z or t_df where df is the degrees of freedom.)

Explain your choice.

The Student's t-distribution should be used because the sample size is small.

The standard normal distribution should be used because the population standard deviation is known.

The Student's t-distribution should be used because the sample standard deviation is known and the sample size is small.

The standard normal distribution should be used because the sample standard deviation is known.

Part (e)
Construct a 95% confidence interval for the population mean length of time.
(i) State the confidence interval. (Round your answers to two decimal places.)

(ii) Sketch the graph.

(iii) Calculate the error bound. (Round your answer to two decimal places.)
(No Response)
Part (f)

What does it mean to be "95% confident" in this problem?

This means that the chances of a tranquilizer being effective is 95%.

This means that we are 95% confident that the average length of effectiveness of tranquilizers in the sample of 9 people is between the interval values.

We are 95% confident that the effectiveness of a tranquilizer lies between the interval values.

This means that if intervals are created from repeated samples, 95% of them will contain the true population average length of effectiveness of tranquilizers.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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Part (a)

Part (b)

Part (f)