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 foreach patient (in hours) was as follows: 2.7; 2.9; 3.0; 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.)O Part (a)(i) x=|(rounded to two decimal places)(ii)S =(rounded to two decimal places)(ii)n =(iv) n- 1 =O Part (b)O Part (c)O Part (d)O Part (e)Construct a 95% confidence interval for the population average length of time.(i) State the confidence interval. (Round your answers to two decimal places.)(ii) Sketch the graph.aaC.L. =(iii) Calculate the error bound. (Round your answer to two decimal places.)

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Description: 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 tranqui

Answered: NOTE: If you are using a Student's…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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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: 2.7; 2.9; 3.0; 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.)
O Part (a)
(i) x=|
(rounded to two decimal places)
(ii)
S =
(rounded to two decimal places)
(ii)
n =
(iv) n- 1 =
O Part (b)
O Part (c)
O Part (d)
O Part (e)
Construct a 95% confidence interval for the population average length of time.
(i) State the confidence interval. (Round your answers to two decimal places.)
(ii) Sketch the graph.
a
a
C.L. =
(iii) Calculate the error bound. (Round your answer to two decimal places.)

Expert Solution

Step 1

Let x be the length of time tranquilizers last.

The data given is as follows

2.7
2.9
3
2.3
2.3
2.2
2.8
2.1
2.4

Step 2: Part (a)

Calculating the sample mean ( $\bar{x}$ ) from the given data

$\bar{x} = \frac{\sum_{} x}{n}$

$\bar{x} = \frac{22.7}{9}$ = 2.522

Rounding to two decimal

$\bar{x} =$ 2.52

ii)

Calculating the sample standard deviation (s_d) from the given data

$s_{d} = \sqrt{\frac{\sum_{}^{} {(x - \bar{x})}^{2}}{n - 1}}$

s_d = 0.3308

Rounding to two decimal

s_d = 0.33

iii)

n = 9

iv)

n - 1 = 8

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