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NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distri O Part (a) | (rounded to two decimal places) | (rounded to two decimal places) () 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. ) State the confidence interval. (Round your answers to two decimal places.)

NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distri O Part (a) | (rounded to two decimal places) | (rounded to two decimal places) () 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. ) State the confidence interval. (Round your answers to two decimal places.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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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.)
Transcribed Image Text: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)

i) 

Calculating the sample mean ( x¯ ) from the given data

x¯ = ∑xn

x¯ = 22.79 = 2.522

Rounding to two decimal

x¯ =2.52

 

ii)

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

sd = ∑(x - x¯)2n - 1

sd = 0.3308

Rounding to two decimal

sd = 0.33

 

iii) 

n =  9

 

iv) 

n - 1 =  8

 

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