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Chapter 3: Q 3.31. (page 102)

Sleep. In 1908. W.S Gosset published the article " The probable Error of a mean" ( Biometrika, vOL.6, pp. 1-25) In this pioneering paper written under the pseudonym "Student" Gosset introduced What later became known as Student's t distribution which we discuss in a later chapter. Gosset used the following dataset, which shown the additional sleep in hours obtained by a sample of 10 patients given laevohysocyamine hydrobromide.

Part (a) find n

Part (b) Compute

Part (c) Determine the sample mean. Round your answer to one more decimal place than that used for the observation.

Short Answer

Expert verified

Part (a) 10

Part (b) 23.3

Part (c) 2.33

Step by step solution

01

Part (a) Step 1. Given information.

The provided data set is:

1.9, 0.8, 1.1, 0.1, -0.1, 4.4, 5.5, 1.6, 4.6, 3.4

02

Part (a) Step 2. The value of n

The given collection is: 1.9, 0.8, 1.1, 0.1, -0.1, 4.4, 5.5, 1.6, 4.6, 3.4

The number of samples is 10

Then

n=10

As a result, the value of n is 10.

03

Part (b) Step 1. Given information.

The provided data set is:

1.9, 0.8, 1.1, 0.1, -0.1, 4.4, 5.5, 1.6, 4.6, 3.4

04

Part (b) Step 2. The value of ∑xi.

The value of ∑xiis calculated as follows:

∑xi=1.9+0.8+1.1+0.1-0.1+4.4+5.5+1.6+4.6+3.4∑xi=23.3

As a result, the value of ∑xiis 23.3

05

Part (c) Step 1. Given information.

The provided data set is:

1.9, 0.8, 1.1, 0.1, -0.1, 4.4, 5.5, 1.6, 4.6, 3.4

06

Part (c) Step 2 The sample average.

Mean is expressed as follows:

x¯=∑xn

The mean of the given data set is computed as follows:

x¯=23.310x¯=2.33

As a result, the sample mean days is 2.33.

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