Q 3.31. - Elementary Statistics

Question

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.

Step-by-Step Solution

Answer

Part (a) 10

Part (b) 23.3

Part (c) 2.33

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

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.

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 

Part (b) Step 2. The value of ∑ x i .

The value of $\sum _{}{x}_i$ is calculated as follows:

$$\begin{gathered} \sum _{}{x}_i=1.9+ 0.8+ 1.1+ 0.1 -0.1+ 4.4+ 5.5+ 1.6+ 4.6+ 3.4 \\ \sum _{}{x}_i=23.3 \end{gathered}$$

As a result, the value of $\sum _{}{x}_i$ is 23.3

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 

Part (c) Step 2 The sample average.

Mean is expressed as follows:

$\overline{x}=\frac{\sum _{}x}{n}$

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

$$\begin{gathered} \overline{x}=\frac{23.3}{10} \\ \overline{x}=2.33 \end{gathered}$$

As a result, the sample mean days is 2.33.