Question

A geologist is making repeated measurements (in grams) on the mass of a rock. It is not known whether the measurements are a random sample from an approximately normal population. Below are three sets of replicate measurements, listed in the order they were made. For each set of readings, state whether the assumptions necessary for the validdity of the t-test appear to be met. If the assumptions are not met, explain why?

a. 213.03 212.95 213.04 213.00 212.99 213.01 221.03 213.05
b. 213.05 213.00 212.94 213.09 212.98 213.02 213.06 212.99
c. 212.92 212.95 212.97 213.00 213.01 213.04 213.05 213.06

Answer 1

Answer:

Step-by-step explanation:

The objective of this question is to known whether the assumptions of the known data set follows normal distribution or not and if it is appropriate to use t-test or not.

TO solve this question ; we construct a box plot for the known data set by using a MINITAB software

The process is as follows to guide you:

Enter your data in the worksheet

Then select Graph→ Boxplot→ EDA→ Boxplot

Under One Y , select simple, Then click OK

In Variables , enter measurements. Then click OK

So; for the first data set (a)  213.03 212.95 213.04 213.00 212.99 213.01 221.03 213.05  as shown in the attached file  in word document for the  boxplot below;

We will observe that there is a outliner present in the data set and the measurement do not meet the normal assumption ; as a result to that ; the t-distribution is not appropriate for this data.

(b) From the document attached below; we will realize and observe that the boxplot doesn't contains an outliner. Also; it is clear and obvious that the shape of the distribution is right skewed. The measurement thus did not meet the assumptions and as a result t- distribution is not appropriate for this data.

(c)

From the document attached below; we will realize and observe that the boxplot doesn't contains an outliner. Also; it is clear and obvious that the shape of the distribution is left skewed. The measurement thus did not meet the assumptions and as a result t- distribution is not appropriate for this data.

Answer 2

(a): The $t-$distribution is not appropriate for this data.

(b): The $t$-distribution is not appropriate for this data.

(c): The $t$- distribution is not appropriate for this data.

$t-$test:

A t-test is a statistical test that is used to compare the means of two groups.

Part(a):

Check whether the unknown data set follows the normal distribution or not and is it appropriate to use the $t$-test or not.

Use the following MS excel instructions to draw a box plot.

Step-1: Enter the data into an excel sheet.

Step-2: Click add-ins-Mega stat-Descriptive statistics.

Step-3: Input the data into the input range box.

Step-4: Click Box-Plot -Click OK

It is observed that there is an outlier in the data set.

The obtained output is as follows:

So, the measurements do not satisfy the normality assumption.

Part(b):

Check whether the known data set follows normal distribution or not and is it appropriate to use the $t$-test or not.

Use the above MS excel instruction to draw a Box plot.

The obtained output is as follows.

It is observed that there is no outlier in the data set and the shape of the distribution is appears to be right-skewed.

So, the measurement do not satisfy the normality assumption.

Part(c):

Check whether the known data set follows normal distribution or not and is it appropriate to use the $t$- test or not.

Use the above MS Excel instruction to draw a Box-plot.

The obtained output is as follows.

It is observed that there is no outlier in the data set and the shape of the distribution is appears skewed to the left.

So, the measurement do not satisfy the normality assumption.

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