To support a tree damaged in a storm, a 12-foot wire is secured from the ground to the tree at a point 10 feet off the ground. T
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Answer:
At 0.05 level of significance, the abrasive wear of material 1 exceeds that of material 2 by more than 2 units
Step-by-step explanation:
We hypothesize that mean difference between abrasive wear of material 1 and material 2 is greater than 2.
So we write the null hypothesis ,
and the alternative hypothesis .
We will find the T-score as well as the p-value. If the p-value is less than the level of significance, we will reject the null hypothesis, i.e. we will conclude that the abrasive wear of material 1 is less than that of material 2. Otherwise, we will accept the null hypothesis.
Since the variance is unknown and assumed to be equal, we will use the pooled variance
,
where .
The mean of material 1 and material 2 are respectively and mean difference
is equal to 4. The hypothesize difference
is equal to 2.
To find the T-score, we use the following formula
Substituting all the values into the T-score formula gives us , and the respective p-value is equal to 0.31. This means we have enough statistical evidence not to reject the null hypothesis, and at 5% significance level, the abrasive wear of material 1 exceeds that of material 2 by more than 2 units.
The cube root values and a graph of them are shown in the attachment.
_____
The cube root of a negative number is negative. These all have exact (rational) cube roots.
