An engineering student is studying the effects of cryogenic treatments on a particular material. The treatment involves cooling
the material with
specific applications of liquid nitrogen
The temperature of the material in degrees Celsius, y, can be modeled by the following graph, where x represents the time, in hours, since the
treatment began
specific applications of liquid nitrogen
The temperature of the material in degrees Celsius, y, can be modeled by the following graph, where x represents the time, in hours, since the
treatment began
2 answers:
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Answer:
Yes. At this significance level, there is evidence to support the claim that there is a difference in the ability of the brands to absorb water.
Step-by-step explanation:
<em>The question is incomplete:</em>
<em>The significance level is 0.05.</em>
<em>The data is:</em>
<em>Brand X: 91, 100, 88, 89</em>
<em>Brand Y: 99, 96, 94, 99</em>
<em>Brand Z: 83, 88, 89, 76</em>
We have to check if there is a significant difference between the absorbency rating of each brand.
Null hypothesis: all means are equal
Alternative hypothesis: the means are not equal
We have to apply a one-way ANOVA
We start by calculating the standard deviation for each brand:
Then, we calculate the mean standard error (MSE):
Now, we calculate the mean square between (MSB), but we previously have to know the sample means and the mean of the sample means:
The MSB is then:
Now we calculate the F statistic as:
The degrees of freedom of the numerator are:
The degrees of freedom of the denominator are:
The P-value of F=7.23, dfn=2 and dfd=9 is:
As the P-value (0.013) is smaller than the significance level (0.05), the null hypothesis is rejected.
There is evidence to support the claim that there is a difference in the ability of the brands to absorb water.