Answer:
So the p value is a very high value and using any significance level for example we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis and we have enough evidence to support the claim. Since the mean for Hylite is not significantly less than the mean for Permafresh.
Step-by-step explanation:
1) Data given and notation
Hylite:[140,139, 138 , 117, 141, 102, 127, 137, 164, 142, 131]
Permafresh:[124,144,136,133,139,132,141,133]
represent the mean for the sample Hylite
represent the mean for the sample LPermafresh
represent the sample standard deviation for the sample Stick
represent the sample standard deviation for the sample Liquid
sample size for the group Hylite
sample size for the group Permafresh
t would represent the statistic (variable of interest)
2) Concepts and formulas to use
We need to conduct a hypothesis in order to check if the mean for Hylite is better for Hylie:
H0:
H1:
If we analyze the size for the samples both are less than 30 so for this case is better apply a t test to compare means, and the statistic is given by:
(1)
t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.
In order to calculate the mean and the sample deviation we can use the following formulas:
(2)
(3)
3) Calculate the statistic
First we need to calculate the mean and deviation for each sample, after apply the formulas (2) and (3) we got the following results:
And with this we can replace in formula (1) like this:
4) Statistical decision
For this case we don't have a significance level provided , but we can calculate the p value for this test. The first step is calculate the degrees of freedom, on this case:
Since is a left tailed test the p value would be:
So the p value is a very high value and using any significance level for example we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis and we have enough evidence to support the claim. Since the mean for Hylite is not significantly less than the mean for Permafresh.