Find the sum of the Infinite Series Below. 20 pts.
2 answers:
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Answer:
Comparing the p value with the significance level given we see that
so we can conclude that we can reject the null hypothesis, so the mean for the compound 1 is significantly less than the mean for the compound 2.
Step-by-step explanation:
Data given and notation
represent the mean for the compound 1
represent the mean for the compound 2
represent the sample standard deviation for compound 1
represent the sample standard deviation for compund 2
sample size for the group compound 1
sample size for the group compound 2
t would represent the statistic (variable of interest)
significance level provided
Develop the null and alternative hypotheses for this study?
We need to conduct a hypothesis in order to check if the means for compound 1 is less than the mean for compound 2, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Since we don't know the population deviations for each group, 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.
Determine the critical value(s).
Based on the significance level, we can find the critical values with the t distribution with 86+86-2=170 degrees of freedom, we are looking for values that accumulates 0.05 of the left tail of the distirbution.
For this case the value is
Calculate the value of the test statistic for this hypothesis testing.
Since we have all the values we can replace in formula (1) like this:
What is the p-value for this hypothesis test?
Since is a left tailed test the p value would be:
Based on the p-value, what is your conclusion?
Comparing the p value with the significance level given we see that
so we can conclude that we can reject the null hypothesis, so the mean for the compound 1 is significantly less than the mean for the compound 2.