Valentino starts with a population of 1,500 amoebas that increases 35% in size every hour for a number of hours, h. The expressi
2 answers:
Answer: It is the product of the initial population and the growth factor after h hours.
Step-by-step explanation:
Given: Valentino starts with a population of 1,500 amoebas that increases 35% in size every hour for a number of hours, h.
The expression finds the number of amoebas after h hours.
On simplifying the above expression we get, .
At h=0, the initial population of amoebas = 1,500
At h=1, the population of amoebas =
The growth factor =
Hence, the expression , is the product of the initial population and the growth factor after h hours.
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Answer:
If we compare the p value and the significance level assumed we see that
so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the mean is less than 140 pounds at 5% of signficance.
Step-by-step explanation:
Data given and notation
represent the sample mean
represent the sample standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is less than 140, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, 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 if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
P-value
The first step is calculate the degrees of freedom, on this case:
Since is a one left tailed test the p value would be:
Conclusion
If we compare the p value and the significance level assumed we see that
so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the mean is less than 140 pounds at 5% of signficance.