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Answer:
A whole number first term to render as fifth term a value larger than 10000, should be at least 121
Step-by-step explanation:
The formula is given as recursive since it involves the previous number of the sequence, and defined as:
we also know that the first term is 4
Then in this case, the first five terms are:
So if we want to find the first term in the case that the fifth one is greater than 10,000 using this recursive formula, now we have to start backwards, and say that the fifth term is "> 10000" and what the fourth one is.
Notice that if you have this definition for the nth term, we can obtain from it, what the previous term is to find the general rule:
So the rule is to subtract 6 from he term, and divide the subtraction by 3. Then working backwards:
therefore, the starting first term should be at least about 121 to give a fifth term larger than 10,000
Answer:
If we compare the p value and the significance level given for example we see that
so we can conclude that we to reject the null hypothesis, and the actual mean is significantly higher than 20000.
Step-by-step explanation:
1) 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 determine if the true mean is higher than 20000, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
We don't know the population deviation, so for this case 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:
Calculate the P-value
First we need to calculate the degrees of freedom given by:
Since is a one-side upper test the p value would be:
Conclusion
If we compare the p value and the significance level given for example we see that
so we can conclude that we to reject the null hypothesis, and the actual mean is significantly higher than 20000.