The value of the 2 in 5072 is how many times more than the value of 2 in 2481?
1 answer:
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Start by dividing both sides by 2 to get 
. Doing the math on the right, keeping in mind that logs have an unwritten base of 10, gives us 
. Rewriting this in exponential form is 
. That means that x = 8. Not negative, only positive.
Answer:
a) Null hypothesis:
Alternative hypothesis:
b)
c)
d) If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 15 at 1% of signficance.
Step-by-step explanation:
Data given and notation
The sample mean is given by:
And the sample deviation is:
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.
z would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
Part a State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is less or equal than 15, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Since we don't know the population deviation, 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".
Part b Calculate the statistic
We can replace in formula (1) the info given like this:
Part c P-value
The degrees of freedom are given by:
Since is a right tailed test the p value would be:
Part d Conclusion
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 15 at 1% of signficance.