Ik this is the easiest question but who wanna do it for me?:(
2 answers:
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An arithmetic sequence takes the form
where
is the common difference between terms. You can solve for 
in terms of any of the previous terms of the sequence:
for some integer
Continuing in this way, you know that the sequence can be defined explicitly in terms of the first term
Given that the 4th term is
and the 11th term is 
, you have the following system of equations.
Solving this system for the two unknowns yields
and 
.
So, the sequence is given explicitly by
where
for some integer
Continuing in this way, you know that the sequence can be defined explicitly in terms of the first term
Given that the 4th term is
Solving this system for the two unknowns yields
So, the sequence is given explicitly by
Using the z-distribution, it is found that since the p-value is less than 0.05, there is evidence that the mean amount of cereal in each box is different from 16 ounces at 0.05 significance.
<h3>What are the hypothesis tested?</h3>At the null hypothesis, it is tested if the mean is not different to 16 ounces, that is:
At the alternative hypothesis, it is tested if the mean is different, hence:
The test statistic is:
In which:
is the sample mean.
is the value tested at the null hypothesis.
is the standard deviation of the population.
- n is the sample size.
The parameters for this problem are:
.
Hence:
z = -2.1
<h3>What is the p-value and the conclusion?</h3>Using a z-distribution calculator, for a two-tailed test, as we are testing if the mean is different of a value, with z = -2.1, the p-value is of 0.0357.
Since the p-value is less than 0.05, there is evidence that the mean amount of cereal in each box is different from 16 ounces at 0.05 significance.
More can be learned about the z-distribution at brainly.com/question/16313918
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