Find the common ratio of the geometric sequence 18,-72,288,...
1 answer:
Answer:
<em>The common ratio of the geometric sequence is -4</em>
Step-by-step explanation:
<u>Geometric Sequence</u>
A geometric sequence is defined as a series of numbers that follow a fixed pattern: Each term equals the previous term times a fixed number called the common ratio. The recursive formula is:
Where r is the common ratio.
We are given three terms of a geometric sequence:
18,-72,288,...
To find the common ratio, just divide each term by the previous term:
Make sure it's a fixed number and test with the third term:
Since both numbers coincide, the common ratio of the geometric sequence is -4
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Answer:
So the p value obtained was a very high value and using the significance level given we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of graduate students show that only 44 students have ever done so is not significantly lower than 0.6
Step-by-step explanation:
Data given and notation
n=80 represent the random sample taken
X=44 represent the students that have bought merchandise on-line at their site
estimated proportion of graduate students show that only 44 students have ever done so
is the value that we want to test
represent the significance level
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportion of interest is lower than 0.6 or 60%, so then the system of hypothesis are.:
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statistic, and the is given by:
(1)
The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value
.
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level assumed for this case is . The next step would be calculate the p value for this test.
Since is a left tailed test the p value would be:
So the p value obtained was a very high value and using the significance level given we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of graduate students show that only 44 students have ever done so is not significantly lower than 0.6