Bill measures the circumference of a circular fish pond to be 28 ft. What is the diameter of the fish pond, rounded to the neare
1 answer:
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Answer:
Part a: P-value
The first step is calculate the degrees of freedom, on this case:
Since is a one sided test the p value would be:
Part b: 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 fail reject the null hypothesis, and we can conclude that the true mean is not lower than 20 at 1% of signficance.
a. There is insufficient evidence to reject h^0
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 lower than 20, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the sample is > 30 but 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:
Part a: P-value
The first step is calculate the degrees of freedom, on this case:
Since is a one sided test the p value would be:
Part b: 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 fail reject the null hypothesis, and we can conclude that the true mean is not lower than 20 at 1% of signficance.
a. There is insufficient evidence to reject h^0
Two years ago, Sally had 5,000 dogs in her dog shelter. Now she has 24,575 dogs. The rate of change is 391.5 % increase
<em><u>Solution:</u></em>
Given that Two years ago, Sally had 5,000 dogs in her dog shelter
Now she has 24,575 dogs
To find: rate of change
A rate of change is a rate that describes how one quantity changes in relation to another quantity
<h3><u>Steps to follow:</u></h3>- First: work out the difference (increase) between the two numbers you are comparing.
- Increase = New Number - Original Number.
- Then: divide the increase by the original number and multiply the answer by 100.
- % change = Increase ÷ Original Number x 100
Thus the rate of change is 391.5 % increase