Complete all the problems. Use the two-way-table to answer the questions.
1 answer:
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Okay, first, given the equation, we need to find out what the radius of the circle is. Let us state the general equation of a circle:
Where
is the centre of the circle. In this case, we don't need to know the centre. Just the radius.
Let us start by converting the equation into standard for, which I typed above. Divide both sides by 81.
Great! We now know the radius of the circle. It is
because it is the bottom fraction. Now we know that the radius is 9.
So now lets input this into the area of circle formula:
Now we insert our radius.
You can convert that into a decimal if you wish.
Hope this helped!
~Cam943, Moderator
Where
Let us start by converting the equation into standard for, which I typed above. Divide both sides by 81.
Great! We now know the radius of the circle. It is
So now lets input this into the area of circle formula:
Now we insert our radius.
You can convert that into a decimal if you wish.
Hope this helped!
~Cam943, Moderator
Question:
You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals. A random sample of 45 home theater systems has a mean price of $114.00. Assume the population standard deviation is $15.30. Construct a 90% confidence interval for the population mean.
Answer:
At the 90% confidence level, confidence interval = 110.2484 < μ < 117.7516
At the 95% confidence level, confidence interval = 109.53 < μ < 118.48
The 95% confidence interval is wider
Step-by-step explanation:
Here, we have
Sample size, n = 45
Sample mean, = $114.00
Population standard deviation, σ = $15.30
The formula for Confidence Interval, CI is given by the following relation;
Where, z is found for the 90% confidence level as ±1.645
Plugging in the values, we have;
or CI: 110.2484 < μ < 117.7516
At 95% confidence level, we have our z value given as z = ±1.96
From which we have
Hence CI: 109.53 < μ < 118.48
To find the wider interval, we subtract their minimum from the maximum as follows;
90% Confidence level: 117.7516 - 110.2484 = 7.5
95% Confidence level: 118.47503 - 109.5297 = 8.94
Therefore, the 95% confidence interval is wider.