Aspen has six sections of equal shape and size each section is either black or white. The table shows the results of the experim
ent with the spirit was spent 84 times. Based on the data, which of the following best scribes the experimental probability of the air landing on a black or white section of the spinner?
1 answer:
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Answer:
a) The 99% confidence interval would be given by (589.588;731.038)
b) If we see the confidence interval the 620 is included on the interval we don't have enough evidence to reject the rating is 620. But since we need a score that at least 620 and our lower limit is 589.588 we cant conclude that all the clients would have a score that at least of 620.
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The data is:
661 595 548 730 791 678 672 491 492 583 762 624 769 729 734 706
Part a
Compute the sample mean and sample standard deviation.
In order to calculate the mean and the sample deviation we need to have on mind the following formulas:
=AVERAGE(661, 595, 548, 730, 791, 678, 672, 491 ,492, 583, 762 ,624 ,769, 729, 734, 706)
On this case the average is
=STDEV.S(661, 595, 548, 730, 791, 678, 672, 491 ,492, 583, 762 ,624 ,769, 729, 734, 706)
The sample standard deviation obtained was s=95.898
Find the critical value t* Use the formula for a CI to find upper and lower endpoints
In order to find the critical value we need to take in count that our sample size n =16<30 and on this case we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 99% of confidence, our significance level would be given by and
. The degrees of freedom are given by:
We can find the critical values in excel using the following formulas:
"=T.INV(0.005,15)" for
"=T.INV(1-0.005,15)" for
The confidence interval for the mean is given by the following formula:
And if we find the limits we got:
[tex]660.313+ 2.95\frac{95.898}{\sqrt{16}}=731.038/tex]
So the 99% confidence interval would be given by (589.588;731.038)
Part b
If we see the confidence interval the 620 is included on the interval we don't have enough evidence to reject the rating is 620. But since we need a score that at least 620 and our lower limit is 589.588 we cant conclude that all the clients would have a score that at least of 620.