Evaluate the following: a to the power 3 times a to the power 6 times a to the power 4
2 answers:
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Answer:
a) 16.6
b) The 95% confidence level of the mean of the time playing video games is between 15.7 and 17.5 hours.
c) The 99% confidence level of the mean of the time playing video games is between 15.4 and 17.8 hours.
d) The margin of error increases as the confidence level increases, due to the value of z, which means that the 99% confidence interval is larger.
Step-by-step explanation:
a. Find the best point of estimate of the population mean
The best estimate for the population mean is the sample mean, which is 16.6
b. Find the 95% confidence level of the mean of the time playing video games
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of .
That is z with a pvalue of , so Z = 1.96.
Now, find the margin of error M as such
In which is the standard deviation of the population and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 16.6 - 0.9 = 15.7 hours
The upper end of the interval is the sample mean added to M. So it is 16.6 - 0.9 = 17.5 hours
The 95% confidence level of the mean of the time playing video games is between 15.7 and 17.5 hours.
c. Find the 99% confidence interval of the mean time playing video games
Following the same logic as above, we have that . So
The lower end of the interval is the sample mean subtracted by M. So it is 16.6 - 1.2 = 15.4 hours.
The upper end of the interval is the sample mean added to M. So it is 16.6 + 1.2 = 17.8 hours.
The 99% confidence level of the mean of the time playing video games is between 15.4 and 17.8 hours.
d. Which is larger? Explain why.
The margin of error increases as the confidence level increases, due to the value of z, which means that the 99% confidence interval is larger.