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cmfuentes0816
06.01.2021 •
Mathematics
A restaurant customer left $1.35 as a tip...
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Ответ:
The tax was 4%- I have done this question in EnVision before...
Step-by-step explanation:
Ответ:
The 99% confidence interval is be given by (4.872;8.628)
Step-by-step explanation:
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 dataset is:
6, 9, 3, 9, 6, 6, 7, 7, 8, 9, 3, 8
2) 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:
The value obtained is![\bar X=6.75](/tpl/images/0395/7571/3131e.png)
The sample deviation obtained is![s=2.094](/tpl/images/0395/7571/249e4.png)
3) 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 =12 <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(0.005,11)" for![t_{\alpha/2}=-3.106](/tpl/images/0395/7571/14d79.png)
"=T.INV(1-0.005,11)" for![t_{1-\alpha/2}=3.106](/tpl/images/0395/7571/42a32.png)
The confidence interval for the mean is given by the following formula:
The next step would be calculate the limits for the interval
Lower interval :
Upper interval :
So the 99% confidence interval would be given by (4.872;8.628)
99% of the time, when we calculate a confidence interval with a sample of n=12, the true mean of rate of attractiveness of their female dates will be between the 4.872 and 8.628.