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marabic22
29.11.2019 •
Mathematics
Alakefront resort is planning for its summer busy season. it wishes to estimate with 95% confidence the average number of nights each guest will stay for a consecutive visit. using a sample of guests who stayed last year, the average number of nights per guest is calculated at 5 nights. the standard deviation of the sample is 1.5 nights. the size of the sample used is 120 guests and the resort desires a precision of plus or minus .5 nights. what is the standard error of the mean in the lakefront resort example? within what range below can the resort expect with 95% confidence for the true population means to fall? show the calculation; otherwise, the answer will not be accepted.
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Ответ:
The 95% confidence interval would be given by (4.729;5.271)
Step-by-step explanation:
1) 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".
The standard error of a statistic is "the standard deviation of its sampling distribution or an estimate of that standard deviation"
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".
s represent the sample standard deviation
n represent the sample size
The confidence interval for the mean is given by the following formula:
We use the t distirbution for this case since we don't know the population standard deviation
.
Where the standard error is given by:![SE=\frac{s}{\sqrt{n}}](/tpl/images/0395/6952/feca8.png)
And the margin of error would be given by:![ME=t_{\alpha/2}\frac{s}{\sqrt{n}}](/tpl/images/0395/6952/6e0a2.png)
In order to calculate the critical value
we need to find first the degrees of freedom, given by:
Since the Confidence is 0.95 or 95%, the value of
and
, and we can use excel, a calculator or a table to find the critical value. And we see that ![t_{\alpha/2}=1.98](/tpl/images/0395/6952/cbe95.png)
The standard error would be given by:
Now we have everything in order to replace into formula (1) and calculate the interval:
So on this case the 95% confidence interval would be given by (4.729;5.271)
Ответ:
proved tanA =sinA/cos A cut cosA sina A proved
Step-by-step explanation:
cosA TanA =sinA
cosA sinA/cosA=sinA
SinA =sinA