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moowalden1239
23.12.2019 •
Mathematics
Achemist made eight independent measurements of the melting point of tungsten. she obtained a sample mean of 3410.14 degrees celsius and a sample standard deviation of 1.018 degrees. a) use the student’s t distribution to find a 95% confidence interval for the melting point of tungsten. b) use the student’s t distribution to find a 98% confidence interval for the melting point of tungsten.
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Ответ:
a) The 95% confidence interval would be given by (3409.291;3410.989)
b) The 98% confidence interval would be given by (3409.060;3411.220)
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".
Part a
n=8 represent the sample size
95% confidence interval
The confidence interval for the mean is given by the following formula:
First we need to find 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. The excel command would be: "=-T.INV(0.025,7)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 95% confidence interval would be given by (3409.291;3410.989)
Part b
Since the Confidence is 0.98 or 98%, the value of
and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.01,7)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 98% confidence interval would be given by (3409.060;3411.220)
Ответ:
Not sure, the probability is 8
Step-by-step explanation: