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.

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

represent the sample mean  

population mean (variable of interest)  

represent the sample standard deviation  

n=8 represent the sample size  

95% confidence interval  

The confidence interval for the mean is given by the following formula:  

(1)

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)  

here

step-by-step explanation:

answer: the answer is 127 degrees