Question

In: Statistics and Probability

A chemist made six independent measurements of the sublimation point of carbon dioxide (the temperature at...

A chemist made six independent measurements of the sublimation point of carbon dioxide (the temperature at which it changes to dry ice). She obtained a sample mean of 196.64 K with a standard deviation of 0.67 K. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part.

Use the Student’s t distribution to find a 95% confidence interval for the sublimation point of carbon dioxide. (Round the final answers to two decimal places.)

Use the Student’s t distribution to find a 98% confidence interval for the sublimation point of carbon dioxide. (Round the final answers to two decimal places.)

Solutions

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 196.64

sample standard deviation = s = 0.67

sample size = n = 6

Degrees of freedom = df = n - 1 = 6 - 1 = 5

a) At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

t/2,df = t0.025,5 = 2.571

Margin of error = E = t/2,df * (s /n)

= 2.571 * ( 0.67/ 6)

Margin of error = E = 0.70

The 95% confidence interval estimate of the population mean is,

  ± E  

= 196.64 ± 0.70

= ( 195.94, 197.34 )

b) At 98% confidence level

= 1 - 98%

=1 - 0.98 =0.02

/2 = 0.01

t/2,df = t0.01,5 = 3.365

Margin of error = E = t/2,df * (s /n)

= 3.365 * ( 0.67/ 6)

Margin of error = E = 0.92

The 98% confidence interval estimate of the population mean is,

  ± E  

= 196.64 ± 0.92

= ( 195.72, 197.56 )


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