MATH SOLVE

3 months ago

Q:
# student conducts a high temperature experiment using a thermister with a guaranteed accuracy of +/- 1.3 degrees Fahrenheit. The student takes an initial set of 11 measurements,and calculates a sample average of 224 and a sample deviation of 19.8 degrees. Assuming a confidence level of 99%, estimate the total number of samples needed to ensure a total measurement uncertainty less than 3.5 degrees. (the number of samples should be an integer)

Accepted Solution

A:

Answer:213 samples needed for 99% confidence intervalStep-by-step explanation:We know that:minimum size of sample needed to be sure about total measurement less than 3.5 degree is given as[tex]n = [\frac{z_{\alpha/2}\times s}{E}]^2[/tex]where,s is standard deviation = 19.8 degreeE IS MARGIN OF ERROR = 3.5 degree[tex]z _{\frac{\alpha}{2}}[/tex] right tail critical value of Z [tex]z _{\frac{\alpha}{2}} = z _{\frac{0.01}{2}} = z_{0.005} = 2.58[/tex]so, minimum size of sample needed is [tex]n = [\frac{2.58\times 19.8}{3.5}]^2[/tex]n = 213.02 Therefor 213 samples needed for 99% confidence interval