Question

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)

Answer 1

Answer:

213 samples needed for 99% confidence interval

Step-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

$n = [\frac{z_{\alpha/2}\times s}{E}]^2$

where,

s is standard deviation = 19.8 degree

E IS MARGIN OF ERROR = 3.5 degree

$z _{\frac{\alpha}{2}}$ right tail critical value of

Z $z _{\frac{\alpha}{2}} = z _{\frac{0.01}{2}} = z_{0.005} = 2.58$

so, minimum size of sample needed is

$n = [\frac{2.58\times 19.8}{3.5}]^2$

n = 213.02

Therefor 213 samples needed for 99% confidence interval