Question

20-D. The table shows signal-to-noise ratios recorded in a nuclear magnetic resonance experiment. Construct graphs of

(a) signal-to-noise ratio versus n and

(b) signal-to-noise ratio versus $\sqrt{\mathbf{n}}$, where n is the number of scans. Draw error bars corresponding to the standard deviation at each point. Is the signal-to-noise ratio proportional to $\sqrt{\mathbf{n}}$? Find the 95% confidence interval for each row of the table.

Short answer

(a). The signal-to-noise ratio is plotted against the number of experiments

(b). The signal-to-noise ratio is plotted against the $\sqrt{\mathrm{n}}$

Step-by-step solution

Explain signal-to-noise ratio versus n:

Consider,

S is the standard deviation,

N is the number of experiments

T is student's t from the given table

Degree of freedom n-1. The first line of the table

n = 8

s = 1.9

t = 2.365 for 7 degree of freedom

95% of confidence level$=\pm \left(2.365\right)\left(1.9\right)/\sqrt{8}=\pm 1$

6 for the remaining rows another graph.

Explain signal-to-noise ratio versus n :

The confidence interval is $\pm \mathrm{tsl}\sqrt{\mathrm{n}}$

Consider,

S is the standard deviation,

N is the number of experiments

T is student's t from the given table

Degree of freedom n-1. The first line of the table

n = 8

s = 1.9

t = 2.365 for 7 degree of freedom,

95% confidence level =3.9 , 5.1 , 1, 9.0 , 11.12,14.0, 24.0 , 23.9 , and 27.2

Second graph, signal-to-noise ratio is plotted against the $\sqrt{\mathrm{n}}$