47. The article The Incorporation of Uranium and Silver by Hydrothermally Synthesized Galena (Econ.

Geol., 1964: 1003—1024) reports on the determination of silver content of galena crystals grown in a closed hydrothermal system over a range of temperature.

With x  crystallization temperature in C and y Ag2S in mol%, the data follows:

x 398 292 352 575 568 450 550 y .15 .05 .23 .43 .23 .40 .44 x 408 484 350 503 600 600 y .44 .45 .09 .59 .63 .60 sY ˆ

sY ˆ yˆ sY ˆ

yˆ

from which , 

4.73, 

.00143, .311, and s  .131.

a. Estimate true average silver contentwhentemperature is 500C using a 95% con dence interval.

b. How would the width of a 95% CI for true average silver content when temperature is 400C compare to the width of the interval in part (a)?

Answer without computing this new interval.

c. Calculate a 95% CI for the true average change in silver content associated with a 1C increase in temperature.

d. Suppose it had previously been believed that when crystallization temperaturewas 400C, true average silver content would be .25. Carry out a test at signi cance level .05 to decide whether the sample data contradicts this prior belief.