1) Table 1 below contains two sets of counting data obtained using a gas proportional counter and 90Sr check source. The counting interval for data set #1 was 1 min, and was 2 min for data set #2. For each measurement, the 90Sr check source was removed from its sample changer and then replaced. For each data set, the background counts were negligible compared to the net counts. 55% a) Calculate all the statistics for each data sets as determined in the example calculations provided in class. Also, perform all the statistical tests and make conclusions to reject or accept the null hypotheses of Poisson variance, acceptable randomness, and acceptable normality based on the test results. To make your conclusions, use the same type I error probability of 0.05 in each tail when performing hypothesis tests. 10% b) For each data set, report the 95% occurrence interval for the counts (C), and the 95% confidence interval for the sample means (C). 10% c) For each data set, determine the relative variance for the counts and the relative variance for the sample means. 10% d) For each data set, determine the average counting rate (R) and its standard deviation (in units of counts per second), and determine the standard deviation for the counting rates (R). 15% e) Discuss the different conclusions reached for each data set, and why one data set may be more effective than the other for detecting the existence of non-Poisson variance.

Table 1. Counting data sets #1 and #2. The counting interval T was 1 min for data set #1 and 2 min for data set #2. The data were obtained using a gas-flow proportional counter and 'Sr check source. For each measurement, the 9Sr check source was removed from its sample changer and then replaced. Index, i Counting data set #1 (T = 1 min) Counting data set #2 (T = 2 min) 1 16,396 32,843 2 16,059 32,668 16,314 32,562 16,245 32,933 16,423 32,834 16,241 32,057 16,315 33,002 8 16,527 32,677 16,330 32,565 10 16,358 32,356 11 16,460 32,487 12 16,380 32,525 13 16,368 32,752 14 16,217 32,683 15 16,341 32,018 16 16,433 32,728 17 16,308 32,333 18 16,025 32,368 19 16,437 32,586 20 16,248 32,560 21 16,023 32,031 22 16,323 32,820 23 16,529 32,720 24 16,245 32,469 25 16,332 32,457 26 16,570 32,964 27 16,361 32,556 28 16,273 32,786 29 16,491 32,310 30 16,243 32,413 Table 1. Counting data sets #1 and #2. The counting interval T was 1 min for data set #1 and 2 min for data set #2. The data were obtained using a gas-flow proportional counter and 'Sr check source. For each measurement, the 9Sr check source was removed from its sample changer and then replaced. Index, i Counting data set #1 (T = 1 min) Counting data set #2 (T = 2 min) 1 16,396 32,843 2 16,059 32,668 16,314 32,562 16,245 32,933 16,423 32,834 16,241 32,057 16,315 33,002 8 16,527 32,677 16,330 32,565 10 16,358 32,356 11 16,460 32,487 12 16,380 32,525 13 16,368 32,752 14 16,217 32,683 15 16,341 32,018 16 16,433 32,728 17 16,308 32,333 18 16,025 32,368 19 16,437 32,586 20 16,248 32,560 21 16,023 32,031 22 16,323 32,820 23 16,529 32,720 24 16,245 32,469 25 16,332 32,457 26 16,570 32,964 27 16,361 32,556 28 16,273 32,786 29 16,491 32,310 30 16,243 32,413