Question

You have a SRS of 15 ?(?,?) distributed observations (where ? is known but ? is not). You conduct a test of ?₀:?=10 vs. ?_A:?<10. You compute a test statistic value of ?=2.4. Using only the 68-95-99.7 rule (i.e., not the qnorm() function or tables) and a sketch of an appropriate density curve (with informative labels and shading), give an approximate value for the p-value (i.e., find values ? and ? such that that ?< p-value <?).

Answer 1

for this pair of hypothesis ?₀:?=10 vs. ?_A:?<10. ( this is left one-tailed test )

the observed z=2.4 and corresponding p-value=0.0082

0.001<p-value<0.0001

a=0.001 and b=0.0001

Using only the 68-95-99.7 rule, for approximately normal data set, the values within one standard deviation of the mean account for about 68%(A) of the set; while within two standard deviations account for about 95% (B); and within three standard deviations account for about 99.7%(C)..