Question

A sample of 12 radon detectors of a certain type was selected, and each was exposed to 100 pCi/L of radon. The resulting readings were as follows: 104.3, 89.6, 89.9, 95.6, 95.2, 90.0, 98.8, 103.7, 98.3, 106.4, 102.0, 91.1. Does this data suggest that the population mean reading under these conditions differs from 95? State and test the appropriate hypotheses using alpha=.1

A) t = 1.177, do not reject the null B) z = 1.177, do not reject the null C) t = -1.177, do not reject the null D) t = 1.177, reject the null E) z = -1.177, do not reject the null

Answer 1

Answer:

Given,

Sample n = 12

Mean = x/n

= (104.3+89.6+89.9+95.6+95.2+90+98.8+103.7+98.3+106.4+102+91.1)/12

= 97.075

Standard deviation = sqrt((1/(n-1)*(xi-xbar)^2)

= sqrt((1/11)*(xi-97.0975)^2)

= 6.1095

Null hypothesis Ho : u = 95

Alternative hypothesis Ha : u != 95

consider,

test statistic z = (xbar - u)/(s/sqrt(n))

substitute values

= (97.075 - 95)/(6.1095/sqrt(12))

z = 1.177

alpha = 0.1

Here at 90%CI, z critical value is 1.645

Here we observe that, test statistic < critical value, so we fail to reject Ho.

There is no sufficient evidence.