1. For any normal distribution, any value less than the mean would have a _______.

a) negative probability of occurring
b) negative z-score
c) positive z-score
d) negative variance

Answer: b) negative z-score

2. The diameter of 3.5 inch diskettes is normally distributed. Periodically, quality control inspectors at Dallas Diskettes randomly select a sample of 16 diskettes. If the mean diameter of the diskettes is too large or too small the diskette punch is shut down for adjustment; otherwise, the punching process continues. The last sample showed a mean and standard deviation of 3.49 and 0.08 inches, respectively. Using alpha (a) = 0.05, the appropriate decision is _______.

a) do not reject the null hypothesis and shut down the punch
b) reject the null hypothesis and do not shut down the punch
c) reject the null hypothesis and shut down the punch
d) do not reject the null hypothesis and do shut down the punch

Answer: do not reject the null hypothesis and do NOT shut down the punch

Mean=M = 3.5 inches
Standard deviation =s= 0.08 inches
sample size=n= 16
sx=standard error of mean=s/square root of n= 0.02 = ( 0.08 /square root of 16)
Significance level=alpha (a) = 0.05
No of tails= 2
This is a 2 tailed test because we are testing M 1not equal to M 2

Since sample size= 16 < 30
and we are estimating the population standard deviation from sample standard deviation
we will use t distribution
sample mean= 3.49 inches

t at the 0.05 level of significance and 15 degrees of freedom (=n-1) and 2 tailed test= 2.1314

Upper acceptance limit= M +t*sx= 3.54 =3.5+2.1314*0.02
Lower acceptance limit= M -t*sx= 3.46 =3.5-2.1314*0.02

Accept Null Hypothesis since the sample mean is within acceptance region