: Compute a z statistic for each

Question

sample of 43 scores mean of 101,  60 scores mean of 96, sample 29 scores mean of 100. Compute a z statistic for each, assuming population mean of 100 standard deviation of 20

Answer 1

To calculate a z statistic first we find a suitable standard deviation (SD), s. We have the population statistics, so we can write s=20/sqrt(n) where 20 is the pop SD and n is the sample size (n>30). Now z=((sample mean)-(pop mean))/s and a standard normal distribution applies where n>30.

1. n=43, m, the sample mean,=101, s=20/sqrt(43)=3.05 approx. z=(101-100)/3.05=0.3278.

2. n=60, m=96, s=20/sqrt(60)=2.58 approx. z=(96-100)/2.58=-1.5492.

3. n=29, m=100. We don't need to calculate s this time because the sample and pop mean are the same so z=0. That's good because n<30, so the z and t statistics (t statistic applies when n<30) are the same.