Question

Its is known from the records of the city schools that the standard deviation of mathematics test score on the XYZ test is 5. A sample of 200 pupils from the system was taken and it was found out the sample means score is 75.It is safe to conclude that the sample significantly different from the population?

Answer 1

Null hypothesis $H_0:\mu=70.$

Alternative hypothesis $H_a:\mu\ne70.$

Test statistic: 

$$z=\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}=\frac{75-70}{\frac{5}{\sqrt{200}}}=14.14.$$

P-value: $p=2P(Z<-14.14)<0.0001.$

Since the P-value is less than 0.05, reject the null hypothesis.

It is safe to conclude at 0.05 significance level that the sample is significantly different from the population.