Answer to Question #173764 in Statistics and Probability for Cif666

Question

It is known from the records of the city schools that the standard deviation of mathematics test scores on problem solving is 5. A sample of 200 bright students was taken and it was found out that the sample mean score is 75. Previous test showed out the population mean to be 70. Is it safe to conclude at 0.025 level of significance that the sample is significantly different from the population?

Answer 1

Null hypothesis $H_0: \mu=70$

Alternative hypothesis $H_{\alpha}:\mu\neq70$

Test statistic:

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

P-value:

$p=2P(z<-14.14)<0.0001$

Since the P-value is less than 0.025, reject the null hypothesis.

We can conclude at 0.025 significance level that the sample is significantly different from the population.