Question

how to answer this two methods of teaching statistics are being trued by a professor. a class of 40 students is taught by method a and a class of 36 students is taught by method b. the two classes are given the same final examination. the scores are: first sample mean= 78 and second sample mean 74. at alpha = .01 can we conclude that the average final examination scores produced by the two methods are different if the population standard deviation is 5? given: tabular value is 5

Answer 1

$H_0:\mu _1=\mu_2;\\ H_1:\mu_1 \ne\mu _2;$

$z=\frac{|\mu_1-\mu_2|}{\sigma\cdot \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}$ =

=$\frac{78-74}{5\cdot \sqrt{\frac{1}{40}+\frac{1}{36}}}=$ 3.4823 is a statistics of the z-test;

z*=$qnorm(1-\frac{0.01}{2},0,1)=2.576$ is the critical value of test;

Thus z*>z therefore with reliability 99% two methods have different

effectiveness.