Answer to Question #339918 in Statistics and Probability for None

Question

A teacher claims that the average of students enrolled in Statistics is 88. A sample of 25 Statistics students has an average of 86 and standard deviation of 4. Is there enough evidence to reject the teacher's claim?

a) formulate the null and alternative hypothesis

b) determine what test statistic to use

c) Calculate the test statistic value

Answer 1

a) The following null and alternative hypotheses need to be tested:

$H_0:\mu=88$

$H_a:\mu\not=88$

b) This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation, using the sample standard deviation, will be used.

c) The t-statistic is computed as follows:

$$t=\dfrac{\bar{x}-\mu}{s/\sqrt{n}}=\dfrac{86-88}{4/\sqrt{25}}=-2.5$$