Answer to Question #193399 in Statistics and Probability for jasper

Question

. It is claimed that the average age of working students in a certain university is 35 years. a researcher selected a random sample of 25 working students. the computation of their age resulted to an average of 32 years with a standard deviation of 10 years. Does this mean that the average age of the working students is different from 35 years? Use 0.05 level of significance and assume normality in the population.

Answer 1

$n=25 \\ \bar{x} =32 \\ s=10$

$Null\; hypothesis :\:\mu=35\:\: \\alternative\; hypothesis :\mu \neq 35​​​​​​$

Test statistic is given by

 $t=\dfrac{\bar{x} - \mu}{s/ \sqrt{n} }=\dfrac{32-35}{10/ \sqrt{25}}=-1.5$

Critical value for two tailed test for $24(i.e \;n-1= 25-1)$ degrees of freedom for 5% level of significance is - 2.048 and 2.048.

The p-value for this test is 0.1348

Since, p-value is greater than $\alpha(0.05)$ . Hence we accept the null hypothesis, that is, average age of graduate students on this particular University campus is equal to 35 years.