Answer to Question #154615 in Statistics and Probability for Shailesh desai

Question

A sample of size 10 drawn from a normal population has a mean 31 and a variance 2.25. Is it reasonable to assume that the mean of the population is 30? 

(Use 1% level of significance, given that P(|t| )=0.1, for 9 d.f)

Answer 1

Null hypothesis $H_0:\mu=30.$

Alternative hypothesis $H_a:\mu\ne30.$

Test statistic: $t=\frac{\bar x-mu}{\frac{s}{\sqrt{n}}}=\frac{31-30}{\frac{\sqrt{2.25}}{\sqrt{10}}}=2.11.$

P-value: $p=0.0641.$

Since the P-value is greater than 0.01, fail to reject the null hypothesis.

There is no sufficient evidence that the mean of of population does not equal 30.