Answer to Question #204480 in Statistics and Probability for ekim

Question

 A random sample of 81 deaths in a certain area during the past year showed an average life span of 71.8 years. Assuming that the population standard deviation is 8.9, does this seem to indicate that the average life span today is significantly greater than 70 years old? Use a 0.05 level of significance. 

Answer 1

One sample z-test.

$H_0:\mu=70.$

$H_a:\mu>70.$

Test statistic: $z=\frac{71.8-70}{\frac{8.9}{\sqrt{81}}}=1.82.$

P-value: $p=P(Z>1.82)=0.0344.$

Since the P-value is less than 0.05, reject the null hypothesis.

There is a sufficient evidence that the average life span today is significantly greater than 70 years old.