Answer to Question #194728 in Statistics and Probability for Alice

Question

A TV manufacturer claims that the lifespan of its regular TV sets is longer than 10 years with a standard deviation of 1.8 years. Using a random sample of their 25 TV sets, the average lifespan is found to be 11.9 years. Test the hypothesis that the TV sets' lifespan is longer than 10 years at a=0.05

Answer 1

Null hypothesis $H_0:\mu=10.$

Alternative hypothesis $H_a:\mu>10.$

Test statistic: $z=\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}=\frac{11.9-10}{\frac{1.8}{\sqrt{25}}}=5.28.$

P-value: $p=P(Z>5.28)<0.0001$.

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

There is a sufficient evidence that the lifespan of its regular TV sets is longer than 10 years.