Answer to Question #132913 in Statistics and Probability for Johannes

Question

A new internet provider claims their system you can get transmission speed of 400 kilobits per second. Specify both statically and in English, the null and alternative hypotheses a potential customer should investigate if she is worried that the connection is really slower than advertised.explain your reasoning

Answer 1

In this problem our alternatives are;

1. The company's speed is as advertised, that is, it has a mean µ of 400 Kilobits per second or higher.
2. The company's speed is lower than the advertised 400 Kilobits per second

The correct null hypothesis for (1) is H0 : µ ≥ 400 or H0 µ = 400

Alternative is HA: µ < 400 

A customer would want to prove to themselves that a product is good before buying. The burden is really on the company to convince the customer to buy their product and not someone else.

If the sample mean is far below 400 kilobits per second, then customer should reject the null hypothesis that the mean speed is above 400 kilobits and accept the alternative hypothesis, namely that the connection speed is lower than advertised. In this situation, the customer will probably not want to purchase the service.