MHB Testing the Assumption of Car Model's km/L Performance

[mathmari]

Hey! :giggle:

Some people assume that a specific car model does at least $\mu_0=120$ km with $1$ Lt benzin.

$10$ independent tests give the following results: $$104, \ 96, \ 80, \ 100, \ 108, \ 100, \ 112, \ 120, \ 130, \ 132$$

(a) Give the Null Hypothesis $H_0$ and the alternative Hypothesis $H_1$, for the test of that assumption.

(b) Give the statistic function of that test.

(c) late the p-value of the test.

(d) In what confidence level can the assumption be rejected?
For (a) is the null hypothesis $H_0: \ m_0=120$ and the alternative $H_1: \ \mu_1\neq 120$ ?

 

[I like Serena]

Some people assume that a specific car model does at least $\mu_0=120$ km with $1$ Lt benzin.

(a) Give the Null Hypothesis $H_0$ and the alternative Hypothesis $H_1$, for the test of that assumption.

For (a) is the null hypothesis $H_0: \ m_0=120$ and the alternative $H_1: \ \mu_1\neq 120$ ?

Hey mathmari!

The assumption says "at least". We're not covering that with $\mu_1\ne 120$.

 

[mathmari]

The assumption says "at least". We're not covering that with $\mu_1\ne 120$.

So the assumption should be at the alternative hypothesis, or not?

So is it $H_1: \ \mu_1\geq 120$ ? :unsre:

 

[I like Serena]

So the assumption should be at the alternative hypothesis, or not?

So is it $H_1: \ \mu_1\geq 120$ ? :unsre:

Yep. (Nod)

Generally, if the problem statement contains a word like "less than", "more", or "at least", then we need an inequality in the alternative hypothesis.
It also means that the test is "one-sided".