Question

HSD Power Company claims that the mean battery life of their MP5 player is at least 30 hours. Christina, a local consumer watchdog, does not believe that the company is being truthful. She collected 23 MP5 manufactured by HSD and computed a mean battery span of 27.2 hours. The population standard deviation was previously tabulated and is believed to be 1.6 hours. Is there enough evidence to reject the claim at α=0.1?

a) Set up the Hypotheses

B) Decision rule (in complete sentence)

c)Computation

d)Decision (complete sentence)

e)Interpretation (in a complete sentence)

Answer 1

a)The hypothesis being tested is:

Null Hypothesis, H0: The mean battery life of the company MP5 player is equal to 30 i.e µ1 =30.

Ha: The mean battery life of the company MP5 player is at least 30 i.e µ1 >30.

b) Decision Rule

A decision rule is a procedure that the researcher uses to decide whether to accept or reject the null hypothesis.

Level of significance, =0.1

Critical value=1.28

The null hypothesis will be rejected if the test statistic is larger than a Critical value.

c) Test statistic:

The test statistic, t = (x - µ)/(σ/√n)

=(27.2-30)/(1.6/√23)

=-8.39

d) Since test statistic(t)< Critical value(1.28). We fail to reject the null hypothesis.

e) Interpretation

There is not sufficient evidence to conclude that the mean battery life of the company MP5 player is at least 30 at 10% level of significance.