Chapter 8, Problem 1CQQ

Wristwatch Accuracy Students of the author collected a simple random sample of times (see) of wristwatch errors, and a few of those times are listed below. Negative values correspond to watches that are running ahead of the actual time. Assuming that we want to use a 0.05 significance level to test the claim that the sample is from a population with a mean equal to 0 sec. identify the null hypothesis and the alternative hypothesis.

140 −85 325 20 305 205 20 −93

To determine

To identify: The null hypothesis and alternative hypothesis.

Answer to Problem 1CQQ

The null hypothesis is $\mu =0\sec$.

The alternative hypothesis is $\mu \ne 0\sec$.

Explanation of Solution

Given info:

The test of the claim is that the population with mean time of the wristwatches equal to 0 sec. and significance level is 0.05.

Calculation:

Here, the test is to claim the population with mean time of the wristwatches is equal to 0 sec. represents the null hypothesis. Thus, the alternative hypothesis is the population with mean time of the wristwatches is not equal to 0 sec.

The null and alternative hypotheses are given below:

Null hypothesis:

$H_0:\mu =0\sec$

That is, there is no evidence to reject the claim that the population with mean equal to 0 sec.

Alternative hypothesis:

$H_1:\mu \ne 0\sec$

That is, there is evidence to reject the claim that the population with mean not equal to 0 sec.

Thus, the null hypothesis is $\mu =0\sec$  and the alternative hypothesis is $\mu \ne 0\sec$.