Question

Dullco Manufacturing claims that its alkaline batteries last at least 40 hours on average in a certain type of portable CD player. But tests on a random sample of 18 batteries from a day's large production run showed a mean battery life of 37.8 hours with a standard deviation of 5.4 hours. In a left-tailed test at a-.05, which is the most accurate statement? O We would strongly reject the claim. O We would clearly fail to reject the claim. O We would face a rather close decision. O We would switch to a-.01 for a more powerful test.

Answer 1

Let's write the given information

n = sample size = 18

$\bar x$ = sample mean = 37.8

s = sample standard deviation = 5.4

From the alternative hypothesis the given test is left tailed test

Hypothesis testing

Here population standard deviation is not given and we use sample standard deviation(s) instead of population standard deviation . Also sample size is not sufficiently large( <30) so we need to assume that the sample comes from normal populatio. So we can used one sample t test

Using minitab we get following result

The command is Stat>>>Basic Statistics >>1 sample t...

Select summary Statistics

Look the following image:

then click on Perform hypothesis test enter hypothesis mean (40)

then click on Option select level of confidence = (1 - alpha)*100 = (1 - 0.05)*100 = 95.0

Alternative " less than"

then click on Ok

We get the following output

From the above output

t test statistic value = -1.73

p- value = 0.051

Decision rule: 1) If p-value <= level of significance (alpha) then we reject null hypothesis

2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.

Here p value = 0.051 > 0.01 so we used second rule.

That is we fail to reject null hypothesis

So correct choice is C) We would face a rather close decision.

Because p-value is very close to 0.05.