Question

Durco 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. To test DullCo's hypothesis, the test statistic is
Multiple Choice
a. −1.980
b. −2.101
c. −1.960
d. −1.728

Answer 1

Answer: d. −1.728

Step-by-step explanation:

As per given , we have

Null hypothesis : $H_0: \mu\geq40$

Alternative hypothesis :  $H_a: \mu<40$  (against Null hypothesis )

Alternative hypothesis is one-tailed , then the test is one-tailed test.

Sample size : n= 18

Sample mean : $\overline{x}=37.8$

Sample standard deviation : s= 5.4

Population standard deviation is unknown , so we should perform t-test.

Test statistic : $t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}$

Substitute the values, we get

$t=\dfrac{37.8-40}{\dfrac{5.4}{\sqrt{18}}}$

$t=\dfrac{-2.2}{\dfrac{5.4}{4.24264068712}}$

$t=\dfrac{-2.2}{1.27279220614}$

$t=-1.72848324289\approx1.728$

Hence, the test statistic is −1.728.