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

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=\frac{\overline{x}-\mu}{(s)/(√(n))}`

Substitute the values, we get

`t=(37.8-40)/((5.4)/(√(18)))`

`t=(-2.2)/((5.4)/(4.24264068712))`

`t=(-2.2)/(1.27279220614)`

`t=-1.72848324289\approx1.728`

Hence, the test statistic is −1.728.