The life in hours of a battery is known to be approximately

The life in hours of a battery is known to be approximately normally distributed, with standard deviation = 1.25 hours. A random sample of 10 batteries has a mean life of x =40.5 hours.

(a) Is there evidence to support the claim that battery life exceeds 40 hours? Use = 0.05.

(b) What is the P-value for the test in part (a)?

(c) Calculate an appropriate condence interval on life and use to answer part (a)

Solution

Set Up Hypothesis
Null, H0: U=40
Alternate, H1: U>40
Test Statistic
Population Mean(U)=40
Given That X(Mean)=40.5
Standard Deviation(S.D)=1.25
Number (n)=10
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=40.5-40/(1.25/Sqrt(10)
Zo =1.2649
| Zo | =1.2649
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =1.2649 & | Z | =1.64
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value : Right Tail - Ha : ( P > 1.2649 ) = 0.103
Hence Value of P0.05 < 0.103, Here We Do not Reject Ho

[ANSWERS]
a) there is n\'t evidence to support the claim that battery life exceeds 40 hours

b) ( P > 1.2649 ) = 0.103

c)

CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=40.5
Standard deviation( sd )=1.25
Sample Size(n)=10
Confidence Interval = [ 40.5 ± Z a/2 ( 1.25/ Sqrt ( 10) ) ]
= [ 40.5 - 1.96 * (0.395) , 40.5 + 1.96 * (0.395) ]
= [ 39.725,41.275 ]

c) there is n\'t evidence to support the claim that battery life exceeds 40 hours