Question 1029356: A mobile phone manufacturer is promoting a new mobile because of its excellent battery life.
The company states that the battery life follows a normal distribution with a mean of 24 hours and a standard deviation of 4 hours. An independent review takes a sample of 36 mobiles and tests the battery life.
(i) Assuming the company’s claim is true
a) Calculate the standard error of the distribution of the sample mean.
b) Calculate the probability that the sample mean battery life exceeds 26 hours.
(ii) The independent review found the mean battery life from their sample was 20 hours.
a) Using this sample mean, construct a 95% confidence interval for the population mean battery life.
b) Using your answer from part a), explain in one sentence whether or not there is any evidence
from the independent review sample to refute the mobile manufacturer’s claim of a “mean battery life of 24 hours”.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Ho: mean is 24 hours
Ha: mean isn't 24 hours
alpha=0.05
test statistic t df=35= (x-mean)/s/sqrt(36)
reject if |t|>2.0301
standard error is 4/6=0.6667
probability it exceeds 26 hours is where t=2/(2/3)=3, which is just less than 0.0025, so I will use 0.0024
the t value for 20 hours of battery life in the sample of 36 is -4/(2/3)=-6
95%CI uses 2.0301 *(2/3)=1.3534
put those limits around the sample mean
(18.65,21.35)
The confidence interval does not contain the postulated mean of 24 hours. The null hypothesis is rejected. It happens to be rejected with a p-value of much less than 0.0001.
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