Apple claims that the battery in the new iPhones lasts Up to 10 days on standby.

Question

Apple claims that the battery in the new iPhones lasts Up to 10 days on standby. Tests on a random sample of 30 phones showed a mean battery life of 8.3 days with a standard deviation of 1.4 hours. A left-tailed hypothesis test will be conducted, but all you have to do is complete the steps below 2. (2) Calculate the test statistic using the sample data. For this calculation, assume that the value of under the null hypothesis is 10 days. (a) (2) b) How many standard deviations away from the population mean is the sample mean? In your answer, you must also include the direction. (2) (c) Suppose that the test statistic for the problem above had been -2.567. Find the p-value (2) (d Provide a calculation for the standard error of the mean

Explanation / Answer

Solution2a:

pop mean=10

sample size=n=30

sample mean=8.3

sample sd=1.49

t=sample mean-pop mean/samplesd/sqrt(n)

=8.3-10/1.4/sqrt(30)

=-1.7/1.4/sqrt(30)

t =-6.6509

Solution2b:

since t value is negative

it is 6.6509 standard deviations below mean

direction is left tailed

Solution2c:

df=n-1=30-1=29

alpha=0.05

p=0.0078

p>0.05

Reject null hypothesis

Solution2d:

std error of mean=sample sd/sqrt(smaple size)

=1.4/sqrt(30)

=0.25556

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