Question

Apple claims that MacBook battery lasts 10 hours. A sample of 15 MacBooks showed a sample mean of 9.2 hours and a sample standard deviation of 1. hours. Assume the population is normal. Perform a hypothesis test to see if the MacBook lasts less than 10 hours with a level of significance of α=0.05

a) What are the null and alternative hypotheses?

b) what is the P-value and is it > or < α? (note, if you don't have the proper calculator, what is the test statistic and the critical value, ad is the test statistic "more extreme" than the critical value)

c) Do we reject or fail to reject the null hypothesis?

d) Does the data imply that the MacBooks average less than 10 hours? (write a complete sentence)

Answer 1

Here we have to use one sample t test for mean.Since population standard deviation is not given, we will use t test otherwise we use Z test.

Here sample mean = hours

Sample standard deviation = s = 1 hour

n = sample size = 15, alpha = 0.05,

a) Here Null hypothesis:

Alternative hypothesis:

b) Test statistic:

   =

= -3.10           (Round to 2 decimal)

Test statistic = t = -3.10

Here test is one tailed test (left tail test)

P value using excel:(Since statistical table does not gives us exact p value of t est)

"=TDIST(positive value of test statistic,df=n-1, tail of test)"

=TDIST(3.10,14,1)

=0.00392

P value = 0.00392

Critical value using excel:

"=T.INV(0.05,14)"

= - 1.761    (Round to 3 decimal)

Critical value = -1.761

c) Here p value < alpha = 0.05

We reject null hypothesis.

d) The data imply that the MacBooks average is less than 10 hours.