Question

1.

A manufacturer claims that the mean lifetime of its lithium batteries is 1200 hours. A homeowner selects 26 of these batteries and finds the mean lifetime to be 1100 hours with a standard deviation of 85 hours.

Test the manufacturer's claim. Use α = 0.05. Round the test statistic to the nearest thousandth.

Please solve using excel

Answer 1

n = sample size = 26

s= sample standard deviation = 85

Claim is

Test statics formula

our test is two tailed because H_a alternative hypothesis has not equal to sign.

We can calculate p value using excel

Select empty cell from the excel and type

=tdist( positive value of test statistics , df , tail)

Positive test statistics = 5.998846487

df = n - 1 = 26 -1 = 25

Tail = 2 ( because test is two tailed)  

So above command becomes

=tdist(5.998846487,25, 2)

then press enter

P value = 2.8937260080 E^-6

That E^-6 means we have to shift the decimal point to left by 6 units

p value = 0.0000028937260080

decision rule

p value is less than   Then we reject H₀

p value greater than then we fail to reject H₀

0.0000028937260080 is less than 0.05 so we reject H₀

As we are rejecting the H₀ That means we do not support  

Final conclusion about the claim.

There is insufficient eveidevce to support the claim that mean lifetime of its lithium batteries is 1200 hours.

I hope this will help you :)