Question

A company advertises that its car battery lasts 6 years on average. Assume that the life of a car battery has
a normal distribution and a population standard deviation of 1.2 years. Use this information to perform
tests of significance for the following problems in 1-6. (if possible also show TI calculator solution)
a. A random sample of 30 batteries has a mean life span of 5.7 years. Is there evidence at the ? = 0.05 level that the
batteries have an average life that is less than advertised?
b. A random sample of 30 batteries has a mean life span of 5.5 years. Is there evidence at the ? = 0.05 level that the
batteries have an average life that is less than advertised?
c. 2. A random sample of 30 batteries has a mean life span of 5.5 years. Is there evidence at the ? = 0.05 level that
the batteries have an average life that is different than advertised?
d. A random sample of 45 batteries has a mean life span of 6.3 years. Is there evidence at the ? = 0.05 level that the
batteries have an average life that is greater than advertised?
e. A random sample of 45 batteries has a mean life span of 6.3 years. Is there evidence at the ? = 0.05 level that the
batteries have an average life that is different than advertised?
f. A random sample of 45 batteries has a mean life span of 6.3 years. Is there evidence at the ? = 0.1 level that the
batteries have an average life that is different than advertised?

Answer 1

Q.a

Hypothesis:

Test statistic,

Critical value= z0.05 = 1.645

Since calculated |Z| < critical value, we accept null hypothesis that batteries has mean life span of 6 years.

In Ti-84 Press 'STAT' ----> 'TESTS' ----> Select 'Z Test' --->Select 'Inpt : Stats' ---> Enter all required values and press Enter you will get following output.