A company claims that its battery has a mean life of 65 months. A consumer protection agency tested 15 batteries and found the mean 63 months with a standard deviation of 2 months. The life such a battery has approximately normal distribution. Assume that a = .05.
Test hypothesis if all such batteries has mean less than 65 months.

• State the null and alternate hypotheses.
• What is the name of the distribution to use to calculate the sample test statistic?
• Under what assumption, this distribution is used?
• What is the value for the point estimator of the parameter of interest?
• Sketch the rejection region and show the critical values on the sketch.
• Compute the value of the sample test statistic and show it's location on the sketch.
• Find the P- value for the sample test statistic.
• Give a conclusion and explain it in simple non-technical terms.