Mean hypothesis testing with t-distribution

Mean hypothesis testing with t-distribution


If σ\sigma is not known, then we cannot use the test statistic:
We will instead use the test-statistic:
So at the very least we must know the sample standard deviation, ss. Furthermore we will be using a t-distribution instead of our standard normal distribution to find our fail to reject region and our rejection region.
  • Introduction
    How do we test hypotheses about mean, when we don’t know σ\sigma?

  • 1.
    Hypothesis Testing Mean Claims without Knowing σ\sigma
    A gravel company has been known in the past to overload their trucks. The load capacity is 2500lbs of gravel for one of their standard trucks. A total of 41 trucks were sampled and had an average load of 2550lbs, with a standard deviation of 150lbs. With a significance level of α\alpha=0.01 can it be said that this company overloads their trucks?

  • 2.
    “Redline motorcycles” is a company that fixes and tunes motorcycles. A sample of 75 of their motorcycles had an average of 135hp, and a standard deviation of 35hp. Test the following claims with a 99% confidence level:
    “The average motorcycle produced by Redline has more than 125hp”

    "The average motorcycle produced by Redline doesn’t have 125 hp”

    Compare the two answer found in the previous two parts