Mean hypothesis testing with t-distribution

Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

Get the most by viewing this topic in your current grade. Pick your course now.

?
Intros
Lessons
  1. How do we test hypotheses about mean, when we don't know σ\sigma?
?
Examples
Lessons
  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?
    1. "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:
      1. "The average motorcycle produced by Redline has more than 125hp"
      2. "The average motorcycle produced by Redline doesn't have 125 hp"
      3. Compare the two answer found in the previous two parts
    Topic Notes
    ?
    If σ\sigma is not known, then we cannot use the test statistic:
    Z=xμσnZ=\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}}}
    We will instead use the test-statistic:
    Z=xμsnZ=\frac{\overline{x}-\mu}{\frac{s}{\sqrt{n}}}
    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.