# Mean hypothesis testing with t-distribution

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**Hypothesis Testing Mean Claims without Knowing $\sigma$**

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 $\alpha$=0.01 can it be said that this company overloads their trucks?- "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: