. Should the statistician use a t distribution, a normal distribution, or neithe

Question

. Should the statistician use a t distribution, a normal distribution, or neither to test the null hypothesis in the following? a. In a series of measurem ents on a machine part,X-0.0022, s 0.0001, n 23. The data is normally distributed and ? is not known. Ho: ? 0.0020; Hi : ? 0.0020 ts Use t dist Use normal distUse neither dist -for a data set is 2.47, s is 6.3 and n-153. The population is not normally distributed and ? is unknown. Ho: ? 3.1 Hi: H 3.1 Use t di Use normal dist Use neither dist st

Explanation / Answer

Our basic assumption to use normal dist or t dist is that data should be random and sample should either come from normal distribution or have a large sample (ie n> 30).

In case(a), data is normally distributed though n is small , standard deviation is unknown . So, we will use t-test when hypothesis is done on mean.

In case(b), data is not normally distributed but n is large (153>30) , standard deviation is unknown. So we will use t dist when hypothesis is done on mean.

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