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### 45-733 PROBABILITY AND STATISTICS I

A SHORT GUIDE TO HYPOTHESIS TESTING

1. Ho: m = mo
H1: m = m1 > mo

Test: If > mo + c then reject Ho

1. To find c when s2 is known

To solve for c (a) fix a (c) and use Z table.

2. To find c when s2 is not known, large sample

To solve for c (a) fix a (c) and use Z table.

3. To find c when s2 is not known, small sample from N(m, s2)

Where T has a t distribution with n - 1 degrees of freedom. To solve for c (a) fix a (c) and use t table.

2. Ho: m = mo
H1: m ¹ mo

Test: If > mo + c or - < mo - c then reject Ho.

1. To find c when s2 is known

To solve for c (a) fix a (c) and use Z table.

2. To find c when s 2 is not known, large sample

To solve for c (a) fix a (c) and use Z table.

3. To find c when s2 is not known, small sample from N(m , s2)

Where T has a t distribution with n - 1 degrees of freedom. To solve for c (a) fix a (c) and use t table.

3. Ho: m 1 - m2 = 0
H1: m1 - m2 ¹ 0

Test: If then reject Ho.

1. To find c when s12 and s22 are known

To solve for c (a) fix a (c) and use Z table.

2. To find c when are not known, large sample

To solve for c (a) fix a (c) and use Z table.

3. To find c when are not known, small samples from N(m , s2)

Where T has a t distribution with n + m - 2 degrees of freedom and s2 is given by:

To solve for c (a) fix a (c) and use t table.

4. Ho: s2 =
H1: s2 =

Test: If then reject Ho.

To find c2 set

and use the chi-square table with n - 1 degrees of freedom.

5. Ho: s2 =
H1: s2 =

Test: If then reject Ho.

To find c1 and c2 set

and use the chi-square table with n - 1 degrees of freedom.

6. Ho:
H1:

Test: If or

then reject Ho. To find k1 and k2 set

Use the F table with n - 1 and m - 1 degrees of freedom to find k2 and then use the reciprocal of the entry for m - 1 and n - 1 degrees of freedom for k1.