Null and alternative hypotheses for a test are given below. Give the notation ( x , for example) for a sample statistic we might record for each simulated sample to create the randomization distribution. H 0 rho 0 versus H a rho 0 Null and alternative hypotheses for a test are given below. Give the notation ( x , for example) for a sample statistic we might record for each simulated sample to create the randomization distribution. H 0 rho 0 versus H a rho 0

Simulate many samples assuming the null hypothesis is true. Collect the values of a sample statistic for each simulated sample to create a randomization distribution.

The randomization distribution will be centered at the value indicated by the null hyothesis and shows what values of the sample statistics are likely to occur by random chance, if the null hypothesis is true.

Example 1

Null hpothesis: [tex]H_0:\rho = 0[/tex]

Alternative hypothesis: [tex]H_1:\rho\neq 0[/tex]

The randomization statistics is : r (Here, r represents the correlation coefficient)

Example 2

Null hpothesis: [tex]H_0:\mu_1= \mu_2[/tex]

Alternative hypothesis: [tex]H_1:\mu_1\neq \mu_2[/tex]

The randomization statistics is : [tex]\bar x_1 -\bar x_2[/tex] (Here, [tex]\bar x_1\,and \bar x_2[/tex] sample means)

Example 3

Null hpothesis: [tex]H_0:p_1 = p_2[/tex]

Alternative hypothesis: [tex]H_1:p_1>p_2[/tex]

The randomization statistics is : [tex]\vec p_1-\vec p_2[/tex] (Here, [tex]\vec p_1\, and \vec p_2[/tex] sample proportions)

Example 4

Null hpothesis: [tex]H_0:p = 0.5[/tex]

Alternative hypothesis: [tex]H_1:p< 0.5[/tex]

The randomization statistics is : [tex]\vec p[/tex] (Here, [tex]\vec p[/tex] sample proportion)