If P1=0.7, P2=0.75, n1=200 and n2=120 (a) Standard error for the difference between sample proportions 𝑝 2 − 𝑝 1 ?

To calculate the standard error for the difference between sample proportions, we can use the formula:

SE = sqrt( (P1*(1-P1)/n1) + (P2*(1-P2)/n2) )

Given:
P1 = 0.7
P2 = 0.75
n1 = 200
n2 = 120

Substitute the values into the formula:

SE = sqrt( (0.7*(1-0.7)/200) + (0.75*(1-0.75)/120) )
SE = sqrt( (0.21/200) + (0.1875/120) )
SE = sqrt( 0.00105 + 0.0015625 )
SE = sqrt( 0.0026125 )
SE = 0.0511

Therefore, the standard error for the difference between sample proportions 𝑝2 − 𝑝1 is 0.0511.

The standard error for the difference between sample proportions is given by:

```
SE(p2 - p1) = sqrt((p1(1-p1)/n1) + (p2(1-p2)/n2))
```

Plugging in the given values, we get:

```
SE(p2 - p1) = sqrt((0.7(1-0.7)/200) + (0.75(1-0.75)/120))
```

```
SE(p2 - p1) = 0.065
```

Therefore, the standard error for the difference between sample proportions is 0.065.