Komal R. answered • 04/05/21

Statistician-------

Favorable Cases X = | 12 | Sample Size N = | 40 |

The sample proportion is computed as follows, based on the sample size N=40 and the number of favorable cases X=12:

p^{^}=N/X=4012=0.3

The critical value for α=0.01 is zc=z(1−α/2)=2.576. The corresponding confidence interval is computed as shown below:

CI(Proportion)===(p−zc ((sqrt(p^(1−p^)/n) , p+zc(sqrt(p^(1−p^)/n))

=(0.3−(2.576× sqrt((0.3(1−0.3)/40)) ,0.3+2.576× sqrt((0.3(1−0.3)/40))

=(0.113,0.487)

Therefore, based on the data provided, the 99% confidence interval for the population proportion is 0.113<p<0.487, which indicates that we are 99% confident that the true population proportion p is contained by the interval (0.113,0.487).

Round off to two decimal it will become 0.11 and 0.49

=

so Answer for this question option. A