According to a recent census, 15% of the people in the United States are of Hispanic origin. One county supervisor believes her county has a lower proportion of Hispanic people than the nation as a whole (p < 0.15). She looks at their most recent survey data, which was a random sample of 485 county residents, and found that 43 of those surveyed are of Hispanic origin. Test statistic Z is found to be -3.78, calculate p-value.

The P-value of the given test is 0.00008.

Step-by-step explanation:

We are given that according to a recent census, 15% of the people in the United States are of Hispanic origin.

She looks at their most recent survey data, which was a random sample of 485 county residents, and found that 43 of those surveyed are of Hispanic origin.

Let p = proportion of Hispanic people than the nation as a whole.

So, Null Hypothesis, : p = 0.15      {means that county has a 15% proportion of Hispanic people than the nation as a whole}

Alternate Hypothesis, : p < 0.15     {means that county has a lower proportion of Hispanic people than the nation as a whole}

The test statistics that would be used here One-sample z-test for proportions;

                              T.S. =    ~ N(0,1)

where, = sample proportion of Hispanic origin people = = 0.09

           n = sample of county residents = 485

So, the test statistics  =  

                                     =  -3.78

The value of z test statistic is -3.78.

Now, P-value of the test statistics is given by the following formula;

            P-value = P(Z < -3.78) = 1 - P(Z 3.78)

                          = 1 - 0.99992 = 0.00008

it would be 6xy and -16xy.