An article in the Washington Post on March 16, 1993 stated that nearly 45% of all Americans have brown eyes. A random sample of 55 students found 43 with brown eyes. Give the numerical value of the sample proportion, p^p^, and find the value of the test statistic. Sample Proportion p^=p^= (round to four decimal places). Test Statistic z=z= (round to four decimal places).

Sample proportion, = 0.7818

Test statistics, z = 5.9577

Step-by-step explanation:

We are given that an article in the Washington Post on March 16, 1993 stated that nearly 45% of all Americans have brown eyes. A random sample of 55 students found 43 with brown eyes.

Let p = population proportion Americans having brown eyes

SO, Null Hypothesis, : p = 45%   {means that the proportion of all Americans having brown eyes is 45%}

Alternate Hypothesis, : p 45%  {means that the proportion of all Americans having brown eyes is different from 45%}

The test statistics that will be used here is One-sample z proportion statistics;

                 T.S.  =    ~ N(0,1)

where,   = sample proportion of Americans having brown eyes in a sample of 55 students = = 0.7818

             n = sample of students = 55

So, test statistics  =  

                               =  5.9577

Therefore, the value of test statistics, z = 5.9577.

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step-by-step explanation:

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°