Question

1. A poll of President Trump’s approval rating indicated that 44% of registered voters approve of his job performance. This result is based on a random sample of 435 registered voters across the country. Conduct a test to determine whether less than half of the population of registered voters approve of the president’s job performance. Write a short sentence interpreting the results. Be sure to include the appropriate statistical evidence: test statistic used, degrees of freedom, value of the test statistic, and test statistic critical value. Use α = .05.
   

Answer 1

H0: p = 0.50

Ha: p < 0.50

Critical value at 0.05 level = -1.645

Rejection region = Reject H0 if test statistics z < -1.645

Test statistics

z = - p / sqrt( p (1 - p) / n)

= 0.44 - 0.50 / sqrt( 0.50 * 0.50 / 435 )

= -2.50

This is test statistics value. .

Since test statistics z falls in rejection region, we have sufficient evidence to reject H0.

We conclude at 0.05 level that we have enough evidence to support the claim that less than half of the population of

registered voters approve of the president’s job performance.