Question

The U.S. and many other countries have recently tightened airport security. A sociologist is interested in estimating the proportion of the travelers who feel that airports are safe. The sociologist found that 300 of the 400 travelers randomly selected and interviewed indicated that the airports were safe. With an alpha level of 0.1, conduct a test to determine whether the true proportion of interest is higher than 0.7.

(a) State the null and alternative hypotheses.

H0:p

Ha : p

(b) Calculate the test statistic. z=p̂ −p0p0(1−p0)/n‾‾‾‾‾‾‾‾‾‾‾√= z = p ^ − p 0 p 0 ( 1 − p 0 ) / n = (Round to 2 decimal places.)

(c) Calculate the p-value. (Round to 4 decimal places.) Please explain this step!!

(d) State the decision. the null hypothesis.

Answer 1

a) H₀: P = 0.7

    H₁: P > 0.7

b) = 300/400 = 0.75

The test statistic z = ( - P)/sqrt(P(1 - P)/n)

                             = (0.75 - 0.7)/sqrt(0.7 * (1 - 0.7)/400)

                             = 2.18

c) P-value = P(Z > 2.18)

                 = 1 - P(Z < 2.18)

                 = 1 - 0.9854 = 0.0146

d) Since the P-value is less than alpha (0.0146 < 0.1), so we should reject the null hypothesis.