A random sample of 40 binomial trials resulted in 16 successes. Test the claim that the population proportion of successes does not equal 0.50. Use a level of significance of 0.05.

(a) Can a normal distribution be used for the distribution? Explain.

Yes, np and nq are both greater than 5.

No, nq is greater than 5, but np is less than 5.

No, np is greater than 5, but nq is less than 5.

No, np and nq are both less than 5.

Yes, np and nq are both less than 5.

(b) State the hypotheses.

H₀: p < 0.5; H₁: p = 0.5

H₀: p = 0.5; H₁: p < 0.5

H₀: p = 0.5; H₁: p 0.5

H₀: p = 0.5; H₁: p > 0.5

(c) Compute . (Enter a number.)

p^ =

Compute the corresponding standardized sample test statistic. (Enter a number. Round your answer to two decimal places.)

(d) Find the P-value of the test statistic. (Enter a number. Round your answer to four decimal places.)