A random sample of30binomial trials resulted in12successes. 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 thedistribution? Explain.

No,nqis greater than 5, butnpis less than 5.

Yes,npandnqare both less than 5.

No,npandnqare both less than 5.

No,npis greater than 5, butnqis less than 5.

Yes,npandnqare both greater 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:p0.5

H₀:p<0.5;H₁:p= 0.5

(c)Compute. (Enter a number.)

p hat =

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

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