A random sample of 50 binomial trials resulted in 20 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 p distribution? Explain. Yes, n.p and n.q are both less than 5. O No, n.q is greater than 5, but n.p is less than 5. O No, n.p and n-q are both less than 5. O No, nop is greater than 5, but n-q is less than 5. O Yes, n.p and n.q are both greater than 5. (b) State the hypotheses. O Ho: p 0.5 O Ho: p = 0.5; Hj: p = 0.5 (c) Compute p. (Enter a number.) 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.) (e) Do you reject or fail to reject Ho? Explain. O At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (f) What do the results tell you? The sample p value based on 50 trials is sufficiently different from 0.50 to justify rejecting H, for a = 0.05. O The sample p value based on 50 trials is not sufficiently different from 0.50 to not reject H, for a = 0.05. O The sample p value based on 50 trials is not sufficiently different from 0.50 to justify rejecting Ho for a = 0.05. The sample p value based on 50 trials is sufficiently different from 0.50 to not reject Ho for a = 0.05