4. [120 Points] I DETAILS I BBBASICSTATBACC 9.3.005.M|.S. 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 signicance of 0.05. (a) Can a normal distribution be used for the 6 distribution? Explain. 0 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. 0 Yes, np and n-q are both greater than 5. O No, n-p is greater than 5, but n-q is less than 5. (b) State the hypotheses. O HO: p = 0.5; H1: p z 0.5 0 H0: p = 0.5; H1: p 0.5 (c) Compute 5. (Enter a number.) :I Compute the corresponding standardized sample test statistic. (Enter a number. Round your answer to two decimal places.) :I (d) Find the Pvalue of the test statistic. (Enter a number. Round your answer to four decimal places.) :I (e) Do you reject or fail to reject Ho? Explain. C) At the a: : 0.05 level, we reject the null hypothesis and conclude the data are statistically signicant. 0 At the ct : 0.05 level, we reject the null hypothesis and conclude the data are not statistically signicant. 0 At the :1 = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically signicant. 0 At the :1 = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically signicant. (f) What do the results tell you? 0 The sample 5 value based on 40 trials is not sufciently different from 0.50 to not reject HD for a : 0.05. O The sample 5 value based on 40 trials is sufciently different from 0.50 tojustify rejecting \"U for a = 0.05. O The sample p value based on 40 trials is not sufciently different from 0.50 to justify rejecting HD for a = 0.05. O The sample 5 value based on 40 trials is sufciently different from 0.50 to not reject H0 for a: = 0.05