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 p̂ distribution? Explain.
No, np is greater than 5, but nq is less than 5.
(b) State the hypotheses.
H0: p = 0.5;
H1: p ≠0.5
(c) Compute p̂. Compute the corresponding standardized sample test statistic. (Round your answer to two decimal places.)
(d) Find the P-value of the test statistic. (Round your answer to four decimal places.)
(e) Do you reject or fail to reject H0? Explain.
At the α = 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 p̂ value based on 50 trials is not sufficiently different from 0.50 to justify rejecting H0 for α = 0.05.