Question

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.

(e)

Do you reject or fail to reject H₀? Explain.

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.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  value based on 50 trials is sufficiently different from 0.50 to justify rejecting H₀ for α = 0.05.The sample  value based on 50 trials is not sufficiently different from 0.50 to not reject H₀ for α = 0.05.    The sample  value based on 50 trials is not sufficiently different from 0.50 to justify rejecting H₀ for α = 0.05.The sample  value based on 50 trials is sufficiently different from 0.50 to not reject H₀ for α = 0.05.

Answer 1

The statistical software output for this problem is:

From above output:

p - Value is greater than 0.05 so we fail to reject Ho. Hence,

e) At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

f) The sample  value based on 50 trials is not sufficiently different from 0.50 to justify rejecting H0 for α = 0.05.