Reference no: EM132522922

A random sample of 30 binomial trials resulted in 12 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.

• No, n·p and n·q are both less than 5.
• Yes, n·p and n·q are both greater than 5.
• No, n·q is greater than 5, but n·p is less than 5.
• No, n·p is greater than 5, but n·q is less than 5.
• Yes, n·p and n·q are both less 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: p < 0.5
• H0: p = 0.5; H1: p ≠ 0.5

(c) Find (or estimate) the P-value. (Enter a number. Round your answer to four decimal places.)

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 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 ^p value based on 30 trials is not sufficiently different from 0.50 to justify rejecting H0 for α = 0.05.
• The sample ^p value based on 30 trials is not sufficiently different from 0.50 to not reject H0 for α = 0.05.
• The sample ^p value based on 30 trials is sufficiently different from 0.50 to not reject H0 for α = 0.05.
• The sample ^p value based on 30 trials is sufficiently different from 0.50 to justify rejecting H0 for α = 0.05.