A random sample of 50 binomial trials resulted in 20 successes....

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 distribution? Explain.

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.

    

No, n·p and n·q are both less than 5.

No, n·q is greater than 5, but n·p is less than 5.

Yes, n·p and n·q are both greater 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) Compute . (Enter a number.)

p hat =

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 value based on 50 trials is 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 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 justify rejecting H₀ for α = 0.05.