A random sample of 20 binomial trials resulted in 8 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.

Yes, np and nq are both less than 5.

No, np is greater than 5, but nq is less than 5.

No, nq is greater than 5, but np is less than 5.

Yes, np and nq are both greater than 5.

No, np and nq 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)

Compute . (Enter a number.)

p hat =

Compute the corresponding standardized sample test statistic. (Enter a #. Round up to two decimal places.)

(d)

Find the P-value of the test statistic. (Enter a #. Roundup to four decimal places.)

(e)

Do you reject or fail to reject H₀?

At the = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

At the = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

At the = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the = 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 20 trials is sufficiently different from 0.50 to not reject H₀ for = 0.05.

The sample value based on 20 trials is not sufficiently different from 0.50 to justify rejecting H₀ for = 0.05.

The sample value based on 20 trials is not sufficiently different from 0.50 to not reject H₀ for = 0.05.

The sample value based on 20 trials is sufficiently different from 0.50 to justify rejecting H₀ for = 0.05.