A random sample of20binomial trials resulted in8successes. 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 thedistribution? Explain.

No,npis greater than 5, butnqis less than 5.

No,nqis greater than 5, butnpis less than 5.

No,npandnqare both less than 5.

Yes,npandnqare both less than 5.

Yes,npandnqare 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:p0.5

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 theP-value of the test statistic. (Enter a number. Round your answer to four decimal places.)

(e)Do you reject or fail to rejectH₀? Explain.

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 samplevalue based on 20 trials is not sufficiently different from 0.50 to not rejectH₀for= 0.05.

The samplevalue based on 20 trials is sufficiently different from 0.50 to justify rejectingH₀for= 0.05.

The samplevalue based on 20 trials is sufficiently different from 0.50 to not rejectH₀for= 0.05.

The samplevalue based on 20 trials is not sufficiently different from 0.50 to justify rejectingH₀for= 0.05.