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 p̂ distribution? Explain. Yes, np and nq are both greater than 5.No, nq is greater than 5, but np is less than 5. No, np and nq are both less than 5.Yes, np and nq are both less than 5.No, np is greater than 5, but nq is less than 5. (b) State the hypotheses. H0: p = 0.5; H1: p < 0.5H0: p = 0.5; H1: p > 0.5 H0: p < 0.5; H1: p = 0.5H0: p = 0.5; H1: p ≠ 0.5 (c) Compute p̂.Compute the corresponding standardized sample test statistic. (Round your answer to two decimal places.)(d) Find the P-value of the test statistic. (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 p̂ value based on 50 trials is sufficiently different from 0.50 to justify rejecting H0 for α = 0.05.The sample p̂ value based on 50 trials is sufficiently different from 0.50 to not reject H0 for α = 0.05. The sample p̂ value based on 50 trials is not sufficiently different from 0.50 to justify rejecting H0 for α = 0.05.The sample p̂ value based on 50 trials is not sufficiently different from 0.50 to not reject H0 for α = 0.05.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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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 p̂ distribution? Explain.

Yes, np and nq are both greater than 5.No, nq is greater than 5, but np is less than 5. No, np and nq are both less than 5.Yes, np and nq are both less than 5.No, np is greater than 5, but nq is less than 5.

(b) State the hypotheses.

H₀: p = 0.5; H₁: p < 0.5H₀: p = 0.5; H₁: p > 0.5 H₀: p < 0.5; H₁: p = 0.5H₀: p = 0.5; H₁: p ≠ 0.5

(c) Compute p̂.

Compute the corresponding standardized sample test statistic. (Round your answer to two decimal places.)

(d) Find the P-value of the test statistic. (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 p̂ value based on 50 trials is sufficiently different from 0.50 to justify rejecting H₀ for α = 0.05.The sample p̂ value based on 50 trials is sufficiently different from 0.50 to not reject H₀ for α = 0.05. The sample p̂ value based on 50 trials is not sufficiently different from 0.50 to justify rejecting H₀ for α = 0.05.The sample p̂ value based on 50 trials is not sufficiently different from 0.50 to not reject H₀ for α = 0.05.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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