Question

Last year, 49% of business owners gave a holiday gift to their employees. A survey of business owners conducted this year indicates that 35% planned to provide a holiday gift to their employees. Suppose the survey results are based on a sample of 55 business owners. find the z val, p val, and the highest level of significance for which you could draw such a conclusion

Answer 1

here sample size = n = 55

H₀ : = 0.49

H_a : 0.49

standard proportion = p₀ = 0.49

standard error of sample proportion = sqrt[p₀ * (1- p₀)/n] = sqrt [0.49 * (1-0.49)/55]= 0.0674

sample proportion = p = 0.35

Test statistic

Z = (p - p₀)/se_p = (0.35 - 0.49)/0.0674 = -2.077

p - value = 2 * Pr(Z < -2.077) = 2 * 0.0189 = 0.0378

here asp- value is less than 0.05 but greater than 0.01 so highest level of significance is 0.05 for which we draw a conclusion that the data is statistically significant here.