Question

Last year,40% of business owners gave a holiday gift to their employees. A survey of business owners conducted this year indicates that 30% planned to provide a holiday gift to their employees. Suppose the survey results are based on a sample of 50 business owners.

a. How many business owners in the survey planned to provide a holiday gift to their employees this year? Round your answer to the nearest whole number.

b. Suppose the business owners in the sample did as they planned. Compute the -value for a hypothesis test that can be used to determine if the proportion of business owners providing holiday gifts had decreased from last year. Enter a negative value if your answer is negative.

H0- Select your answer ( <, >, <=. >=, =, not equalto) .40

Ha - Select your answer - ( <, >, <=. >=, =, not equal to) .40

z-value (to 2 decimals)

p-value (to 4 decimals)

c. Using a level of significance, would you conclude that the proportion of business owners providing gifts decreased? - Select your answer - Reject, Do not Reject

d. What is the smallest level of significance for which you could draw such a conclusion? (to 4 decimals)

Answer 1

population proportion (p) = 0.4 sample size (n) = 50 Let x = number of owners in the survey planned to provied holiday gift to thier employees sample proportion (p^) (x/n) = x/50 = 0.30 ==> = 15 a) 15 business owners in the survey planned to provied holiday gift to thier employees х Now, E(p^) = p = 0.4 SE(P^) = sqrt((p*(1-p))/n) = sqrt(( 0.4 * (1 - 0.4)) / 50.0 ) =0.0693 b) The null and alternative hypothesis: Ho :p = 0.40 H1 :p < 0.40 Test statistc: (p^-E(p^)) (0.3-0.4) z = (------------) = (--- -----) = -1.443 S.E(p^) 0.0693 z-value = -1.44 p-value = P(Z < -1.443 ) = 0.0745 c) Reject Ho, at a = 0.08 or (> 0.08) d) At a = 0.08 level of significance, we can draw the conclusion that prportion of business owners provides gifts decreased