Question

Last year, 48% 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 negative value if your answer is negative.

Ho: p ≥ .48
Ha:p < .48

z-value- ______________
p-value-______________

c. Using a .02 level of significance, what is the highest level of significance for which you could draw such a conclusion? (to 4 decimals)

Answer 1

a. How many business owners in the survey planned to provide a holiday gift to their employees this year?

p^=x/n

x=p^*n=0.30*50=15

ANSWER:15

Solutionb:

Ho: p ≥ .48
Ha:p < .48

z=p^-p/sqrt(p^(1-p^)/n

z=0.30-0.48/sqrt(0.48*(1-0.48)/50)

z=-2.55

p value can be found in R using norm

p=pnorm(-2.55,mean=0,sd=1)=0.005386146

p=0.0054

c. Using a .02 level of significance, what is the highest level of significance for which you could draw such a conclusion

alpha=0.02