Question

Last year, 52% of business owners gave a holiday gift to their employees. A survey of business owners indicated that 40% plan to provide a holiday gift to their employees. Suppose the survey results are based on a sample of 60 business owners. How many business owners in the survey plan to provide a holiday gift to their employees? Suppose the business owners in the sample do as they plan. Which of the following represents the hypothesis that can be used to determine if the proportion of business owners providing holiday gifts has decreased from last year.

a. H 0 : p = 0 : 40 H a : p $\neq$ 0 : 40

b. H 0 : p 0 : 40 H a : p> 0 : 40

c. H 0 : p 0 : 52 H a : p> 0 : 52

d. H 0 : p 0 : 52 H a : p< 0 : 52 15.

What is the p-value for the correct hypothesis test above (Recall that P (z < z0)is the cumulative probability of the normal distribution when the zvalue is z0 or simply NORM.S.DIST (z0, TRUE))

Answer 1

No of business owners in the survey plan to provide a holiday gift to their employees = 60*0.40 = 24

Option D hypothesis are correct

No of business owners in the survey plan to provide a holiday gift to their employees = 60*0.40 = 24 Option D hypothesis are correct H_0: P greaterthanorequalto 0.52 H_a: p < 0.52 z = (0.40 - 0.52/squareroot 0.52 - 0.48/60) z = -1.86 P value = P(z < -1.86) use excel function NORMSDIST(-1.86) = 0.0314

$z=(\frac{0.40-0.52}{\sqrt{\frac{0.52*0.48}{60}}})$

z = -1.86

P value = P(z<-1.86)

use excel function

NORMSDIST(-1.86)

= 0.0314