In 2013,56% of business owners gave a holiday gift to their employees. A 2014 su

Question

In 2013,56% of business owners gave a holiday gift to their employees. A 2014 survey of 33 busines owners indicated that 38% plan to provide a holiday gift to their employees. Is there reason to believe the proportion of business owners providing gifts has decreased at a-0.0257 (See exercise 40 on page 418 of your textbook for a similar problem.) or the hypothesis stated above... Question 1 What is/are the critical value(s) Question 2 What is the test statistic? Question 3 What is the conclusion? [ ]

Explanation / Answer

Ho: po = 56% v/s h1: po < 56%

N= 33
p-hat = X/n= 0.380
po= 56%

ALPHA= 2.50%
critical value,-z(a)
z(0.025)
-1.96

Test statistic, Z = (phat-p)/sqrt(p*(1-p)/n)
=(0.38-0.56)/SQRT(0.56*(1-0.56)/33)
-2.08310

P-value
P(Z<z)
P(z<-2.083095)
=NORMSDIST(-2.083095)
0.018621283

With z=-2.08, p<0.025,I reject the null hypothesis at 2.5% level of significance and conclude that po<56%

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