In 2013, 47% of business owners gave a holiday gift to their employees. A 2014 s

Question

In 2013, 47% of business owners gave a holiday gift to their employees. A 2014 survey of 33 business owners indicated that 31% plan to provide a holiday gift to their employees. Is there reason to believe the proportion of business owners providing gifts has decreased at ?=0.005? (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 valuels)? t stat Question 2 What is the test statistie? Question 3 What is the conclusion? T?SETC Click to Grade Your Work Daily Problem+ eady

Explanation / Answer

Ho: po = 47% v/s h1: po < 47%

N= 33
p-hat = X/n= 0.310
po= 47%

ALPHA= 0.50%

Critical value,-z(a)
z(0.005)
-2.5758

test statistics, Z = (phat-p)/sqrt(p*(1-p)/n)
=(0.31-0.47)/SQRT(0.47*(1-0.47)/33)
-1.8416

P-value
P(Z<z)
P(z<-1.841578)
=NORMSDIST(-1.841578)
0.0328

With z=-1.8416, p>0.005,I fail to reject the null hypothesis at 0.5% level of significance and conclude that po=47%

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