Question

Last year, 46% 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.

(a)	How many business owners in the survey plan to provide a holiday gift to their employees?
(b)	Suppose the business owners in the sample do as they plan. Compute the p value for a hypothesis test that can be used to determine if the proportion of business owners providing holiday gifts has decreased from last year. If required, round your answer to four decimal places. If your answer is zero, enter “0”. Do not round your intermediate calculations.
(c)	Using a 0.05 level of significance, would you conclude that the proportion of business owners providing gifts has decreased?
	We - Select your answer -rejectfail to rejectItem 3 the null hypothesis. We - Select your answer -cancannotItem 4 conclude that the proportion of business owners providing gifts has decreased from 2008 to 2009.
	What is the smallest level of significance for which you could draw such a conclusion? If required, round your answer to four decimal places. If your answer is zero, enter “0”. Do not round your intermediate calculations.
	The smallest level of significance for which we could draw this conclusion is  ; because p-value - Select your answer -less than or equal togreater thanItem 6 α=0.05, we - Select your answer -rejectfail to rejectItem 7 the null hypothesis.

Answer 1

Given that,
possible chances (x)=24
sample size(n)=60
success rate ( p )= x/n = 0.4
success probability,( po )=0.46
failure probability,( qo) = 0.54
null, Ho:p=0.46
alternate, H1: p<0.46
level of significance, α = 0.05
from standard normal table,left tailed z α/2 =1.64
since our test is left-tailed
reject Ho, if zo < -1.64
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.4-0.46/(sqrt(0.2484)/60)
zo =-0.9325
| zo | =0.9325
critical value
the value of |z α| at los 0.05% is 1.64
we got |zo| =0.933 & | z α | =1.64
make decision
hence value of |zo | < | z α | and here we do not reject Ho
p-value: left tail - Ha : ( p < -0.9325 ) = 0.17554
hence value of p0.05 < 0.17554,here we do not reject Ho
ANSWERS
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a.
possible chances (x)=24
24 business owners in the survey plan to provide a holiday gift to their employees
sample size(n)=60
success rate ( p )= x/n = 0.4
null, Ho:p=0.46
alternate, H1: p<0.46
test statistic: -0.9325
critical value: -1.64
decision: do not reject Ho
b.

p-value: 0.17554
c.
we do not have enough evidence to support the claim that the proportion of business owners providing gifts has decreased