Question

Last year, 45% of business owners gave a holiday gift to their employees. A survey of business owners conducted this year indicates that 30% plan to provide a holiday gift to their employees. Suppose the survey results are based on a sample of 80 business owners.

(a) How many business owners in the survey plan to provide a holiday gift to their employees this year?
(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 the null hypothesis. We 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?

Answer 1

a)x₁ = 24 business owners plan to provide a gift this year

b) p-value = 0,0017

c)p-value < α we have to eject H₀ And support the claim that the proportion of business owners providing gifts has decrease

Explanation:

a) Sample size 80

proportion p₁ = 30 % p₁ = 0,3

Then x₁ = 80*0,3

x₁ = 24 business owners plan to provide a gift this year

b) Hypothesis Test

Null Hypothesis H₀ p₁ = 0,45

Alternative Hypothesis Hₐ p₁ < 0,45

p₁ = 0,3 then q₁ = 1 - 0,3 q₁ = 0,7

z(s) = ( p₁ - 0,45 )/ √p₁* q₁ / n

z(s) = - 0,15 / √0,002625

z(s) = - 0,15 / 0,05123

z(s) = - 2,9279

b)From z-table we find p-value = 0,0017

c) If α = 0,05 ( significance level ) as

p-value < α we have to eject H₀ And support the claim that the proportion of business owners providing gifts has decrease