Answered

Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Join our platform to connect with experts ready to provide precise answers to your questions in various areas. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

A publisher reports that 55% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 280 found that 51% of the readers owned a laptop. Make the decision to reject or fail to reject the null hypothesis at the 0.05 level.

Sagot :

Answer:

We fail to reject the null hypothesis, we accept H₀

Step-by-step explanation:

Population proportion        p₀   =  55 %    p₀   =  0,55

Sample  size         n  =  280

Sample mean     p =  51 %            p =  0,51       q = 0,49

n*p   and  n*q   are both bigger than 10 therefore we can approximate the binomial distribution to a normal distribution

Test  Hypothesis

Null Hypothesis                             H₀                   p   =  p₀

Alternative Hypothesis                Hₐ                    p   ≠  p₀

Significance level is  α  = 0,05    but we have a two-tail test then

α/2  =  0,025

z(c)  =  - 1,96

Computing  z(s)

z(s)  =  ( p - p₀ ) / √(p*q)/n

z(s)  =  ( 0,51 - 0,55 ) / √(0,51*0,49)/280

z(s)  =  - 0,04 * 16,73 / 0,5

z(s)  =  -  1,34

Comparing

z(s)   and z(c)

- 1,34    <    - 1,96

| z(s) | < | z(c)|

Then z(s) is in the acceptance region,  we accept H₀

We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.