Question

Prior to a special advertising campaign, 23% of all adults recognized a particular companyâs logo. At the close of the campaign the marketing department commissioned a survey in which 311 of 1,200 randomly selected adults recognized the logo. Determine, at the .01 level of significance, whether the data provide sufficient evidence to conclude that more than 23% of all adults now recognize the companyâs logo.

Answer 1

The answer is "2.4049"

Explanation:

Calculating the test of Hypothesis:
`H_(0): 23\% \ \text{off all adults which reconize the compony's logo}\\\\H_(1): \text{more than 23\% of adult recornise the compony's logo}\\\\`

that is

`H_(0): p=0.23\ against \ H_(1):p>0.01\\\\Z=\frac{P-p}{\sqrt{(p(1-p))/(n)}}\sim N(0,1)\\\\`

Given:

`p= 0.23\\\\ \therefore \\\\1-p=0.77\\\\n=1200\\\\ P=(311)/(1200)=0.2591\\\\\therefore\\\\Z= \frac{0.2591-0.23}{\sqrt{((0.23)* ((1-0.23)))/(1200)}}=2.4049`

Z=2.576 tabled value. Because Z is 2.4049, that's less than Z stated, there is no indication that a null hypothesis is rejectable, which means that 23% of all adults record the logo of the Company.