There are 41 NOs and 79 YESs The local government is conside

There are 41 NOs and 79 YESs

The local government is considering implementing a roads and public transport infrastructure upgrade project. Before they commit to this however, they would like to canvas public opinion to gauge community support for such a project. If it they are convinced that more than 60% of the community support the proposed upgrade project, then the government will commission the project The following sample was collected by asking a randomly selected group of 120 people whether or not they supported the proposed upgrade project Survey results: yes yes yes no yes yes yes yesyes yes yes yes no yes yes yes yes no no yes yes no yes yes | yes yes yes yes |yes no yes yes yes no yes yes yes yes |yes no yes yes no no yesno no yes yes no yes yes no yes yes yes yes no no yes no no no yes yes yes yes yes no yes no yes yes yes no yes no no no yes no yes no yes no no no yes no yes yes yes no yes no yes yes no no yes yes yes yes yes no yes yes noyes yes no no yes yesyesno no yes yes yes

Solution

a)

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.6
Ha:   p   >   0.6 [ANSWER, D]

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b)

As we see, the hypothesized po =   0.6      

Getting the point estimate of p, p^,          
          
p^ = x / n =    0.658333333      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.04472136      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    1.304372987   [ANSWER]

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c)  
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.09605322      

Therefore, at a significance level of 0.05, the null hypothesis is ACCEPTED.

That is, you can state that the is no significant evidence to conclude that the proportion of people who support the proposed upgrade project is greater than 0.6. [ANSWER]