A reputable wineproducing firm claims that 85 of its product

A reputable wine-producing firm claims that 85% of its products arc grade A. One of its distributors took a sample 45 products and subjected them to test. It was discovered that 30 met the grade A benchmark. At a=5%, what is the value of test statistic and is there a sufficient evidence to reject the firm\'s claim regarding the proportion of the grade A products -1.96, No 1.96, Yes -3.38,No -3.38, Yes

Solution

15.

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.85
Ha:   p   =/=   0.85
As we see, the hypothesized po =   0.85      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.666666667      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.053229065      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -3.38      
          
As alpha = 0.05, two tailed, zcrit = +/- 1.96.

Hence, as |z| > 1.96, we reject Ho.

hence,

OPTION D: -3.38, YES [ANSWER, D]