Chicken Delight claims that 91 of its orders are delivered w

Chicken Delight claims that 91% of its orders are delivered within 10 minutes of the time the order is placed. A sample of 90 orders revealed that 81 were delivered within the promised time. At the 0.10 significance level, can we conclude that less than 91% of the orders are delivered in less than 10 minutes?

What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round the intermediate values and final answer to 2 decimal places.)

Solution

a)

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   >=   0.91
Ha:   p   <   0.91
As we see, the hypothesized po =   0.91

As this is left tailed at 0.10 level, then we reject Ho if

z < -1.28 [ANSWER]

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b)
      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.9      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.030166206      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -0.331496772   [ANSWER]

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c)

As z > -1.28, we CANNOT REJECT HO: p >= 0.91. [ANSWER]