Chicken Delight claims that 82% of its orders are delivered within 10 minutes of

Question

Chicken Delight claims that 82% of its orders are delivered within 10 minutes of the time the order is placed. A sample of 70 orders revealed that 50 were delivered within the promised time. At the 0.01 significance level, can we conclude that less than 82% 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.)

Chicken Delight claims that 82% of its orders are delivered within 10 minutes of the time the order is placed. A sample of 70 orders revealed that 50 were delivered within the promised time. At the 0.01 significance level, can we conclude that less than 82% of the orders are delivered in less than 10 minutes?

Explanation / Answer

(a) Null hypothesis, H0 : p >= 0.82

alternate hypothesis, H1 : p < 0.82

significance level = 0.01

Since it is a one sided test critical value of z at 0.01 significance level is -2.33 (left talied)

so reject H0 if z< -2.33

(b) sample proportion : p' = 50/70 and n = 70

z statistic : (p' - p)/(p(1-p)/n)0.5

= (50/70 - 0.82)/((0.82*0.18)/70)0.5

z statistic : -2.30

(c) z statistic < z critical value

We do not have sufficient evidence to reject the null hypothesis (cannot reject)

hence we can conclude that p>=0.82

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