Question

Shipping time. An internet company claims that 90% of its orders are shipped within two days.  Suppose that last month they received 4000 orders.  A consumer group questioning the claim took a random sample of 200 orders and found that 168 were shipped within 2 days.  Is this strong enough evidence to conclude that less than 90% of all orders received were shipped within two days?  Use a significance level of 5%. Then, qualify your findings to a range of percentages.

A)  Identify problem type:  mean or proportion?  one population or two?

Confidence Interval or Hypothesis Test? (most will ask for both to be performed)

      B)  Write a sentence or delineate the defining parameters and statistics. (include its symbol; n = numbers; population, sample, etc as you have done previously)

C)    Write the symbol for the sample estimate and the formula for the SE of the sample estimate.

D) Complete the necessary calculations to answer the question.

Answer 1

A)

proportion

one population

Hypothesis Test

B)

n = 200, N = 4000, x = 168

C)

Since

So it is not necessary to apply the finite population correction factor.

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C-D)

The sample estimate is

The standard error is

SE = 0.0212

Conclusion:  There is strong enough evidence to conclude that less than 90% of all orders received were shipped within two days.