A catalog company promises to deliver online orders within 3 days of the order being placed. Follow-up calls were made to randomly selected customers to see whether their orders arrived on time (within 3 days). A 95% confidence interval for percentage of on-time arrival is 88% + / - 6%. What does this mean? Are these conclusions correct? Explain.

a) 95% of all random samples of customers will show that 88% of orders arrive on time.

b) 95% of all random samples of customers will show that 82% to 94% of orders arrive on time.

c) we are 95% sure that between 82% and 94% of the orders placed by the sampled customers arrived on time.

d) on 95% of the days, between 82% and 94% of the orders will arrive on time.

Question

Conner Duncan

Mathematics

8 June, 07:03

A catalog company promises to deliver online orders within 3 days of the order being placed. Follow-up calls were made to randomly selected customers to see whether their orders arrived on time (within 3 days). A 95% confidence interval for percentage of on-time arrival is 88% + / - 6%. What does this mean? Are these conclusions correct? Explain.

a) 95% of all random samples of customers will show that 88% of orders arrive on time.

b) 95% of all random samples of customers will show that 82% to 94% of orders arrive on time.

c) we are 95% sure that between 82% and 94% of the orders placed by the sampled customers arrived on time.

d) on 95% of the days, between 82% and 94% of the orders will arrive on time.

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Answers (1)

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Emeline · Answer 1

c) 95% of all random samples of customers will show that 82% to 94% oders arrive on time

Step-by-step explanation:

From problem statement we take 88 as a mean of a normal distribution, in that case we know, about relation between mean and standard deviation

μ ± σ ⇒ [ μ - σ; μ + σ ] ⇒ [ 88 - 6; 88 + 6 ] ⇒ [ 82; 94 ]

The above mentioned interval get 95.7 % of all values for a normal distribution, so we must be sure that a 95 % of all random samples of customers will show that 82% to 94% of orders arrive on time