Dominos Pizza for years made a claim that they would deliver your pizza within 30 minutes (“30 minutes or less”) of your order being placed

Question

Dominos Pizza for years made a claim that they would deliver your pizza within 30 minutes (“30 minutes or less”) of your order being placed (provided you live within a certain radius of their restaurant). A group of college students make the ultimate sacrifice and order Dominos from the same location for 20 straight days for the good of statistics. They find a mean of 23.7 minutes and a standard deviation of 2.15.
A) In constructing a 95% confidence interval for mean wait time for Dominos Pizza delivery using the data collected by the students, would your critical value be a z* or a t*? Explain your answer.
B) Staying consistent with your answer to part A, construct a 95% confidence interval for mean wait time of Dominos Pizza delivery.
C) Do you think this confidence interval is accurate for Dominos Pizza in general? Why or why not?

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2 weeks 2021-09-13T08:56:13+00:00 1 Answer 0

Answers ( )

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    2021-09-13T08:57:53+00:00

    Answer:

    a. t*

    b. (22.87, 24.53)

    c. yes

    Step-by-step explanation:

    We have the following data:

    mean = m = 23.7

    standard deviation = sd = 2.15

    x = 20

    Thus:

    a. The critical value would be t * since the value is m <30

    b. whenever the mean is less than 30, the t distribution is used, for 95% confidence interval with degree of freedom = (x – 1) df

     = 20 – 1

     = 19

    now, for this value we look in the table of t, we find that t * = 1.729

    m + – t * (sd / x ^ 81/2))

    replacing

    23.7 + – 1.729 * (2.15 / 20 ^ (1/2))

    23.7 + – 0.8312

    then the inverval would be:

    23.7 + 0.8312 = 24.5312

    23.7 – 0.8312 = 22.8688

    (22.87, 24.53)

    c. yes, the interval is accurate since the mean of 23.7 is within this value

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