A fast food franchiser is considering building a restaurant at a certain locatio

Question

A fast food franchiser is considering building a restaurant at a certain location. According to a financial analysis, a site is acceptable only if the number of pedestrians passing the location averages more than 100 per hour. A random sample of 50 hours produced x = 110 and s = 12 pedestrians per hour. a. Do these data provide sufficient evidence to establish that the site is acceptable? Use P-value with alpha = 0.05. b. What are the consequences of Type I and Type II errors? Which error is more expensive to make? c. Considering your answer in part (b), should you select alpha to be large or small? Explain. d. What assumptions about the number of pedestrians passing the location in an hour are necessary for your hypothesis test to be valid?

Explanation / Answer

Solution:

a) TestHypothesis:
H0: = 100
H1: >100
Test Statistics: z = x-/(/n)
Rejection Region: {Z : Z Z = Z0.05 = 1.645}
Z = (110-100)/(12/50) = 5.89
Reject H0 since the value of the test statistic 5.89, is greater than the critical value 1.645
There is sufficient evidence to conclude that the mean number of people per hour is more than 100.

b) Type I error is rejecting H0 when it is true and the result of this error is to construct the site when there are not enough pedestrians passing the location. (bankruptcy). Type II error is to accept H 0 when it is not true, so the site does not construct in location more than 100 pedestrians. (missing a good location). Type I error is more expensive. (It is possible type II error be more expensive. Accept if it supports with good explanation).

c) should be small. The smaller is the less likely it is for Type I error, i.e., rejecting H0 falsely, to happen.

d) We assumed that the mean number of pedestrians passing the location in an hour is normally distributed.

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