Question

A fast-food franchiser is considering building a restaurant at a certain location. Based on financial analyses, a site is acceptable only if the number of pedestrians passing the location averages more than 100 per hour. The number of pedestrians observed for each of 40 hours was recorded. Assuming that the population standard deviation is known to be 16, Estimate with 95% confidence the mean number of pedestrians passing the location. Can we conclude at the 5% significance level that the site is acceptable? Determine the probability of a Type II error when the mean is actually 101.

data Pedestrians 97 101 97 106 116 113 100 96 102 106 99 114 96 100 119 111 88 114 93 87 117 128 126 114 114 97 113 113 110 104 97 109 108 83 95 103 91 116 112 123

Answer 1

solution:

given

n=40

standard deviation=16

μ=100

mean=( Σ x_i ) / n

    =97+101+97+106+116+113+100+96+102+106+99+114+96+100+119+111+88+114+93+87+117+128+126+114+114+97+113+113+110+104+97+109+108+83+95+103+91+116+112+113/40

=4228/40

=105.7

test statistic

z=x-miu/s/sqr(n)

=105.7-100/16/sqr(40)

=2.25

for alpha 0.01 z alpha=2.326

test statistic value is less than critical value so we fail to reject null hypothesis

we conclude that site not acceptale