A suburban realtor is studying commuter time in the Houston metropolitan area. S

Question

A suburban realtor is studying commuter time in the Houston metropolitan area. She has been told the average weekday travel time from a southern suburb at 8 a.m. is 45 minutes. For five months she counts the number of days that it takes her more than 45 minutes to arrive in downtown when she leaves her house at 8 a.m. She expects the data are uniformly distributed across the five months. Her sample of observed data yields the following frequencies: 9 days, 15 days, 8 days, 11 days, 12 days. Using = .10, the appropriate decision is _______.

do not reject the null hypothesis that the observed distribution is uniform

do not reject the null hypothesis that the observed distribution is not uniform

reject the null hypothesis that the observed distribution is uniform

reject the null hypothesis that the observed distribution is not uniform

do nothing

a)

do not reject the null hypothesis that the observed distribution is uniform

b)

do not reject the null hypothesis that the observed distribution is not uniform

c)

reject the null hypothesis that the observed distribution is uniform

d)

reject the null hypothesis that the observed distribution is not uniform

e)

do nothing

Explanation / Answer

Here the if the data is uniform distribution,

expected number of days it will take more than 45 minutes = (9 + 15 + 8 + 11 + 12)/5 = 11

Here observed expected table

X2 = 2.7273

Here dF = 5 - 1 = 4  

X2critical = 7.7794

SO here option a is correct as we do not reject the null hypothesis that the observed distribution is uniform.

Number Observed Expected (O - E)^2/E 1 9 11 0.3636 2 15 11 1.4545 3 8 11 0.8182 4 11 11 0 5 12 11 0.0909 Sum 55 55 2.7273

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