A city council is deciding whether or not to spend additional money to reduce th

Question

A city council is deciding whether or not to spend additional money to reduce the amount of traffic. The council decides that it will increase the transportation budget if the amount of waiting time for drivers exceeds 30 minutes. A sample of 32 main roads results in a mean waiting time of 31.76 minutes with a standard deviation of 6.31 minutes. Use Table 2. a. Select the relevant null and the alternative hypotheses. H0: 30; HA: < 30 H0: = 30; HA: 30 H0: 30; HA: > 30 b. Compute the value of the appropriate test statistic. (Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.) Test statistic c-1. Calculate the critical value at a 5% level of significance. (Round your answer to 3 decimal places.) Critical value c-2. Determine whether or not the city should increase its transportation budget. Reject H0; the city should increase its transportation budget Do not reject H0; the city should increase its transportation budget Reject H0; the city should not increase its transportation budget Do not reject H0; the city should not increase its transportation budget

Explanation / Answer

The statistical software output for this problem is:

One sample T hypothesis test:
: Mean of population
H0 : < 30
HA : > 30

Hypothesis test results:

Hence,

a) Null and alternative hypotheses:

H0: 30; HA: > 30

Option 3 is correct.

b) Test statistic = 1.58 [T - Stat value in the output]

c - 1: Degrees of freedom = n - 1 = 32 - 1 = 31

So for a right tailed test with 31 degrees of freedom and 0.05 level of signifcance,

Critical value = 1.696

c - 2: Since test statistical do not fall in the rejection region,

Do not reject H0; the city should not increase its transportation budget.

Optiion 4 is correct.

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