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Quick Statistics Question?

I have the following question for my statistics homework:

The Lincoln Tunnel connects New Jersey to midtown Manhattan. On Mondays at 8:30 A.M. the mean number of cars is 1,220. Because of substantial wait time for cars waiting in line to pay, the Port Authority of New York and New Jersey is considering raising the toll between 7:30 A.M. and 8:30 A.M. ton encourage drivers to use the tunnel at different times. Suppose the Port Authority experiments with peak-hour pricing for 6 months, increasing the toll from $4 to $7 during rush hour. On 10 different workdays at 8:30 am aerial photos of the tunnel queues are taken and the number of vehicles are counted: 1,260 1,052 1,201 942 1,062 999 931 849 867 735. Analyze the data for the purpose of determining whether peak-hour pricing succeeded in reducing the average number of vehicles attempting to use the Lincoln Tunnel during the peak rush hour.

I have a program to analyze data but I'm trying to figure out if the way to answer this problem would be to use a Null and Alternative hypothesis such as:

Ho=1,220

Ha<>1,220

Would this be the correct way to set up this problem?

Update:

I performed a One-Sample T-Test and set the null hypothesis to less than 1220 and received a p-value of .0007 at a 95% CI so I think I've done it right and that I can now answer the question that changing the price did affect traffic at the time. Confirmation?

1 Answer

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  • 8 years ago
    Favorite Answer

    Ryan

    One correction to your Ha: mean < 1220 because the problem states ...

    "determining whether peak-hour pricing succeeded in REDUCING the average number of vehicles"

    Reducing means "less than" for your hypothesis

    For the T-test ...

    mean = 989.8000

    std. dev. = 160.6755

    t-statistic = (989.8000 - 1220) / (160.6755/ sqrt 10) = -4.53

    P-value = P(t < -4.53) = 0.0007 [one-sided test, otherwise you would have multiplied by 2]

    Since P-value is < 0.05, REJECT the null hypothesis. There is significant evidence that the mean traffic is LESS THAN 1220

    Hope that helps

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