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Hypothesis testing

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Most traffic lights are set so that there is enough time for pedestrians to cross the road safely. A recent study indicates that a large number of elderly cannot get across the road in the usual 15 seconds allowed. To determine the average amount of time it takes senior citizens to cross the street, a study was taken of 25 seniors. On the average, it took them 19.5 seconds to cross the street, with a sample standard deviation of five seconds. Assume the time to cross the road has a normal distribution.

a). Set up the null and alternative hypotheses to see if the data show that it does indeed take seniors longer than 15 seconds to cross the street.

b). In terms of traffic flow, what are the implications of a Type I error?

c). What are the implications of a Type II error?

d). Find the value of the test statistic.

e). If alpha = 0.05, what is the rejection region?

f). What is your recommendation to the city?

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Solution Summary

The solution answers the question(s) below.

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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