Question

Reserve Problems Chapter 10 Section 1 Problem 3 The time delay is measured for a city street. Variability in this value is estimated as o = 0.3 (for time in minutes) by experience. Traffic signs and lights were recently altered to facilitate traffic and reduce delays. Delay times in minutes for a random car sample before and after the rearrangement are shown below. Before 7.4 7.1 7.1 7.4 7.4 7.0 6.9 6.5 7.3 7.2 7.4 7.2 After 6.3 6.7 6.2 6.5 6.7 5.8 5.9 5.8 6.3 6.0 7.1 7.0 Assume that the time delay variability is unaffected by the traffic signs change. If the difference in the time delay is 1 minute or less, we would like to detect it. (a) Formulate and test an appropriate hypothesis using a = 0.1. What is your conclusions? Find the P-value. 1) The parameter of interest is the difference in the mean time delay before and after the rearrangement, H1 - H2. 2) Ho : 41 - 12 = 3) H1 : 41-42 < Find the test statistic. Round your answers to three decimal places (e.g. 98.765). ZO P-value = (b) Find a 90% confidence interval for the difference in the mean time delay. Round your answers to three decimal places (e.g. 98.765). We are 90% confident that the difference in the mean time delay lies between <Mi - M2

Answer 1

First we need to find the mean of both samples. Using excel, mean of both samples are:

Descriptive statistics count mean sample standard deviation sample variance minimum maximum range Before, X1 After, X2 12 12 7.158 6.358 0.268 0.448 0.072 0.201 6.5 5.8 7.4 7.1 0.9 1.3

2)

$H_{0}:\mu_{1}-\mu_{2}=1$

3)

$H_{a}:\mu_{1}-\mu_{2}<1$

Here we have x =7.158,01=0.3, n =12 X2 =6.358,0 =0.3, n2 =12

ZE Test Statistics: (5 - )-(41 – 12). ((7.158-6.358)-1)/(sqrt((0.09/12)+(0.09/12))) o, o + = -1.633 n n2

P-value: P-value=0.0512 Decision: Since p-value is less than level of significance so we reject the null hypothesis. Excel function for critical value: Excel function for p-value: =NORMSINV(0.1) =NORMSDIST(-1.633)

Answers:

test statistics = -1.633

p-value = 0.051

(b)

Level of significance: Confidence level: a=0.1 CL =0.9 Critical value: 26 =1.645 The standard error is: SE = + =sqrt((0.09/12)+(0.09/12)) n n2 = 0.1225 Margon of error: ME = t . SE =0.202 Confidence interval is: (11-12) ME =(7.158-6.358) + 0.202 =(0.598, 1.002) Excel function for critical value: ENORMSINV(1-(0.1/2)) Hence, the required confidence interval is (0.598,1.002).

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