Listed in the accompanying table are waiting times (seconds) of observed cars at a Delaware inspection station. The data from two waiting lines are real observations, and the data from the single waiting line are modeled from those real observations. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b). a. Use a 0.01 significance level to test the claim that cars in two queues have a mean waiting time equal to that of cars in a single queue. Let population 1 correspond to the single waiting line and let population 2 correspond to two waiting lines. What are the null and alternative hypotheses? A. H0: μ1≠μ2 H1: μ1=μ2 B. H0: μ1=μ2 H1: μ1>μ2 C. H0: μ1<μ2 H1: μ1=μ2 D. H0: μ1=μ2 H1: μ1≠μ2 Calculate the test statistic. t=___ (Round to two decimal places as needed.) Find the P-value. P-value=_ (Round to three decimal places as needed.) Make a conclusion about the null hypothesis and a final conclusion that addresses the original claim. Use a significance level of 0.01. ▼ Fail to reject Reject H0 because the P-value is ▼ greater than less than or equal to the significance level. There ▼ is is not sufficient evidence to warrant ▼ support for rejection of the claim that cars in two queues have a mean waiting time equal to that of cars in a single queue. b. Construct the confidence interval suitable for testing the claim in part (a). _ <μ1−μ2< ___ (Round to one decimal place as needed.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Listed in the accompanying table are waiting times (seconds) of observed cars at a Delaware inspection station. The data from two waiting lines are real observations, and the data from the single waiting line are modeled from those real observations. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b).

a. Use a 0.01 significance level to test the claim that cars in two queues have a mean waiting time equal to that of cars in a single queue.

Let population 1 correspond to the single waiting line and let population 2 correspond to two waiting lines. What are the null and alternative hypotheses?

H0:

μ1≠μ2

H1:

μ1=μ2

H0:

μ1=μ2

H1:

μ1>μ2

H0:

μ1<μ2

H1:

μ1=μ2

H0:

μ1=μ2

H1:

μ1≠μ2

Calculate the test statistic.

t=_____

(Round to two decimal places as needed.)

Find the P-value.

P-value=_____

(Round to three decimal places as needed.)

Make a conclusion about the null hypothesis and a final conclusion that addresses the original claim. Use a significance level of

0.01.

▼

Fail to reject

Reject

because the P-value is

▼

greater than

less than or equal to

the significance level. There

▼

is not

sufficient evidence to warrant

▼

support for

rejection of

the claim that cars in two queues have a mean waiting time equal to that of cars in a single queue.

b. Construct the confidence interval suitable for testing the claim in part (a).

_____ <μ1−μ2< _____

(Round to one decimal place as needed.)

Waiting times
One Line
Two Lines
64.2
733.9
63.8
865.2
157.1
606.2
215.8
1089.8
142.1
268.1
86.2
662.6
278.8
309.6
339.9
518.4
252.5
129.3
200.1
565.6
476.4
133.2
629.8
267.5
478.2
122.2
332.7
349.9
474.2
128.7
328.6
94.7
402.3
233.1
915.3
99.8
721.9
460.8
552.8
163.1
760.6
481.8
597.2
100.9
691.7
517.5
836.9
508.6
903.1
580.3

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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