Question

A public bus company official claims that the mean waiting time for bus number 14 during peak hours is less than 10 minutes. Karen took bus 14 during peak hours on 18 different occasions. Her mean waiting time was 7.4 minutes. Assume that the standard deviation has been historically known to be 2.2 minutes. At the .05 significance level, test the claim that the mean waiting time is less than 10 minutes.

1. State the null hypothesis H0: _____________

2. State the alternative hypothesis H1: _____________

3. What is the test statistic used for the test (z or t)

4. State the significance or alpha (?) level

5. Determine the p-value.

6. Do you or do you not reject the null hypothesis? Why?

7. Write a clear conclusion using a complete sentence.

Answer 1

X?= 7.4

n= 18

sigma= 2.2 ..............( as it told standard deviation is historically known so we can consider population standard deviation)

in this question sample size is less but population standard deviation is give so we should use z test.

1)

H0: u= 10

2)

H1: u< 10 left tail test

3)

Z-Test Statistics

$Z=(\overline{x})-u)*sqrt(n)/\sigma$

$=(7.4-10)*sqrt(18)/2.2$

=-5.0140

4) alpha level =0.05

5)

P-value=1-P(Z<-5.0140)= 2.66508E-07

rounded p-value=0.0000

6) Decision making

P-value < Alpha .......Reject H0

0.0000 <0.05

7)

There is enough evidence to claim that mean waiting time for bus number 14 is less than 10 minutes .

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