Question

1. The Missouri Highway Patrol claims that drivers are averaging 79 m/h on the Interstates. A statistics student wishes to prove the average is much higher. In order to study the issue, the student borrows her uncles radar gun and tests 25 drivers. She finds they have an average of 83 m/h with a standard deviation of 7.9 m/h. At the 0.05 level of significance, can the student prove her point that they are driving faster?

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Answer 1

Solution :

The null and alternative hypothesis is ,

= 83

= 79

= 7.9

n = 25

This will be a right-tailed test because the alternative hypothesis is showing a specific direction

This is the right-tailed test .

The null and alternative hypothesis is ,

H0 :   = 79

Ha : > 79

Test statistic = z

= ( - ) / / n

= (83 - 79) / 7.9 / 25

= 2.53

p(Z > ) = 1-P (Z < 2.53) = 1 - 0.9943 = 0.0057

P-value = 0.0057

= 0.05  

0.0057 < 0.05

P-value <

Reject the null hypothesis .