Question

A police Captain claims a Public Safety Film will reduce the number of speeding tickets at seven locations on the highway. The number of tickets at these locations before and after the film are as follows: Location1.234567 Before Film 21. 33 31 30 34 30 24 After Film 17 28 32 28 34 29 17 Difference45-1 20L7 The mean of these Differences is Z = 2.57,with st dev sd : 2.88 a) I4trhat is the parameter we test? b) what are the NuIl and Alternative Hypotheses? c) Using a = .05 find the Rejection Region and Test Stat. d) State the conclusion of your test.

Answer 1

a) Here we use dependent sample t-test and this is a statistical procedure used to test whether the mean difference between the two sets of observations is zero. The parameter we test in a dependent sample t-test is the mean difference.

b) The null and alternative hypothesis are given by,

H₀: There is no significant reduction in the number of speeding tickets before and after the public safety film.

H₁: There is a significant reduction in the number of speeding tickets before and after the public safety film.

c) The test statistic is given by,

Given

From t-table with and n-1=6 degrees of freedom, the critical value is given by,

Test statistic=2.36

Critical value=1.943

d) We reject H₀ if  

Here, 2.36<1.943. That is,

Hence we fail to reject H₀.

the conclusion is,

There is no significant reduction in the number of speeding tickets before and after the public safety film.

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