Question 3 1B pf: To determine whether a driver\'s education course improves the

Question

Question 3 1B pf: To determine whether a driver's education course improves the scores on a driving exam, a sample of 6 students were given the exam before and after taking the course. The results are shown below Score Score Student Before the Course After the Course 87 83 89 93 2 91 4 93 83 86 79 a) Does the course improve the score on the driving exam? Usea0.05 b) State and check the assumptions for the above test. c) Give a 95% confidence interval for the gain in exam score after taking the course

Explanation / Answer

a)

Null Hypothesis : H0: ?1 - ?2 >= 0

Alternate Hypothesis: Ha: ?1 - ?2 < 0

dbar = ?(before) - ?(after) = -2

s(dbar) = 3.5214

SE = s(dbar)/sqrt(n) = 1.4376

Test Statisitcs, t = dbar/SE = -1.3912

degrees of freedom = n-1 = 5

p-value = 0.1114

As p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis.

There are not significant evidence to conclude that exam improves the scores.

b)

Assumptions are

1. The difference of the test scores are normally distributed.

2. sample is randomly selected

c)

x1bar - x2bar = -2.00

SE = 1.4376

CI = 95%

DF = 5

t-value = 2.5706

ME = t*SE = 3.6954

Confidence Interval is (x1bar - x2bar) +/- ME

Lower bound = -5.69544

Upper bound = 1.69544

Confidence Interval is (-5.6954 , 1.6954 )

Before After dbar 83 87 -4 89 88 1 93 91 2 77 77 0 86 93 -7 79 83 -4 Mean -2

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