For an exercise is received speed measurements on two road points. The cars drove along an urban road (30mph) that opened into a rural road (60mph). The speed measurement of each car is taken 200 meters before (speed1) the end of the urban area and a second measurement 600 meters past (speed2) the end of the urban area.

I want to check the data if the cars that violate the speed on the urban road (30 mph) also tend to violate the speed on the rural road (60mph).

The speed1 is truly normally distributed, however speed 2 does not show a nice bell shaped histogram, but skewness and kurtosis are within limits. I recoded the data to test my question. So I'm not sure if I'm allowed to still do a One Sample T-Test:

First I copied only the speed1 violaters (>30mph) into a new variable.

Next I copied all the speed 2 values of the cars that violated speed1 into a new variable (speed 2 violated).

To prove that the cars who violated speed1 also tend to violate speed2 I was thinking of doing a One Sample T test over 'speed 2 violated' with 60mph as test value.

The One Sample T-test results show a significant difference to the test value (60mph):

t= 10.806

df=14

p<.001 (2-tailed)

Mean Diff=11.8

Is this a valid analysis to prove speed1 violators (30mph) also tend to violate speed 2 (60mph)?

Edit: In class we didn't discuss the One Sample Wilcoxon Signed Rank test, so I'm not allowed to use it. However this test also rejected significantly the Null Hypothesis, thus Speed2Over is significantly violated.

I want to check the data if the cars that violate the speed on the urban road (30 mph) also tend to violate the speed on the rural road (60mph).

The speed1 is truly normally distributed, however speed 2 does not show a nice bell shaped histogram, but skewness and kurtosis are within limits. I recoded the data to test my question. So I'm not sure if I'm allowed to still do a One Sample T-Test:

First I copied only the speed1 violaters (>30mph) into a new variable.

Next I copied all the speed 2 values of the cars that violated speed1 into a new variable (speed 2 violated).

To prove that the cars who violated speed1 also tend to violate speed2 I was thinking of doing a One Sample T test over 'speed 2 violated' with 60mph as test value.

The One Sample T-test results show a significant difference to the test value (60mph):

t= 10.806

df=14

p<.001 (2-tailed)

Mean Diff=11.8

Is this a valid analysis to prove speed1 violators (30mph) also tend to violate speed 2 (60mph)?

Edit: In class we didn't discuss the One Sample Wilcoxon Signed Rank test, so I'm not allowed to use it. However this test also rejected significantly the Null Hypothesis, thus Speed2Over is significantly violated.

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