1)Does a large proportion of all car drivers break speed limit (in the long run)

Question

1)Does a large proportion of all car drivers break speed limit (in the long run)?

2)What is the probability that a randomly chosen car has a speed between 60 and 70 km / h?

In one speed check we register the speed to n = 30 cars. The result gives an average peak summit Y=60 and an empirical standard deviation S = 8.4. On the basis of these information,

3)can we say that average road traffic has increased (and thus more than 56 km / h)? Set up a null hypothesis and test this with the significance level 0.05. What do you hypothesize?chose one and explain:

4)What do you conclude in Task 3?chose one and explain:

a)Accept Ho

b)Dismiss Ho

c)None of the parts, I do not have enough data to conclude.

5)What is the lowest level of significance you can choose from Table 1.5 and still reject the zero hypothesis you selected in task 3?

Table 1.5:

0.25

0.1

0.05

0.025

0.01

0.005

Explanation / Answer

Mu = 56
Sigma = 8
Spped limit , Xbar = 60

1. P(X>60) = P(Z> 60-56/8) = P(Z>.5) = .3085

2. P(60<X<70) = P(.5<Z<1.75) = .9599-.5 = .4599

3. B is correct hypothesis set.

4. P(X>56) = P(Z>60-56/(8.4/sqrt(30)) = P(Z>2.61) = 1-.9955 = .0045, which is muh smaller than .05
b. We reject null hypothesis

5. .005 is the lowest significance you can have, and still reject null hypothesis

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