Question

A traffic engineer believes that the number of cars passing through a certain intersection between 2 and 6 pm on weekdays follows a normal distribution with mean 750 and standard deviation 100.

A new highway is opened, and it is hypothesized that the number or cars passing through the intersection should decrease as a result. A sample of 15 weekdays is taken, and the mean number of cars passing through the intersection is 710. Decide whether this reduction in traffic is statistically significant. The sampling distribution is:

a) None of the above

b) Student t

c) Normal

We would reject the null hypothesis at a 5% significance level if the observed sample mean was less than_______

The value of the test statistic is:________

The p-value of the hypothesis test is:_______

Select all the conclusions below which are correct.

-At a 10% significance level, we would conclude that there has been a significant reduction in traffic volume.

-At a 10% significance level, we would not conclude that there has been a significant reduction in traffic volume.

-At a 5% significance level, we would conclude that there has been a significant reduction in traffic volume.

-At a 5% significance level, we would not conclude that there has been a significant reduction in traffic volume.

Answer 1

From given information,

Population Mean μ = 750

Population standard deviation σ = 100

Sample size n = 15

Sample mean Xbar = 710

The sampling distribution is normal.

Because population data follows normal distribution. Population standard deviation is known so we are using z test.

Null Hypothesis H_{0 :} μ = 750

Alternative Hypothesis is H_{1 :} μ < 750

We would reject null hypothesis at 5% significance level if the observed sample mean was less than 750.

Since this is one sided test.

Test statistics

z score =

z = (710 - 750) / (100/sqrt(15))= - 1.549

The value if the test statistics is -1.549

P value = P( Z < -1.549) = 0.0607

The P-value of the hypothesis test is 0.0607

Since P-value = 0.0607 > 0.05 so we cannot reject null hypothesis at 5% significant level.

P-value = 0.0607 < 0.10 so we reject null hypothesis at 10% significant level.

Conclusion:

At a 10% significance level, we would conclude that there has been a significant reduction in traffic volume.

At a 5% significance level, we would not conclude that there has been a significant reduction in traffic volume.