The number of cars that roll through a stop sign at a particular intersection has had an historical average of 1.75 cars rolling through per hour. On a particular week, a random sample of 20 hours had a mean number of cars rolling through equal to 1.8 with a standard deviation equal to 1.04. At the 5 percent level of significance, does this sample show that the average number of cars rolling through the stop sign is higher than the historical average? Steps: 1. Open Minitab on your computer. 2. There is no data file for this example. The information above contains summarized data (take info from story and plug into Minitab) (a) Choose the correct null and alternative hypotheses. a. H0: μ ≥ 1.75 vs. H1: μ < 1.75 b. H0: μ ≤ 1.75 vs. H1: μ > 1.75 c. H0: μ = 1.75 vs. H1: μ ≠ 1.75

We are given that the number of cars that roll through a stop sign at a particular intersection has had an historical average of 1.75 cars rolling through per hour. And a random sample of 20 hours had a mean number of cars rolling through equal to 1.8 with a standard deviation equal to 1.04.

Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] <= 1.75 {means that the average number of cars rolling through the stop sign is less than or equal to the historical average}

Alternate Hypothesis, [tex]H_1[/tex] : [tex]\mu[/tex] > 1.75 {means that the average number of cars rolling through the stop sign is higher than the historical average}

The test statistics used here will be;

T.S. = [tex]\frac{Xbar -\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]

where, X bar = sample mean = 1.8

s = sample standard deviation = 1.04

n = sample size = 20

So, test statistics = [tex]\frac{1.8 -1.75}{\frac{1.04}{\sqrt{20} } }[/tex] ~ [tex]t_1_9[/tex]

= 0.215

Now, at 5% level of significance t table gives critical value of 1.729 .Since our test statistics is less than the critical value so we have insufficient evidence to reject null hypothesis.

Therefore, we conclude that the average number of cars rolling through the stop sign is not higher than the historical average.