Question

A city is considering widening a busy intersection in town. Last year, the city reported 16,000 cars passed through the intersection per day. The city conducted a survey for 49 days this year and found an average of 17,000 cars passed through the intersection, with a standard deviation of 5,000. Specify the null and alternative hypotheses to determine whether the intersection has seen an increase in traffic. The city is going to widen the intersection if it believes traffic has increased. At the 5% significance level, can you conclude that the intersection has seen an increase in traffic? Should the city widen the intersection? please show all work

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 16000
Alternative Hypothesis, Ha: μ > 16000

Rejection Region
This is right tailed test, for α = 0.05 and df = 48
Critical value of t is 1.677.
Hence reject H0 if t > 1.677

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (17000 - 16000)/(5000/sqrt(49))
t = 1.4

P-value Approach
P-value = 0.084
As P-value >= 0.05, fail to reject null hypothesis.

There is not sufficient evidence to conclude that the intersectin has seen an increase in traffic

City should not widen the intersection