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.

a. Specify the null and alternative hypotheses to determine whether the intersection has seen an increase in traffic.

b. Calculate the value of the test statistic and approximate the p-value.

c. 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?