An article in the San Francisco Chronicle indicated that just 38% of drivers crossing the San Francisco Bay Area’s seven state-owned bridges pay their tolls electronically, compared with rates nearing 80% at systems elsewhere in the nation. Albert Yee, director of highway and arterial operations for the regional Metropolitan Transportation Commission, indicated that the commission is eager to drive up the percentage of tolls paid electronically. In an attempt to see if its efforts are producing the required results, 15 vehicles each day are tracked through the toll lanes of the Bay Area bridges. The number of drivers using electronic payment to pay their toll for a period of three months appears in the file titled Fastrak.
a. Determine if the distribution of the number of FasTrak users could be described as a binomial distribution with a population proportion equal to 0.50. Use a chi-square goodness-of-fit test and a significance level of 0.05.
b. Conduct a test of hypothesis to determine if the percent of tolls paid electronically has increased to more than 70% since Yee’s efforts.