Question

a data set includes times (in minutes) of taxi cab rides in new york city yellow cabs during a friday morning same day in a recent year. using 35 of the times to test the claim that the mean of all such times is less than minutes, the accompanying minitab display is obtained. test the given claim by using the display provided fro minitab. use a 0.05 significance level. click the icon to view the minitab display. identify the null and alternative hypotheses. h₀: μ = 15 h₁: μ < 15 (type integers or decimals. do not round.) identify the test statistic. -1.56 (round to two decimal places as needed.) identify the p - value. (round to three decimal places as needed.)

Explanation:

Step1: Determine the type of test

This is a one - tailed (left - tailed) t - test since the alternative hypothesis is \(H_1:\mu < 15\) and the population standard deviation \(\sigma\) is unknown (we assume this as it is not given and we are using sample data). The degrees of freedom \(df=n - 1\), where \(n = 35\), so \(df=35 - 1=34\).

Step2: Find the P - value

For a t - test with test statistic \(t=-1.56\) and \(df = 34\), we can use a t - distribution table or a statistical software (since it is similar to the Minitab context). Using a t - table or a calculator (e.g., in R: pt(-1.56,34)), we calculate the P - value.
The formula for the P - value in a left - tailed t - test is \(P(T<t)\) where \(T\) follows a t - distribution with \(df\) degrees of freedom.
Using a calculator or software, \(P(T < - 1.56)\) with \(df = 34\) gives \(P\approx0.064\)

Answer:

\(0.064\)