Statistics Problem

Question

A car manufacturer is estimating the average gasoline consumption for a new car (mpg). A sample of 100 cars provides the following results (use alpha = 0.05)

n = 100 x bar = 27 mpg S^2 + 36

Can they prove that the mpg is at least 25 miles? YES or NO

State HA

Standard Error?

What's the critical point?

what's the test statistic?

was the null hypothesis rejected?

Did you use z values or t values?

Answer 1

Ho: mu = 25

Ha: mu > 25

standard error = 36/sqrt(100) = 3.6

z-critical value = 1.645

since large sample size, can use z-statistic

z = (27 - 25)/3.6) = 1.8

z > critical value, so rejected null hypothesis