A metropolitan transportation authority has set a bus mechanical reliability goal of 3,800 bus miles. Bus mechanical reliability is measured specifically as the number of bus miles between mechanical road calls. Suppose a sample of 100 buses resulted in a sample mean of 3,825 bus miles and a sample standard deviation of 175 bus miles. Complete parts? (a) and? (b) below.

a. Is there evidence that the population mean bus miles is more than 3,800 bus? miles? (Use a 0.10 level of? significance.)

b. Determine the? p-value and interpret its meaning.

Answer:

a. Is there evidence that the population mean bus miles is more than 3,800 bus? miles: Yes

b. Determine the? p-value and interpret its meaning: 0.078 Since the P-value is less that the significance level of 0.10, we reject the null hypothesis. We conclude that there is enough evidence that the population mean bus miles is more than 3,800 bus? miles

Step-by-step explanation

The hypothesis shall be:

H0: µ = 3800

Ha: µ > 3,800

t = (3825 - 3800 )/(175/√100)

t = 1.429

The P-value associated with a t score of 1.429 and n-1 = 99 degrees of freedom is 0.078 from Excel

Since the P-value is less that the significance level of 0.10, we reject the null hypothesis. We conclude that there is enough evidence that the population mean bus miles is more than 3,800 bus? miles