A metropolitan transportation authority has set a bus mechanical reliability goal of 3 comma 9003,900 bus miles. Bus mechanical reliability is measured specifically as the number of bus miles between mechanical road calls. Suppose a sample of 100100 buses resulted in a sample mean of 3 comma 9753,975 bus miles and a sample standard deviation of 325325 bus miles. Complete parts (a) and (b) below. a. Is there evidence that the population mean bus miles is more than 3 comma 9003,900 bus miles? (Use a 0.050.05 level of significance.)

Since the p value is lower than the significance level we can reject the null hypothesis and then we can conclude that the true mean is significantly higher than 3900 bus miles

Step-by-step explanation:

Data given

[tex]\bar X=3975[/tex] represent the sample mean for the miles

[tex]s=325[/tex] represent the sample standard deviation

[tex]n=100[/tex] sample size

[tex]\mu_o =3900[/tex] represent the value to verify

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

For this case we want to check if there evidence that the population mean bus miles is more than 3,900 bus miles , the system of hypothesis are:

Null hypothesis:[tex]\mu \leq 3900[/tex]

Alternative hypothesis:[tex]\mu > 3900[/tex]

The statistic for this case is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)

Replacing the data given we got:

[tex]t=\frac{3975-3900}{\frac{325}{\sqrt{100}}}=2.308[/tex]

The degrees of freedom are given by:

[tex]df=n-1=100-1=99[/tex]

The p value for this case would be given by:

[tex]p_v =P(t_{(99)}>2.308)=0.0115[/tex]

Since the p value is lower than the significance level we can reject the null hypothesis and then we can conclude that the true mean is significantly higher than 3900 bus miles