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.)

The degrees of freedom are given by:

The p value for this case would be given by:

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

represent the sample mean for the miles

represent the sample standard deviation

sample size  

represent the value to verify

represent the significance level

t would represent the statistic

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:  

Alternative hypothesis:  

The statistic for this case is given by:

 (1)  

Replacing the data given we got:

The degrees of freedom are given by:

The p value for this case would be given by:

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

the first option is the answer.

69.64%

step-by-step explanation: