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

$25

step-by-step explanation:

25 - 4.50 = 20.5

20.5 / 2 = 10.25

10.25 + 10 = 20.25

20.25 - 12.50 = 7.75

therefore the answer is $25 as shown as the first number.

this answer is !