Question

A metropolitan transportation authority has set a bus mechanical reliability goal of 3800 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 3825 bus miles and a sample standard deviation of 225 bus miles. Complete parts​ (a) and​ (b) below. a. Is there evidence that the population mean bus miles is more than 3800 bus​ miles? (Use a 0.05 level of​ significance.)

State the null and alternative hypotheses. H0​: mu less than or equals 3800 H1​: mu greater than 3800 ​(Type integers or​ decimals.) Find the test statistic for this hypothesis test. t Subscript STATequals 1.11 ​(Round to two decimal places as​ needed.)

The critical​ value(s) for the test statistic​ is(are) 1.66. ALSO HOW DID YOU GET THIS ANSWER OF 1.66 PLEASE SHARE DETAILS THANK YOU. ​(Round to two decimal places as needed. Use a comma to separate answers as​ needed.)

Is there sufficient evidence to reject the null hypothesis using alphaequals0.05​?

A. Do not reject the null hypothesis. There is insufficient evidence at the 0.05 level of significance that the population mean bus miles is greater than 3 comma 800 bus miles. This is the correct answer.

B. Reject the null hypothesis. There is sufficient evidence at the 0.05 level of significance that the population mean bus miles is greater than 3 comma 800 bus miles.

C. Reject the null hypothesis. There is sufficient evidence at the 0.05 level of significance that the population mean bus miles is less than 3800 bus miles. Your answer is not correct.

D. Do not reject the null hypothesis. There is insufficient evidence at the 0.05 level of significance that the population mean bus miles is less than 3800 bus miles.

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

The​ p-value is ___? PLEASE GIVE ME DETAILS ON HOW YOU GET THIS ANSWER AND THE TABLE YOU ARE USING BECAUSE IT'S NOT THE ZTABLE PLEASE POST PIC OF TABLE IF YOU CAN. THE ANSWER IS NOT .1335

Answer 1

Null and Alternative Hypotheses

In word form, hypothesis can be written as:

H0​: mu less than or equals 3800

H1​: mu greater than 3800

Test Statistics

Critical Value

Based on the information provided,

The significance level is α=0.05

Degrees of Freedom df = 100 - 1 = 99

The critical t value corresponding to α = 0.05 and df = 99 for a right tailed test is 1.66 (Obtained using t - value calculator. Screenshot attached below)

Conclusion

Since it is observed that t = 1.11 ≤ tc​=1.66, we fail to reject null hypothesis.

There is insufficient evidence at the 0.05 level of significance that the population mean bus miles is greater than 3800 bus miles.

P-value

P-value corresponding to test statistic t = 1.11.and df = 99 for a right tailed test is 0.1346 (Obtained using p-value calculator. Screenshot below)

Please note calculator has been used because it is not possible to obtain accurate p-value from t-Distribution table.

Interpretation

In p-value is less than 0.05, we reject null hypothesis. In this case, p-value (0.1346) is greater than 0.05, so we fail to reject null hypothesis.

In technical terms, there is 13.46% chance of obtaining an effect at least as extreme as the sample data, assuming that the null hypothesis is true.