A car company says that the mean gas mleage for its luocury sedan is at least 24

Question

A car company says that the mean gas mleage for its luocury sedan is at least 24 miles per gallon (mpg).You beliove the claim is incorrect and find that a random sample of 8 cars has a mean gas mleage of 21 mog and a standard deviation of 4 mpg At -0 025, test the company's daim Assume the population is normally dshbuted Click here to view the 1 disrbution table Click hore to view page 1 of the nomal table Click bere to view p Which sampling distribution should be used and wry O B. Use a normal sampling distribution because the population is normal, and a is known O D. Use a normal sampling distrbution becaune the population is normal, and a is unknown O F. Use at sampling distrbution because n e 30 O A. Use a normal sampling distribution because n> 30 C. Use a t sampling dstuton because the population normal, and eh urknown O E. Use a t-sampling distibution because the popuilation is nomal, and o is known State the appropriate hypotheses to test O A. Hou» 24 n, w-24 n,»-24 n, , 24 H. 24 what is he value of standardized test stabi The standardized test statistic is Round to two decimal places as needed )

Explanation / Answer

Solution:

We are given

n = 8

Xbar = 21

S = 4

= 0.025

We have to test

H0: µ 24 versus Ha: µ < 24

Which sampling distribution should be used and why?

Answer: C

Use a t-sampling distribution because the population is normal and is unknown.

State the appropriate hypotheses to test.

Answer: B

H0: µ 24 versus Ha: µ < 24

The test statistic value is given as below:

Test statistic = t = (Xbar - µ) / [S/sqrt(n)]

Test statistic = t = (21 – 24) / [4/sqrt(8)]

Test statistic = t = -2.1213

The standardized test statistic is -2.12.

The critical value is -2.365

P-value = 0.0358

P-value > = 0.025

So, we do not reject the null hypothesis

Fail to reject H0. At the 2.5% significance level, there is sufficient evidence to conclude that the car company’s claim that the mean gas mileage for the heavy sedan is at least 24 miles per gallon.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.