A car company says that the mean gas mleage for its luocury sedan is at least 24
ID: 3326403 • Letter: A
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.