Question

10.A car manufacturer advertised that its new subcompact models get 47 miles per gallon. Let ?? be the mean of mileage distribution for these cars. You suspect that the mileage might be overrated and selected 15 cars of the model; the sample mean mileage was 45.5 miles per gallon and the sample standard deviation of the 16 cars was 2.5 miles per gallon. At 5% level of significance, test whether there is significant evidence that mean miles per gallon is less than 47 miles per gallon.
a)Details given in the problem:
b)Assumptions (if any):
c)Null, Alternate Hypotheses and the tail test?
H0:
H1:
Tail?
d)Find the Critical Statistic (Table value) and Illustrate:
Critical Statistic:
e)State and Compute Test Statistic:
f)Compute p-value:
g)Conclusion using critical method:
h)Conclusion using p-value method:

Answer 1

Since we feel that the mileage is overrated i.e more than what is stated, we use a left tailed test here.

__________________________________

(a) Given: = 47, = 45.5, s = 2.5, n = 16, = 0.05

_________________________________

(b) Assumptions

(i) The selection of cars was random

(ii) Samples are independent of each other

(iii) The population of cars come from an approximately normal or a normal distribution.

_________________________________

(c) The Hypothesis:

H0: = 47

Ha: < 47

This is a Left Tailed Test.

___________________________________

(d) The Critical Value:   The critical value (Left Tail) at = 0.05, for df = n - 1 = 15, t critical = -1.753

_________________________________

(e) The Test Statistic: Since the population standard deviation is unknown, we use the students t test.

The test statistic is given by the equation:

___________________________________

(f) The p Value:    The p value (Left Tail) for t = -2.4, for degrees of freedom (df) = n-1 = 16, is; p value = 0.0149

________________________________

(g) Since t observed (-2.4) is < -t critical (-1.743), We Reject H0.

There is sufficient evidence at the 95% level of significance to conclude that the claim made by the car manufacturer is overrated.

_______________________________

(h) Since P value (0.0149) is < (0.05) , We Reject H0.

There is sufficient evidence at the 95% level of significance to conclude that the claim made by the car manufacturer is overrated.

________________________________