The average gasoline price of one of the major oil companies in Europe has been $1.25 per liter. Recently, the company has undertaken several efficiency measures in order to reduce prices. Management is interested in determining whether their efficiency measures have actually reduced prices. A random sample of 49 of their gas stations is selected and the average price is determined to be $1.20 per liter. Furthermore, assume that the standard deviation of the population is $0.14.

a) Compute the standard error

b) Compute the test statistic

c) What is the p-value?

d) Develop appropriate hypothesis such as the reject of the null will support the contention that management efficiency measures had reduce gas prices in Europe.

e) At α = 0.05, what is your conclusion? Use critical value approach

f) Repeat the preceding hypothesis test using the p-value approach.

a)

b)

c)

d) Null hypothesis:

Alternative hypothesis:

e) For this case we need to find a critical value who accumulate 0.05 of the area in the left at the normal standard distribution and we got:

Since our calculated value is lower than the critical value we have enough evidence to reject the null hypothesis at the significance level provided of 5%

f)

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis at 5% of significance. Same result with the critical value approach.

Step-by-step explanation:

For this case we want to test is the true mean for the gasoline prices are significantly reduced from $1.25 per liter, so then the system of hypothesis are:

Null hypothesis:

Alternative hypothesis:

Part a

The standard error for this case is given by:

Part b

The statistic for this hypothesis is given by:

And replacing the info provided we got:

Part c

Since we are conducting a left tailed test the p value would be given by:

And we can use the following excel code to find it:

=NORM.DIST(-2.5,0,1,TRUE)

Part d

Null hypothesis:

Alternative hypothesis:

Part e

For this case we need to find a critical value who accumulate 0.05 of the area in the left at the normal standard distribution and we got:

Since our calculated value is lower than the critical value we have enough evidence to reject the null hypothesis at the significance level provided of 5%

Part f

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis at 5% of significance. Same result with the critical value approach.

i dont know sorry

step-by-step explanation:

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,