Question

Assume the average gasoline price of one of the major oil companies has been $3.00 per gallon for quite some time. Because of recent shortages in production of crude oil, it is believed that there has now been a significant INCREASE in the average price. In order to test this belief, we randomly selected a sample of 36 of the company's gas stations and determined that the average price for the stations in the sample was $3.06. Assume that the standard deviation of the population (σ) is $0.09. Use a .05 level of significance, and test to determine if there has been an increase in the price.

Group of answer choices

z = 4; therefore, reject H00000. There is sufficient evidence at ααααα = .05 to conclude that there has been an increase in the average price.

z = 4; therefore, do not reject H00000. There is sufficient evidence at ααααα = .05 to conclude that there has been an increase in the average price.

z = 4; therefore, reject H00000. There is not sufficient evidence at ααααα = .05 to conclude that there has been an increase in the average price.

z = 4; therefore, do not reject H00000. There is not sufficient evidence at ααααα = .05 to conclude that there has been an increase in the average price.

none of these answers are correct

Answer 1

Answer:

z = 4; therefore, reject H0. There is sufficient evidence at α = .05 to conclude that there has been an increase in the average price.

Explanation:

Here, we have to use one sample z test for the population mean.

The null and alternative hypotheses are given as below:

H₀: µ = 3 versus H_a: µ > 3

This is an upper tailed test.

The test statistic formula is given as below:

Z = (x̄ - µ)/[σ/sqrt(n)]

From given data, we have

µ = 3

x̄ = 3.06

σ = 0.09

n = 36

α = 0.05

Critical value = 1.6449

(by using z-table or excel)

Z = (3.06 - 3)/[ 0.09/sqrt(36)]

Z = 4.0000

P-value = 0.0000

(by using Z-table)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that there has been an increase in the average price.