Question

A recent market report states that despite the recent drop in price, the mean price of a barrel of oil has historically remained constant at 39.10 USD (US dollars). However, an investor believes this is an inaccurate report, and thinks the mean price of a barrel of oil is something else. The investor collects data on the price per barrel of oil for 24 randomly selected years, and calculates a mean and standard deviation of 41.1 USE and 8.35 USD respectively. Assuming that price per barrel of oil is a normally distributed variable, determine each of the following:

a) What are the appropriate hypotheses:

		H0:X¯=39.10,HA:X¯≠39.10
		H0:μ=39.10,HA:μ>39.10
		H0:X¯=39.10,HA:X¯>39.10
		H0:μ=39.10,HA:μ≠39.10

b) Calculate the appropriate test statistic.

Round your answer to at least 3 decimal places.

c) What is the appropriate conclusion that can be made, at the 5% level of significance?

		There is sufficient evidence to reject the null hypothesis, and therefore conclude that the mean price per barrel of oil is something other than 39.10 USD.
		There is insufficient evidence to reject the null hypothesis, and therefore no significant evidence that the mean price per barrel of oil is different from 39.10 USD.

Answer 1

answer)

A)

H0:μ=39.10,HA:μ≠39.10

b)

Test statistics t = (sample mean - claimed mean)/(s.d/√n)

t = (41.1-39.1)/(8.35/√24)

t = 1.173

C)

As the population s.d is not mentioned in the question we will use t distribution to estimate the p-value

Degrees of freedom is = n-1 = 23

For 23 dof and 1.173 test statistics

P-Value from t distribution is = 0.2528

As the obtained p-value is greater than given significance 0.05

We fail to reject the null hypothesis

There is insufficient evidence to reject the null hypothesis, and therefore no significant evidence that the mean price per barrel of oil is different from 39.10 USD.