Question

A group of engineers perform an experiment to determine whether the fuel efficiency for a new type of engine for an oilfield drill is better than the most commonly used type of engine in existing oilfields. The engineers perform a 2–sample t–test and obtain a p-value of 0.04.

(i) Briefly explain what a p–value of 0.04 means (i.e. what does the p–value actually represent).

(ii) Explain what a Type II error would mean in the context of this problem.

Answer 1

• EXPLANATION
• A more informative approach is to calculate and quote the probability value (pvalue) of the observed test statistic.
• This is the observed significance level of the test statistic – the probability, assuming H0 is true, of observing a test statistic at least as “extreme” (inconsistent with H0) as the value observed.
• The p-value is the lowest level at which H0 can be rejected.
• The smaller the p-value, the stronger is the evidence against the null hypothesis.  
• ANSWER
• HYPOTHESIS TO BE TESTED.
• Let the null hypothesis be that the fuel efficiency for a new type of engine for an oilfield drill is same as that of the most commonly used type of engine in existing oilfields.
• vs
• The alternater hypothesis the fuel efficiency for a new type of engine for an oilfield drill is better than the most commonly used type of engine in existing oilfields.
• CONCLUSION
• Since here the p value obtianed is less than 5% significant level.
• We have enough eveidence to reject the null hypothesis.
• Hence we conlcude that the claim the fuel efficiency for a new type of engine for an oilfield drill is better than the most commonly used type of engine in existing oilfields.
• TYPE 2 ERROR MEANS THAT
• The probability of accepting null hypothesis when it is false
• Hence here if type 2 error occurs we will conclude that the fuel efficiency for a new type of engine for an oilfield drill is same as that of the most commonly used type of engine in existing oilfields.