Assignment
1 What is the hypothesis of interest in this question?
The main hypothesis of interest in this problem is to determinate how improvement will have the use of premium unleaded gasoline, and the hypothesis is to prove that unleaded gasoline is equal to the premium unleaded gasoline and the alternative is that the premium unleaded gasoline will reduce the acceleration time and the hypothesis is represented as follow:
HO : U = 10.2
H1 : U < 10.2
2 Would you recommend a Z-test or t-test? Give a reason for your answer.
I would recommend the Z-test. The problem has a sample size of 41 which is a sample size is greater than 30, and the variance is unknown, we can still use the z test and Statdisk program to find the P-Value.
3 What is the value of the test statistic for this test?
The calculation to find the test statistic:
ZSTAT= (9.7 - 10.2) / (2.1/SQR(41))
ZSTAT= -1.5246
4 What is the distribution of the test statistic you mentioned in the last question?
The distribution test mention in the question above was the normal distribution using the Z test.
5 Perform the test by first computing the p-value for the test.
I used the Statdisk program to calculate the exact P-Value which is 0.0636
z Value: -1.5246
Prob Dens: 0.1247967
Cumulative Probs
Left: 0.063685
Right: 0.936315
2 Tailed: 0.127371
Central: 0.872629
As Table A-2: 0.063685 (Statdisk)
6 Why is a one-sided test better than a two-sided test in this situation
The Institute for digital research and education mentions "Because the one-tailed test provides more power to detect an effect, you may be tempted to use a one-tailed test whenever you have a hypothesis about the direction of an effect." (IdreUcla, 2017). In this problem we need to find only one side of the distribution which is the left side and determinate the reduce time in acceleration.
7 Can you change the situation so that a two-sided test would be appropriate and a one-sided test would not be appropriate?
We could change it but the question should be asking for different parameters. For example, how fast and slow the premium unleaded gasoline can affect the acceleration.
W/C: 368
References
IdreUcla. (2017). FAQ: What are the differences between one-tailed and two-tailed tests? IdreUcla.
Levine, D. M., Szabat, K. A., & Stephan, D. (2017). Statistics for managers using Microsoft Excel (8th ed.). Boston: Pearson.