Q1) One-Sample t-Test (14 points total)
I am shopping for a new sedan and would like to get one with excellent miles per gallon (MPG). I heard that Japanese cars tend to be more fuel efficient than American cars, so I collected MPG data on a random sample of 16
Japanese sedan models to be compar...
Q1) One-Sample t-Test (14 points total)
I am shopping for a new sedan and would like to get one with excellent miles per gallon (MPG). I heard that
Japanese cars tend to be more fuel efficient than American cars, so I collected MPG data on a random sample of 16
Japanese sedan models to be compared to the American car statistics. I would like to see if there is a significant
difference, in either direction, between Japanese sedans and American sedans. The US Environmental Protection
Agency reported that the average MPG for American sedans in 2017 is μ = 30. I set the significance level at α
= .05 for a two-tailed hypothesis test.
Table 1.
Average MPG for Japanese Sedans
Japanese car model MPG
1 32
2 30
3 36
4 36
5 35
6 28
7 32
8 28
9 32
10 28
11 32
12 32
13 28
14 30
15 33
16 32
Total (N=16)
a. Information about the hypothesis test:
- What is the dependent variable in this hypothesis test?
Answer: Miles per gallon (MPG)
- What is the “sample” for this one-sample t test?
Answer: 16 different Japanese sedans
- What is the target population represented by the sample?
Answer: Japanese cars
- What is the comparison population?
Answer: American cars
b. What would be the null and alternative hypotheses in both words and symbol notations for my
analysis?
Answer:
o Null Hypothesis-
Word- There is no significant difference between the average MPG of
Japanese cars and American cars.
Symbol- H0: Japanese = American
o Alternative Hypothesis-
PSY230 FallB2019
Word- There is a significant difference between the MPG of Japanese
cars and American cars.
Symbol- H1: Japanese ≠ American
c. Calculate the sample mean.
Answer: 31.5
Formula: ∑X/N
Process: (28+28+28+28+30+30+32+32+32+32+32+32+33+35+36+36)/16 à
504/16 = 31.5
, PSY230 FallB2019
Word- There is a significant difference between the MPG of Japanese
cars and American cars.
Symbol- H1: Japanese ≠ American
c. Calculate the sample mean.
Answer: 31.5
Formula: ∑X/N
Process: (28+28+28+28+30+30+32+32+32+32+32+32+33+35+36+36)/16 à
504/16 = 31.5
d. Estimate the standard deviation of the population from which the sample was drawn
Answer: 2.70
Formula: σ = σ2 = ∑(X-M)/(N-1)
Process: ((28-31.5)2+(28-31.5)2+(28-31.5)2+(28-31.5)2+(30-31.5)2+(30-31.5)2+(32-
31.5)2+(32-31.5)2+(32-31.5)2+(32-31.5)2+(32-31.5)2+(32-31.5)2+(33-31.5)2+(35-
31.5)2+(36-31.5)2+(36-31.5)2)/(16-1) à ((-3.5)2+(-3.5)2+(-3.5)2+(-3.5)2+(-1.5)2+(-
1.5)2+(0.5)2+(0.5)2+(0.5)2+(0.5)2+(0.5)2+(0.5)2+(1.5)2+(3.5)2+(4.5)2+(4.5)2/15 à
109.5625/15 = 7.304166667 à 7.30 à √7.30 = 2.70262218 à 2.70
e. Calculate the standard error
Answer: .675
Formula: SE= σ/√N
Process: 2.70/√16 à 2.70/4 = 0.675
f. Calculate the t statistic for the sample
Answer: 2.22
Formula: t = (M – μ)/SE
Process: (31.5-30)/0.675 à 1.5/0.675 = 2.2222222222 = 2.22
g. Figure out the degree of freedom, and then determine the critical t value(s) based on the type of test
and the preset alpha level
Answer:
o Degrees of Freedom: 15
Formula: DOF = N - 1
Process: 16-1 = 15
o Critical t Value: ±2.132
Process: I found the DOF & significance level on t chart under the two-
tail category then located the corresponding t value.
h. Compare the t statistic with the critical t value. Is the calculated t statistic more extreme or less
extreme than the critical t value? Based on this comparison, determine whether we “reject” or “fail to
reject” the null hypothesis
Answer:
o Comparison- The t statistic is more extreme than the critical t values.
o Hypothesis- I reject the null hypothesis because the statistic is more extreme
than the critical values, therefore there is a significant difference.
Process: Stat- 2.215647, Critical- + 2.132, - 2.132 à 2.22222222 (2.22) > ± 2.132
PSY230 FallB2019
i. Interpret the result in 1-2 sentences to answer the research question (you may use the wording of the
hypothesis or explain it in your own words)
Answer: The average MPG of Japanese made sedans is significantly higher than the
average MPG of sedans that are made in the United States.
j. Calculate the standardized effect size of this hypothesis test
Answer: .56
Formula: (M – MM) / σ
Process: (31.5-30)/2.7 à 1.5/2.7 = 0.555556 à 0.56
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller ScoreSmart. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $9.49. You're not tied to anything after your purchase.
