Asked by Amrita Nijjer on May 26, 2024
Verified
The average gasoline price of one of the major oil companies has been $2.20 per gallon.Because of cost reduction measures, it is believed that there has been a significant reduction 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 $2.14.Assume that the standard deviation of the population (σ) is $0.12.
a.
State the null and the alternative hypotheses.
b.
Compute the test statistic.
c.
What is the p-value associated with the above sample results?
d.
Using α = .05, test the company's claim.
P-Value
The probability measure indicating the likelihood of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true.
Standard Deviation
A measure of the dispersion or variability within a set of data points, indicating how spread out the data points are from the mean.
Null Hypothesis
A hypothesis used in statistics that proposes no significant difference or effect between specified populations, conditions, or variables.
- Gain proficiency in how to establish null and alternative hypotheses in diverse statistical explorations.
- Calculate test statistics for different types of data and studies.
- Decode the concept of p-value and familiarize with the process of its computation.
Verified Answer
EB
Emily BodieMay 30, 2024
Final Answer :
a.
H0: μ
$2.20
Ha: μ < $2.20
b.
z = -3
c.
p-value = almost zero (.0013)
d.
p-value < .05; reject H0; the average price has been reduced.
a.
H0: μ
$2.20Ha: μ < $2.20
b.
z = -3
c.
p-value = almost zero (.0013)
d.
p-value < .05; reject H0; the average price has been reduced.
Learning Objectives
- Gain proficiency in how to establish null and alternative hypotheses in diverse statistical explorations.
- Calculate test statistics for different types of data and studies.
- Decode the concept of p-value and familiarize with the process of its computation.