Hypothesis testing #2
Brady Knight
Jordan Berkompas
Olivia O’Connor
1a)
P: Population = Price for gallon of unleaded gasoline in Illinois
Given Population Mean, μ = $3.63
Sample size, n =10
Sample mean, = $3.975
H: HO: μ = $3.63
Ha: μ $3.63} That the sample mean μ is greater than the national average price of $3.63.
A: Not an SRS, sample size < 15
N: One-sample t-Test for unknown population mean μ.
T: t = 4.8146
O: p-value= .001
M: We reject the null hypothesis in favor of the Ha because p-value of .001 < alpha of .05.
S: We have significant evidence that the mean price for a gallon of unleaded gasoline in Illinois is greater than the national mean price of $3.63.
1b). We have made a Type-I error, in which we rejected the null hypothesis when it was true that average price of gasoline in Illinois is equal to the national average price.
2)
P: Population 1 are individuals who shopped during the extended Black Friday Weekend in 2012
Population 2 are individuals who shopped during the regular Black Friday Weekend in 2011.
Given Pop. Mean 1, μ1 = $399.40 with a Standard deviation of $171.10 with sample size n=25
Given Pop. Mean 2, μ2 = $381.19 with a Standard deviation of $119.80 with sample size n=25
H: Ho: μ1= μ2
Ha: μ1>μ2}That the average of money spent on Black Friday in 2012 is greater than the average money spent on Black Friday of 2011.
A: Random Sample, sample size < 30
N: Two-sample T-test for difference in population means
T: t= .4359
O: p-value= .3325
M: We will fail to reject the null hypothesis because the p-value of .3325 is greater than the alpha of .05.
S: We do not have significant evidence that the mean amount spent on an extended Black Friday sale in 2012 is greater than the mean amount spent on a regular Black Friday sale in 2011.
2b). This would be a Type-II error, since the sample from 2012 was over-representative. It did not represent the population as a whole, which did spend statistically more than the population in 2011.
3)
- The cadets bought bags of Chips Ahoy! from locations all across the country because they were attempting to make the sample random and representative of all areas that the company distributed to.
- P: Population: Chips Ahoy! chocolate chips
Population mean, μ0 =1000
Sample mean, = 1261.6
Sample standard deviation, s= 117.6
Sample size, n=42
H: Ho: μ = 1000
Ha: μ > 1000
A: We are willing to accept that the sample is a random and representative sample due to the method of sampling
N: One sample t-Test for unknown population mean μ
T: t= 14.42
O: p-value = 0
M: We reject the null hypothesis because the p-value is significant at an alpha level of .05
S: We have significant evidence that the mean number of chocolate chips per bag of Chips Ahoy! is greater than 1000.
- We can confirm their statement that there are at least 1000 chips in every bag, because our test found the average to be much greater than 1000.