Sampling
To obtain our sample, we used observation. We sat at the McDonald’s restaurant in North Olmsted and observed how many males and females approached the cash register. Our population of interest was the customers of McDonald’s, while our sample population was the customers at the North Olmsted McDonald’s on three separate days. 3-4 PM on Friday April 20th, 10am- 12 pm on Saturday the 21st and 3-5pm on Sunday, April 22nd. We counted the number of males and females we observed on 10 minute intervals. Overall the observations included five hours worth of observations divided into six 10 minute intervals per hour giving us a sample size of 30. Our sample size did not include those who went through the drive through but it did include all customers, including children and babies.
Hypothesis Test
We chose to perform a two proportion z test since we had both males and females in our study. We wanted to know if there was a difference between the percent of males who dine in at McDonalds and the percent of females that dine in at McDonalds. We are trying to determine if there is a difference in the proportions so we decided to use a not equal alternative hypothesis.
Statement of the Null and Althernative
π1 = The true proportion of females who dine in at the North Olmsted McDonalds
π2= The true proportion of males who dine in at the North Olmsted McDonalds
H0= π1=π2
Ha: π1≠ π2
Alpha
α=0.05
Assumptions
1. Independent random sample
2. Sample is large enough
π1:
n(p1)=30(85/195)=13.0769>10
n(1- p1)=30(1-(85/195))=25.3521>10
π2:
n(p2)=30(110/195)=16.9231>10
n(1-p2)=30(1-(110/195))=13.0769>10
Test Statistic
Pc=(195)(0.435897)+(195)(0.564103)/195+195)=0.5
Z=0.435897-0.564103/√0.5(1-0.5)/195+0.5(1-0.5)/195=-2.531848
Z=-2.531848
P-value
0.01134634
Conclusion
Conclusion: We can reject the null hypothesis at the 0.05 level of significance since our p-value is less than alpha. Therefore, we have sufficient evidence to say that the true proportion of men and women who dine in at the North Olmsted McDonalds are not equal.