In: Statistics and Probability
You want to determine if the lengths of roller coasters in California is different than those in Texas. Below is data that compares two samples of roller coaster in California and Texas.
CA Roller Coasters | TX Roller Coasters | |
Number with a Length > 500 meters | 20 | 12 |
Number in Sample | 30 | 25 |
Test the hypothesis that the proportion of CA roller coasters that are longer than 500 meters is different than the proportion of TX roller coasters that are longer than 500 meters, using a 5% level of significance. For full points, show all steps except for the sketch. Use the STAT command in your graphing calculator for the degrees of freedom, test statistic, and p-value.
Ho: p1 - p2 = 0
Ha: p1 - p2 ╪ 0
sample #1 ----->
first sample size, n1=
30
number of successes, sample 1 = x1=
20
proportion success of sample 1 , p̂1=
x1/n1= 0.6667
sample #2 ----->
second sample size, n2 =
25
number of successes, sample 2 = x2 =
12
proportion success of sample 1 , p̂ 2= x2/n2 =
0.4800
difference in sample proportions, p̂1 - p̂2 =
0.6667 - 0.4800 =
0.1867
pooled proportion , p = (x1+x2)/(n1+n2)=
0.5818
std error ,SE = =SQRT(p*(1-p)*(1/n1+
1/n2)= 0.13358
Z-statistic = (p̂1 - p̂2)/SE = (
0.187 / 0.1336 ) =
1.3975
p-value =
0.1623
decision : p-value>α,Don't reject null
hypothesis