Please solve the problem in photo: In a test of Murphy\'s law, pieces of toast w
ID: 3134360 • Letter: P
Question
Please solve the problem in photo:
In a test of Murphy's law, pieces of toast were buttered on one side and then dropped. Murphy's law predicts that they will land butter-side down. Out of 9821 slices of toast dropped, 6101 landed butter-side down. (Believe it or not, these are real data!). a. What is a 95% confidence interval for the probability of a piece of toast landing butterside down? b. State the null and alternative hypotheses. c. Perform the appropriate statistical test of the null hypothesis. d. State your conclusions.Explanation / Answer
a.
Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=6101
Sample Size(n)=9821
Sample proportion = x/n =0.621
Confidence Interval = [ 0.621 ±Z a/2 ( Sqrt ( 0.621*0.379) /9821)]
= [ 0.621 - 1.96* Sqrt(0) , 0.621 + 1.96* Sqrt(0) ]
= [ 0.611,0.631]
b.
Z-Test For Proportion
Set Up Hypothesis
Null, H0:P=0.5
Alternate, H1: P!=0.5
Test Statistic
No. Of Success chances Observed (x)=6101
Number of objects in a sample provided(n)=9821
No. Of Success Rate ( P )= x/n = 0.6212
Success Probability ( Po )=0.5
Failure Probability ( Qo) = 0.5
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.62122-0.5/(Sqrt(0.25)/9821)
Zo =24.026
| Zo | =24.026
Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo| =24.026 & | Z | =1.96
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != 24.026 ) = 0
Hence Value of P0.05 > 0,Here we Reject Ho