Homework SourseA research report claims that 20 of all individuals use Fire
A research report claims that 20% of all individuals use Firefox to browse the web. A software company is trying to determine if the proportion of their users who use Firefox is significantly different from 0.2. In a sample of 200 of their users, 36 users stated that they used Firefox. Using this data, conduct the appropriate hypothesis test using a 0.01 level of significance.
a) What are the appropriate hypotheses?
a)H0: p = 0.2 versus Ha: p < 0.2
b)H0: p = 0.2 versus Ha: p 0.2
c)H0: = 0.2 versus Ha: > 0.2
d)H0: p = 0.2 versus Ha: p > 0.2
b) What is the test statistic? Give your answer to four decimal places.
c) What is the P-value for the test? Give your answer to four decimal places.
d) What is the appropriate conclusion?
a)Fail to reject the claim that the Firefox proportion is 0.2 because the P-value is smaller than 0.01.
b)Conclude that the Firefox proportion is not 0.2 because the P-value is smaller than 0.01.
c)Fail to reject the claim that the Firefox proportion is 0.2 because the P-value is larger than 0.01.
d)Conclude that the Firefox proportion is not 0.2 because the P-value is larger than 0.01.
Solution
Set Up Hypothesis
Null, Firefox is similar from 0.2, H0:P=0.2
Alternate, Firefox is significantly different from 0.2 H1: P!=0.2
Test Statistic
No. Of Success chances Observed (x)=36
Number of objects in a sample provided(n)=200
No. Of Success Rate ( P )= x/n = 0.18
Success Probability ( Po )=0.2
Failure Probability ( Qo) = 0.8
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.18-0.2/(Sqrt(0.16)/200)
Zo =-0.7071
| Zo | =0.707
Critical Value
The Value of |Z | at LOS 0.01% is 2.58
We got |Zo| =0.707 & | Z | =2.58
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != -0.70711 ) = 0.4795
Hence Value of P0.01 < 0.4795,Here We Do not Reject Ho
ANS.
1. b)H0: p = 0.2 versus Ha: p 0.2
2. Zo =-0.7071
3. ( P != -0.70711 ) = 0.4795
4. c)Fail to reject the claim that the Firefox proportion is 0.2
because the P-value is larger than 0.01
