The worldwide market share for the Mozilla Firefox web brows

The worldwide market share for the Mozilla Firefox web browser was 19.2% in a recent month. Suppose that you decided to select a sample of 100 students at your university and you found that 25 used the Mozilla Firefox web browser. (Data extracted from J. Swartz, “Race is on in Browser Wars as Users’Habits Shift,” USA Today, December 1, 2010, pp. 1B, 2B.)

Determine if there is evidence that the market share for the Mozilla Firefox web browser at your university is greater than the worldwide market share of 19.2% (Use the 0.05 level of significance.)

Suppose that the sample size was n=400, and you found that 25% of the sample of students at your university (100 out of 400) used the Mozilla Firefox web browser. Determine whether there is evidence that the market share for Mozilla Firefox web browser at your university is greater than the worldwide market share of 19.2%. (Use the 0.05 level of significance.)

Discuss the effect that sample size has on hypothesis testing.

What do you think are your chances of rejecting any null hypothesis concerning a population proportion if a sample size of n=20 is used?

Solution

a)
AT Size n=100
Set Up Hypothesis
Null, H0:P=0.192
Alternate, university is greater than the worldwide market H1: P>0.192
Test Statistic
No. Of Success chances Observed (x)=25
Number of objects in a sample provided(n)=100
No. Of Success Rate ( P )= x/n = 0.25
Success Probability ( Po )=0.192
Failure Probability ( Qo) = 0.808
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.25-0.192/(Sqrt(0.155136)/100)
Zo =1.4726
| Zo | =1.4726
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =1.473 & | Z | =1.64
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Right Tail - Ha : ( P > 1.47256 ) = 0.07044
Hence Value of P0.05 < 0.07044,Here We Do not Reject Ho

We don\'t have evidence that university is greater than the worldwide market

b)
AT size n=400
(x)=100 ; (n)=400 ; ( P )= x/n = 0.25
Success Probability ( Po )=0.192
Failure Probability ( Qo) = 0.808
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.25-0.192/(Sqrt(0.155136)/400)
Zo =2.9451
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =2.945 & | Z | =1.64
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Right Tail - Ha : ( P > 2.94511 ) = 0.00161
Hence Value of P0.05 > 0.00161,Here we Reject Ho

We have evidence that university is greater than the worldwide market

c)
Discuss the effect that sample size has on hypothesis testing.?

Increasing the sample size higher the critical value and get more chance to reject the
Null Hypothesis

d)
What do you think are your chances of rejecting any null hypothesis concerning a population proportion if a sample size of n=20 is used?

Chances are slow down to reject null if n=20 used