A student at a university wants to determine if the proporti

A student at a university wants to determine if the proportion of students that use iPhones is less than 0.38. The hypotheses for this scenario are as follows. Null Hypothesis: p 0.38, Alternative Hypothesis: p < 0.38. If the student randomly samples 29 other students and finds that 12 of them use iPhones, what is the test statistic and p-value?

A. Test Statistic: 0.375, p-value: 0.354

B. Test Statistic: 0.375, p-value: 0.646

C. Test Statistic: 0.375, p-value: 1.292

D. Test Statistic: -0.375, p-value: 0.646

E. Test Statistic: -0.375, p-value: 0.354

Solution

Set Up Hypothesis
Null, H0:P>=0.38
Alternate, H1: P<0.38
Test Statistic
No. Of Success chances Observed (x)=12
Number of objects in a sample provided(n)=29
No. Of Success Rate ( P )= x/n = 0.4138
Success Probability ( Po )=0.38
Failure Probability ( Qo) = 0.62
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.41379-0.38/(Sqrt(0.2356)/29)
Zo =0.3749
| Zo | =0.3749
Critical Value
The Value of |Z | at LOS 0.025% is 1.96
We got |Zo| =0.375 & | Z | =1.96
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Left Tail -Ha : ( P < 0.37492 ) = 0.64614
Hence Value of P0.025 < 0.64614,Here We Do not Reject Ho

ANS:
B. Test Statistic: 0.375, p-value: 0.646