Suppose a random sample of 100 US companies taken in 2005 sh

Suppose a random sample of 100 U.S. companies taken in 2005 showed that 68 offered high-deductible health insurance plans to their workers. A separate random sample of 120 firms taken in 2006 showed that 58 offered high-deductible health insurance plans to their workers. Based on the sample results, can you conclude that there is a higher proportion of U.S. companies offering high-deductible health insurance plans to their workers in 2006 than in 2005? Conduct your hypothesis test at a .05 significant level. a) Stat the null and alternate hypotheses b) What is the level of significance? c)what is the critical value d)compute the value of the test statistic e)What is your decision, interpret the results pictures are very helpfull;.

Solution

Null, Ho: p1 <= p2
Alternate, a higher proportion of U.S. companies offering insurance H1: p1 > p2
Test Statistic
Sample 1 : X1 =68, n1 =100, P1= X1/n1=0.68
Sample 2 : X2 =58, n2 =120, P2= X2/n2=0.483
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.573
Q^ Value For Proportion= 1-P^=0.427
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.68-0.483)/Sqrt((0.573*0.427(1/100+1/120))
Zo =2.936
| Zo | =2.936
Critical Value
The Value of |Z | at LOS 0.05% is 1.645
We got |Zo| =2.936 & | Z | =1.645
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Right Tail -Ha : ( P > 2.9362 ) = 0.00166
Hence Value of P0.05 > 0.00166,Here we Reject Ho

[ANSWERS]
1. Ho: p1 <= p2, H1: p1 > p2
2. LOS 0.05
3. LOS 0.05% is +1.645
4. Zo =2.936
5. We reject Ho, a higher proportion of U.S. companies offering insurance