Before they can be marketed all new medical devices must be

Before they can be marketed, all new medical devices must be approved by the Food and Drug Administration (FDA). A new device has a protective cover which needs to be removed easily. A similar device, already on the market, has a cover that requires an average force of 8 pounds to remove. The laboratory test data on a random sample of 9 of the new device indicates the following removal forces: 6.3, 8.4, 7.8, 6.4, 5.4, 8.0, 7.0, 6.2, 7.5 Assume that the removal force has a normal distribution with a standard deviation =2 lbs. Does the data support the conclusion that the new device requires an average removal force less than 8 lbs? When making decision, let the probability of making a type I error be no more than 0.01. What is the null and alternative hypothesis? Significance level? Test statistic? Computed value? Critical value? Decision? P-value?

Solution

Set Up Hypothesis
Null, H0: U=8
Alternate, H1: U<8
Test Statistic
Population Mean(U)=8
Given That X(Mean)=7
Standard Deviation(S.D)=2
Number (n)=9
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=7-8/(2/Sqrt(9)
Zo =-1.5
| Zo | =1.5
Critical Value
The Value of |Z | at LOS 0.01% is -2.33
We got |Zo| =1.5 & | Z | =2.33
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value : Left Tail - Ha : ( P < -1.5 ) = 0.0668
Hence Value of P0.01 < 0.0668, Here We Do not Reject Ho

[ANSWERS]
1. H0: U=8 , H1: U<8
2. 1% LOS
3. Zo =-1.5
4. Critical value = LOS 0.01% is 2.33
5. Reject Ho, if Z<-2.33
6. Do not Reject Ho, cover that requires an average force of 8 pounds