A company manufactures U-100 insulin syringes designed to contain 1 milliliter (

Question

A company manufactures U-100 insulin syringes designed to contain 1 milliliter (ml) of a solution containing insulin. The actual distribution of solution volumes in these syringes is Normal, with mean µ and standard deviation = 0.05 ml. We randomly select 8 syringes and measure the volume of solution in each. The results of these 8 measurements (all in ml) are: 1.05 1.04 1.06 1.01 0.98 0.98 1.03 0.99 Do these data give evidence that the true population mean solution volume is not 1 ml? The P-value for the appropriate null and alternative hypotheses is
0.018
0.161
0.322
0.989

Explanation / Answer

Set Up Hypothesis
Null Hypothesis H0: U=1
Alternate Hypothesis H1: U!=1
Test Statistic
Population Mean(U)=1
Given That X(Mean)=1.0175
Standard Deviation(S.D)=0.05
Number (n)=8
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=1.0175-1/(0.05/Sqrt(8)
Zo =0.9899
| Zo | =0.9899
Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo| =0.9899 & | Z | =1.96
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value : Two Tailed ( double the one tail ) - Ha : ( P != 0.9899 ) = 0.3222
Hence Value of P0.05 < 0.3222, Here We Do not Reject Ho

[ANSWER] 0.322

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