According to a study conducted for the New Zealand Society o

According to a study conducted for the New Zealand Society of Quality Control, overall, 52% of the women surveyed rated New Zealand products \"high\" in quality. Assuming that the sample survey included 1,000 women, conduct a test to determine whether the true percentage of women who rate New Zealand products \"high\" in quality is more than 50%. Use alpha=0.01. (a) State the null and alternative hypothesis. (b) Show that the conditions for the assumption of normality hold. (c) Calculate the value of the test statistic. Show your workings. (d) Find the p-value associated with this test. (e) Based on the answer obtained in part (d), the decision is: Reason for decision : (f) What type of error are you likely to commit in this test?

Solution

Set Up Hypothesis
Null, H0:P=0.5
Alternate, H1: P>0.5
Test Statistic
Number of objects in a sample provided(n)=1000
No. Of Success Rate ( P )= x/n = 0.52
Success Probability ( Po )=0.5
Failure Probability ( Qo) = 0.5
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.52-0.5/(Sqrt(0.25)/1000)
Zo =1.2649
| Zo | =1.2649
Critical Value
The Value of |Z | at LOS 0.01% is 2.33
We got |Zo| =1.265 & | Z | =2.33
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Right Tail - Ha : ( P > 1.26491 ) = 0.10295
Hence Value of P0.01 < 0.10295,Here We Do not Reject Ho

[ANSWERS]
a. H0:P=0.5 , H1: P>0.5
b. np>0.05, nq>0.05, It follows normality
c. Zo =1.2649
d. Ha : ( P > 1.26491 ) = 0.10295
e. Do not Reject Ho, percentage of women who rate New Zealand products \"high\" in quality is n\'t
more than 50%
f. Type II error