In 1994 on the 25th anniversary of the Apollo moon landing a

In 1994, on the 25th anniversary of the Apollo moon landing, a poll was conducted which asked the following question: “Do you think the original project was too costly?” A researcher wishes to use the results of the poll to show that a minority of the population feel that the project is too costly. a) Describe, in words, what the population proportion, p, is in this situation. b) Set up H0 and Ha (Remember Ha is the research hypothesis). c) A random sample of 800 people was taken. Of these individuals, 390 felt the project was too costly. i) What is the P-value? (Hint: Use the normal approximation to the binomial.) ii) What decision would you make if you were using = .01? iii) What decision would you make if you were using = .05? iv) Based on the observed data, what is the smallest type I error rate for which you could reject H0?

Solution

Set Up Hypothesis
Null, H0:P=0.5
Alternate,minority of the population feel that it is costly H1: P<0.5
Test Statistic
No. Of Success chances Observed (x)=390
Number of objects in a sample provided(n)=800
No. Of Success Rate ( P )= x/n = 0.4875
Success Probability ( Po )=0.5
Failure Probability ( Qo) = 0.5
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.4875-0.5/(Sqrt(0.25)/800)
Zo =-0.7071
| Zo | =0.7071
Critical Value
The Value of |Z | at LOS 0.01% is 2.33
We got |Zo| =0.707 & | Z | =2.33
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Left Tail -Ha : ( P < -0.70711 ) = 0.23975
Hence Value of P0.01 < 0.23975,Here We Do not Reject Ho

[ANSWERS]
a. Proportion of people who feel that a minority of the population is too costly
b. H0:P=0.5 , H1: P<0.5
c.
i. P-Value: Left Tail -Ha : ( P < -0.70711 ) = 0.23975
ii. AT 0.01 Do not Reject Ho
iii. AT 0.05 Do not Reject Ho