A plan for an executive travelers’ club has been developed by airline on the pre

Question

A plan for an executive travelers’ club has been developed by airline on the premise that 5% of its current customers would qualify for membership. A random sample of 500 customers yielded 40 who would qualify.

1.Write down the null and alternative hypotheses. .

2.Explain whether this is a one-sided or a two-sided test, and why.

. 3.What is the value of the test statistic for your observed results? .

4.What is the p-value for your observed results? .

5.What is your conclusion? Please use words that a non-statistics student would understand, and justify your answer. Assume a significance level of .05. .

6.Based on your conclusion, what type of error are you risk at?.

Explanation / Answer

Set Up Hypothesis
Null, H0:P=0.05
Alternate, H1: P!=0.05
Test Statistic
No. Of Success chances Observed (x)=40
Number of objects in a sample provided(n)=500
No. Of Success Rate ( P )= x/n = 0.08
Success Probability ( Po )=0.05
Failure Probability ( Qo) = 0.95
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.08-0.05/(Sqrt(0.0475)/500)
Zo =3.0779
| Zo | =3.0779
Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo| =3.078 & | Z | =1.96
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != 3.07794 ) = 0.00208
Hence Value of P0.05 > 0.0021,Here we Reject Ho

[ANSWERS]
a. H0:P=0.05 , H0:P!=0.05
b. TWO Sided
c. Zo =3.0779
d. P-value, 0.00208
e. A plan for an executive travelers’ club has been developed by airline on the premise that not
5% of its current customers would qualify for membership

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