Question

1. Suppose that a politician is thinking about introducing universal basic income for their state. A recent poll from a neighboring state indicates that .30 of the population supports this policy. The local politician believe that the same proportion supports it in their state. they conducted a survey of 50 people in their state and they found that 22 support the policy. Is there evidence that the population in the state supports the policy by the same amount as the neighboring State? The researcher is going to use a .10 alpha for the study.
   1. What is P and Q? (2)
   2. What is the standard deviation of this sample? What Distribution do we use for this why? (2)
   3. What the Statistic for the sample? (2)
   4. What is the P-Value for the sample? (2)
   5. Using the P-Value should be reject or accept the null? please interpret the results.

Answer 1

Given : n=50 , X=22 , The estimate of the sample proportion is ,

The null and alternative hypothesis is ,

  

The test is two-tailed test.

a. P=0.30 , Q=1-O=1-0.30=0.70

b. The standard deviation of this sample is ,

Here , nP=50*0.30=15>10 and nQ=50*0.70=35>10

Therefore , use the normal distribution.

c. The test statistic is ,

d. The p-value is ,

p-value=

; From standard normal distribution table

e. Decision : Here , p-value=0.0308<0.10

Therefore , reject the null hypothesis.

Conclusion : Hence , The local politician does not believe that the same proportion supports it in their state.