In the Texas senate races, a candidate must clear 50% to avoid a runoff election. In a recent poll of 1040 voters in Texas, 51% of voters preferred candidate. We will a hypothesis test to see if we can say at the 5% significance level that more than 50% of voters in Texas prefer candidate based on this poll. State the null and alternative hypothesis. Find the test-statistic. Find the P-value. Make a conclusion. Interpret your answer.
In the Texas senate races, a candidate must clear 50% to avoid a runoff election. In a recent poll of 1040 voters in Texas, 51% of voters preferred candidate. We will a hypothesis test to see if we can say at the 5% significance level that more than 50% of voters in Texas prefer candidate based on this poll.
- State the null and alternative hypothesis.
- Find the test-statistic.
- Find the P-value.
- Make a conclusion.
- Interpret your answer.
1
Stating the appropriate null and alternative hypotheses:
The hypotheses are given below:
Null hypothesis:
H0 :p =0.50.
Alternative hypothesis:
Ha :p >0.50
2
Since the data deals with proportion, the z-test for proportion can be used for the testing.
Finding the test-statistic for the hypothesis test:
Test statistic:
The test statistic for hypothesis test for proportion is given by:
Z = (p-p0)/(√( p0 q0/n)
= (0.51-0.50)/√(0.50×0.50/1040)
= 0.64498
3)
The p-value is 0.2595 using the Excel function ‘= 1-NORM.S.DIST(0.64498,1)’
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