Question 64429: A random sample of 1000 students showed 535 perfer coffee over tea. If the percentage of students who prefer coffee is p, test Ho: p =.50 versus Ha: p>.50 at the .05 significance level. My conclusion should be:
1. reject Ho and conclude the evidence supports Ha
2. fail to reject Ho
3. gather more data because I am unable to complete the analysis as stated
4. inclusive of Student's (t) test because of the sample size
5. none of these answers
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A random sample of 1000 students showed 535 prefer coffee over tea. If the percentage of students who prefer coffee is p, test Ho: p =.50 versus Ha: p>.50 at the .05 significance level. My conclusion should be:
1. reject Ho and conclude the evidence supports Ha
2. fail to reject Ho
3. gather more data because I am unable to complete the analysis as stated
4. inclusive of Student's (t) test because of the sample size
5. none of these answers
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Ho: p=0.5
Ha: p>0.5
n=1000, x=535, p-hat=535/1000,alpha=5%
This calls for a right-tailed test with a critical t-value =1.65
Test statistic = t(535/1000)=[0.535-0.50)/sqrt[0.5*0.5/1000]=2.21
p-value associated with this test statistic = 0.013...
Since the p-value is less than alpha, "Reject Ho and conclude
the evidence supports Ha".
Cheers,
Stan H.
Cheers,
Stan H.
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