2) Otto is running for mayor in Hamburg. He is interested in whether or not the

Question

2) Otto is running for mayor in Hamburg. He is interested in whether or not the proportion of residents of Hamburg who will vote for him is less than .5

To gain insight into this quetion, Otto took a random sample of 200 residents of Hamburg and determined that 98 of them will vote for him. Also, he estimated the standard error for the sample proportion to be .012

a) set up an appropriate hypothesis test to address Otto's concern.

b) using the above information, find the p - value

c) At a level of significance of .01 is there statistically significant evidence that the proportion of residents of Hamburg who will vote for Otto is less than .5?

Explanation / Answer

a)The null hypothesis is:

H0:P=0.5 (The population proportion is 50%)

Against the alternative hypothesis:

H1:P<0.5 (The population proportion is 50%)

b)The sample proportion is:

p=98/200=0.49

The test statistic is:

(p-P)/standard error for the sample proportion

=(0.49-0.5)/0.012

=-0.83

The P value is: 0.2033.

c)Since the P value is greater than 0.01, thus fail to reject the null hypothesis.

So, there is no statistically significant evidence that the proportion of residents of Hamburg who will vote for Otto is less than .5.

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.