Thread: binomial, hypothesis tests - hard one

1. binomial, hypothesis tests - hard one

I'm really having trouble with this question and its pretty long too. If anyone can help me figure out the answers, i would really appreciate it.

In a recent survey, 480 of 600 Canadians polled stated that they were dissatisfied with politicians. Of the remaining 120 who were polled, 75% were satisfied with politicians and 25% had no opinion. Assuming that these findings can be generalized to all Canadians.

A) In a random sample of 4 Canadians, what is the probability that no more than 1 would be satisfied with politicians?

B) If two random and independent samples of Canadian's were taken, one consisting of 20 people and the other of 25 people, what is the probability that more than 18 of the sample of 20 or that between 19 and 23 (inclusively) of the sample of 25 would state a definite opinion (for or against) about politicians?

C) Among people who initially have no opinion, 50% will typically form an opinion (for or against an issue) after reading a relevant news report. In an attempt to get more people to form an opinion and take one side or the other on political issues, a news service has developed a new approach to presenting information on the issues. It tried this out on a random sample of 20 people who initially claimed that they had no opinion about an issue. The news service will conclude that the new approach is more effective if at least 15 of these 20 report a definite opinion about the issue after reading about it. What is the probability that the news will conclude that the new approach is more effective even if it is in fact no better than previous methods?

D) In a second study, the news service tries out the new approach to presenting information on a random sample of 25 people who initially expressed no opinion about an issue. The news service will test the hypothesis that the new approach is more successful than previous methods in getting people to form an opinion using alpha < 0.03. Suppose that the new approach would actually cause 80% of initially no-opinion people to form a definite opinion. Given this, what is the probability that the news service will draw the correct conclusion based upon their second study.

a) 0.89
b) 0.8302
c) 0.021
d) 0.891

2. Originally Posted by swoopesjr01
I'm really having trouble with this question and its pretty long too. If anyone can help me figure out the answers, i would really appreciate it.

In a recent survey, 480 of 600 Canadians polled stated that they were dissatisfied with politicians. Of the remaining 120 who were polled, 75% were satisfied with politicians and 25% had no opinion. Assuming that these findings can be generalized to all Canadians.

A) In a random sample of 4 Canadians, what is the probability that no more than 1 would be satisfied with politicians?
There are to cases here:
1)All four are dissafisfied
2)Exaclty one is satisfied, i.e. exactly 3 are disatisfyeied.

The probability of 1 is binomial probability problem with $p=480/600=.8$
Thus,
${4 \choose 4}(.8)^4(.2)^0=.4096$

The probability of 2 is,
${4 \choose 3}(.8)^3(.2)^1=.4096$

Thus intotal we have,
$.8192$

3. Originally Posted by ThePerfectHacker
There are to cases here:
1)All four are dissafisfied
2)Exaclty one is satisfied, i.e. exactly 3 are disatisfyeied.

The probability of 1 is binomial probability problem with $p=480/600=.8$
Thus,
${4 \choose 4}(.8)^4(.2)^0=.4096$

The probability of 2 is,
${4 \choose 3}(.8)^3(.2)^1=.4096$

Thus intotal we have,
$.8192$
Here you need to use $p=(120\times 0.75)/600$ as the probability that
someone is satisfied and $q=1-p$ that they were dissatisfied
or expressed no opinion.

RonL