# Math Help - Statistics questions

1. ## Statistics questions

So this is the problem set up:
32% of americans are in favor of outlawing cigarettes.
200 random americans were asked if they are in favor
54 were in favor of outlawing cigarettes
Overall question: At a = 0.05, is there sufficient evidence to conclude that less than 32% of Americans are in favor of outlawing cigarettes?

I've got step I:
Step I:
H0 : u = .32
Ha: u != .32

I need help with the rest (I'm stuck and don't know where to go from here!):

Step II: Standardized statistic and its value (this is all it says)

Step III: Decision rule

Step IV: Conclusion

A couple more problems that I'm not sure how to do:

2: Pulse rates of a random sample of 6 patients were recorded before and after given a certain drug:
Patient Before After
1 82 78
2 81 80
3 83 76
4 80 81
5 85 79
6 81 75

Let ud be the mean reduction in the pulse rates due to the drug and assume that the population of paired differences is normally distributed.

a) Find a 95% confidence interval for ud.
What I have so far:
ud = 3.83
n = 6

I think once I get this far I can do the rest.

Thanks for all your help!!!!

2. Originally Posted by merzbow
So this is the problem set up:
32% of americans are in favor of outlawing cigarettes.
200 random americans were asked if they are in favor
54 were in favor of outlawing cigarettes
Overall question: At a = 0.05, is there sufficient evidence to conclude that less than 32% of Americans are in favor of outlawing cigarettes?

I've got step I:
Step I:
H0 : u = .32
Ha: u != .32 Mr F says: No. It's Ha: u < 0.32.

I need help with the rest (I'm stuck and don't know where to go from here!):

Step II: Standardized statistic and its value (this is all it says)

Step III: Decision rule

Step IV: Conclusion

[snip]
There's a number of apporaches. One approach would be to construct a confidence at the desired significance level. See reply #3 of this thread for an example: http://www.mathhelpforum.com/math-he...-homework.html

Another approach is to calculate the p-value.

p-value = $\Pr(X \leq 54 |$ X ~ Binomial(n = 200, p = 0.32).

Compare this value with your chosen level of significance.

3. Originally Posted by merzbow
[snip]
2: Pulse rates of a random sample of 6 patients were recorded before and after given a certain drug:
Patient Before After
1 82 78
2 81 80
3 83 76
4 80 81
5 85 79
6 81 75

Let ud be the mean reduction in the pulse rates due to the drug and assume that the population of paired differences is normally distributed.

a) Find a 95% confidence interval for ud.
What I have so far:
ud = 3.83
n = 6

I think once I get this far I can do the rest.

Thanks for all your help!!!!
Read this: Paired Differences & Differences of Proportions

Or this: The Paired-T Confidence Interval