I really need help with this problem. I am not sure what the question is asking and how to approach it! Thanks in advance!

Question

Its known that 2/3 of humans have a dominant right foot or eye. Is there also a right-sided dominance in kissing behaviour? In a sample of 124 kissing couples, both people in 80 of the couples leaned more rightward than leftward.

a)If 2/3 of ALL kissing couples have this right-leaning behavior, whats the probability that the number in a sample of 124 who do so differs from the expected value by at least as much as what was actually observed?

b)Does the result of the experiment suggest that 2/3 figure is implausible for kissing behavior? state and test the appropriate hypotheses.

Answer 1

You can try a proportional one-sample z-test for this one since this problem is using proportions.

Here's a few hints to get you started:

Null hypothesis:
Ho: p = .67 -->meaning: population proportion is equal to .67 (converting the fraction 2/3 to a decimal).
Alternative hypothesis:
Ha: p does not equal .67 -->meaning: population proportion does not equal .67 (this is a two-tailed test because the question is just asking if there is a difference).

Using a formula for a proportional one-sample z-test with your data included, we have:
z = .645 - .67 -->test value (80/124 is approximately .645) minus population value (.67) divided by
√[(.67)(.33)/124] --> .33 represents 1-.67 and 124 is sample size.

Finish the calculation. Remember if the null is not rejected, then there is no difference. If you need to find the p-value for the test statistic, check a z-table. The p-value is the actual level of the test statistic.

I hope this will help.

Answer 2

Hi, I understand that part now and got -0.5873 as the z value. However, I do not know how to find the critical z value for the two-tailed test, and without a given alpha value.

Also, if I am correct, this hypothesis corresponds to part b) of the question?
Can you give me suggestions for part a) as well? The book doesn't explain very well and have no similar examples...

Thank you so much.

Answer 3

For the hypothesis test, if i were to use significance level of .10. Is the two tailed critical z value equal to + or - 1.645? Since z (-0.5873) is smaller than critical z, I said that Ho should not be rejected so 2/3 figure is NOT implausible for kissing behavior. Is this correct?

I still need help on part a).

thanks

Answer 4

Your calculations look correct, as well as your conclusion.

Part a) might be looking for the p-value, which is the actual level of the test statistic (z = -0.5873). If that is the case, then you can look up the p-value using the test statistic and a z-table.

Good job!

Answer 5

Hi again. I did more studying on testing the hypothesis and tried the problem again. Can you check if it is correct?

a) I made Ho=2/3, Ha=otherwise. I did the z test and got z=-0.0508. I think this means that 5.08% of the time, the sample will differ by AT LEAST as much as what was observed.(lower-tail) But I have a question here. First does this make sense? Also, because this problem is two-tailed, do I have to multiply by 2 to consider the upper tail as well? (IE. 10.16% probability that the number in a sample of 124 differ from the expected value by at least as much what was actually observed.)

b) I used the hypothesis test from part(a)and a significance level of 0.10. Since this is two-tailed the rejection region is if z>z(a/2) or z<-z(a/2). z(.05)=1.645. Since -0.0508>-1.645, do not reject hypothesis under 90% CI. Therefore the kissing behavior is plausible.

Let me know if this makes sense. Thanks!

Answer 6

since the level of significance is not given you should assume it is at the .05 level.