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

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.

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.

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.

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

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!

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!

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

To understand and approach this problem, let's break it down step by step:

Step 1: Understanding the problem:
The problem presents information about right-sided dominance in humans for foot, eye, and kissing behavior. It focuses on a sample of 124 kissing couples, where 80 of them showed a right-leaning behavior. The goal is to determine the probability of observing such a difference and test if the estimated proportion of 2/3 for right-leaning kissing behavior is plausible.

Step 2: Analyzing the problem:
a) The first part of the problem asks for the probability that the observed number of couples who lean rightward differs from the expected value by at least as much as the observed value.

b) The second part of the problem asks if the observed data supports or suggests that the estimated proportion of 2/3 for right-leaning kissing behavior is unlikely.

Step 3: Calculating the probability:
To calculate the probability in part a), we need to use statistical methods. Specifically, we need to determine the probability of observing a deviation as large as or larger than the observed value of 80 right-leaning couples based on the expected proportion of 2/3.

Step 4: Hypothesis testing
In part b), we need to state and test the appropriate hypotheses to evaluate if the observed data supports the estimated proportion of 2/3 for right-leaning kissing behavior. This involves confirming or rejecting the null hypothesis based on the evidence provided by the data.

Step 5: Calculation and interpretation:
You'll need to use statistical methods such as hypothesis testing and probability calculations to answer both parts of the problem. These methods involve using formulas and conducting appropriate statistical tests.

It's important to note that the exact formulas and tests required may depend on the statistical techniques you have learned or are required to use in your course or assignment. Consider consulting your textbook, lecture notes, or seeking further guidance from your instructor to ensure you are applying the correct statistical methods for this specific problem.

Remember, every problem is unique, and the precise steps may vary. However, by breaking down the problem into smaller steps and using statistical concepts, you can approach it methodically and find a solution.