Question

1. Old Billie is very excited for Letecia, but she is also worried about her. So she conducts a poll of 400 Avocado Park residents who have gone on a first date in the last month and asks them if they are glad they did. Old Billie has decided that she will stop the date from happening if there is less than a 75% chance that Letecia will be happy. Hadey tells her she is being extra, so she settles on a significance level of 0.01 to be safe.
   1. Identify the population of interest.
   2. Identify the variable of interest. What type of variable is it?
   3. What would be a suitable parameter for summarizing the variable you identified in part b?
   4. Write appropriate null and alternative hypotheses for Old Billie’s research goals.
   5. What assumptions must you make to perform a test on the null hypothesis you chose in part d?
   6. Calculate the P-Value and make a decision about the null hypothesis based on it.
   7. Summarize your decision from part f.

Answer 1

a) The population of interest are the Avocado Park residents who have gone on a first date in the last month.

b) The variable of interest is response to question whether the residents of Avocado Park who had gone on a first date in last month are glad they did it or not.

It is binary (or, dichotomous) variable as it can only have two response Yes and No.

c) The parameter for summarising our variable of interest is the Proportion of Avocado Park residents gone on the first date in last month who are glad that they did the date (P).

d) Null hypothesis : P < 0.75

Alternative hypothesis : P 0.75

e) To test the null hypothesis, we can perform the z test for which we have to check the normality assumptions that whethere the population can assumed to be approximately normal or not.

If n*p 10

and n*(1-p) 10

Then, the population can be assumed to be approximately normal.