Question

A famous (in statistical circles) study involves a woman who claimed to be able to tell whether tea or milk was poured first into a cup. She was presented with eight cups containing a mixture of tea and milk, and she correctly identified which had been poured first for all eight cups.

a. Identify the observational units and variable in this study.

b. Identify the parameter for this study. (Hint: Th e long-run proportion that…)

c. Identify the sample size. Also, identify the observed value of the statistic for this study.

d. Is it possible that the woman could get all eight correct if she were randomly guessing with each cup?

e. Is it unlikely that the woman could get all eight correct if she were randomly guessing with each cup? (Answer for now based on your intuition, without doing any analysis

Answer 1

Answer:

(a) To Identify the observational units and variable in this study:

Answer:

The 8 cups are the observational units and binary variable is the  the woman correctly identifies the order of pouring tea and milk.

(b) To Identify the parameter for this study:

Answer:

We know that

The parameter is the unknown value of the population.Here the parameter for this study is the proportion of cups correctly identified by the woman.

(c) To Identify the sample size. Also, identify the observed value of the statistic for this study:

Answer:

Here the number of cups in the sample (n) is 8 so the sample size(n) is 8.

We know that the statistic is the value of the sample.Therefore the number of cups in the sample correctly identified by woman is  the statistic.

Here

x=8

Sample proportion (p) = x/n

= 8/8

Sample proportion (p) = 1

Therefore the Sample proportion of cups correctly identified by the women(p) is 1

(d) Is it possible that the woman could get all eight correct if she were randomly guessing with each cup?

Answer:

On the off chance that the woman was randomly guessing with each cup.then there is an equivalent possibility  of her guessing correct and incorrect answer for each cup.Hence,the probability of the woman guessing the correct order for each cup will be 50%.

(e) Is it unlikely that the woman could get all eight correct if she were randomly guessing with each cup?

Answer:

On the off chance that the woman was randomly guessing with each cup.then there is an equivalent possibility  of her guessing correct and incorrect order.Therefore the probability of guessing the correct and incorrect order is 0.5 for each.

Hence it is unlikely that the woman could get all eight correct answers if she were randomly guessing with each cup.