Question

A professor states that in the United States the proportion of college students who own iPhones is .66. She then splits the class into two groups: Group 1 with students whose last name begins with A-K and Group 2 with students whose last name begins with L-Z. She then asks each group to count how many in that group own iPhones and to calculate the group proportion of iPhone ownership. For Group 1 the proportion is p1 and for Group 2 the proportion is p2. To calculate the proportion you take the number of iPhone owners and divide by the total number of students in the group. You will get a number between 0 and 1.

• What would you expect p1 and p2 to be?
• Do you expect either of these proportions to be vastly different from the population proportion of .66?
• Would you be surprised if p1 was different than p2?
• Would you be surprised if they were the same or similar?
• What statistical concept describes the relationship between the first letter of someone's last name and whether or not they own an iPhone?

I would expect P1 to be close to .66 while P2 would be shy of .66 by a more significant percentage. My reasoning behind these statements is simple. There are bound to be fewer people in group P2 than P1 just due to the letters X and Z being so uncommon as first letters in last names. Also, we have to give a proper examination to the outliers which will give a skewed percentage.

I would be very taken aback if the two sample groups percentages were close. Just because there is not be a very high probability of similarity between the two groups.

Answer 1

p1 and p2 can have any values from 0 to 1 (both end inclusive) or,

0 ≤ p1 , p2 ≤ 1.

No, it can't be expected that the proportions p1 and p2 is vastly different from the population proportion, which is 0.66.

No, there is nothing to get surprised if p1 is different from p2.

Although it may be slightly surprising if p1 and p2 are the same but it is nothing to get surprised if the two are similar or near about the same.

The statistical concept which describes the relation between the first letter of someone's last name and whether or not they own an iPhone is 'Probability'.