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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

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Answer:

The answers are given below.

Step-by-step explanation:

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'.

MrRoyal

The values of p1 and p2 are not dependent on each other. So:

  • The expected values of p1 and p2 is between 0 and 1 (inclusive)
  • p1 and p2 can be vastly different from 0.66
  • p1 and p2 can be similar or different
  • The concept is probability

Given that:

[tex]p= 0.66[/tex]

[tex]p_1 \to[/tex] proportion of group 1

[tex]p_2 \to[/tex] proportion of group 2

The expected values of p1 and p2

Because p1 and p2 are proportions, the values of p1 and p2 cannot be less than 0; and these values cannot be greater than 1.

So, the expected values are:

[tex]0 \le p_1, p_2 \le 1[/tex]

Will p1 and p2 be different from p

As explained earlier, the expected values of p1 and p2 can take any value between 0 and 1.

The values of p1 and p2 are independent of [tex]p= 0.66[/tex].

So, p1 or p2 can be vastly different from [tex]p= 0.66[/tex]

Similar or different values in p1 and p2

Recall that: the expected values are:

[tex]0 \le p_1, p_2 \le 1[/tex]

Both values are independent of each other.

So, it will not be surprising, if both values are similar or different.

The statistical concept

When terms like proportions and selections are used as used in this question, the statistical concept is probability.

Read more about proportions and probabilities at:

https://brainly.com/question/6655434

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