Question

It is believed that the proportion of female college students who friend-zone a study buddy is about 29%.

1. a) Say? w?e s?elected? 15 ?random co?llege females?. I?s t?his? s?amp?le ?"lar?ge e???nough"? to us??e ?the Central Limit Theorem? What about 100? Check by using the assumptions for CLT.

2. b) Fill in the blank to write the sampling distribution when we obtain 100 females. Round to three decimal points if possible. ?̂~? (? , ?)

3. c) Find the probability that from the 100 females sampled, the sample proportion of friend-zoning a study buddy will be greater than 35%. Round to three decimal points.

Answer 1

a)

given

the proportion of female college students who friend-zone a study buddy is =  0.29 = p

a)

sample size 15 is not large enough to apply central liimit theorem.

to apply CLT we need atleast 30 sample size.

conditons to check assumption -

n*p >= 10 and n*(1-p) >=10

now when n = 15

15 * 0.29 = 4.35 < 10 and 15*(1-0.29) =  10.65 > 10

conditon not met

when n = 100

100 * 0.29 = 29 > 10 and 100 * (1-0.29) = 71 > 10

both conditions met.

b)

the sampling distribution when we obtain 100 females =

c)

We need to compute Pr(p^​≥0.35).

Based on the information provided, the population men of sample proportions and the corresponding standard error are:

Observe that:

np=100⋅0.29=29≥10 , nq=100⋅0.71=71≥10

which indicates that the assumption for normal approximation for the sampling distribution is met.

Now, the following is obtained using normal approximation:

Therefore, based on the information provided, it is concluded that

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