Question

A national charity contacted 100 randomly selected people by phone, and 7 percent of those contacted made a donation to the charity. The population proportion of those who make a donation when contacted by phone is known to be p=0.05. For samples of size 100, which of the following best interprets the mean of the sampling distribution of the sample proportion of people who make a donation when contacted by phone?

a. For all random samples of 100 people contacted by phone, the sample proportion of those who make a donation will be 0.05.
b. For all random samples of 100 people contacted by phone, the sample proportion of those who make a donation will be 0.07.
c. The mean of all sample proportions of those who make a donation from all random samples of 100 people contacted by phone is 0.05.
d. The mean of all sample proportions of those who make a donation from all random samples of 100 people contacted by phone is 0.07.
e. The probability that the mean of the sampling distribution of sample proportions is greater than 0.07 is 0.05.

Answer 1

Answer: c. The mean of all sample proportions of those who make a donation from all random samples of 100 people contacted by phone is 0.05.

Step-by-step explanation:

Mean of the sampling distribution of the sample proportion = p (Population proportion.)

Here, the population proportion of those who make a donation when contacted by phone is known to be p=0.05.

Then, Mean = p = 0.05

Hence, the correct option is

c. The mean of all sample proportions of those who make a donation from all random samples of 100 people contacted by phone is 0.05.

Answer 2

This question is based on the concept of statistics. Hence, the correct option is  (c) The mean of all sample proportions of those who make a donation from all random samples of 100 people contacted by phone is 0.05.

Given:

A national charity contacted 100 randomly selected people by phone, and 7 percent of those contacted made a donation to the charity. The population proportion p=0.05. For samples of size 100.

According to the question,

Mean of  sampling distribution of the sample proportion = p (Population proportion.)

It is given that, the population proportion of those who make donation when contacted by phone is known to be p=0.05.

Thus, Mean = p = 0.05

Hence, the correct option is  (c) The mean of all sample proportions of those who make a donation from all random samples of 100 people contacted by phone is 0.05.

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