Question

A random sample of 300 teenagers were surveyed. 180 stated that they preferred to receive communication via text message rather than via email. Calculate the mean of the sampling distribution. Provide your answer below: ​

Answer 1

The mean of the sampling distribution for the proportion of teenagers who prefer texting over email is 180, calculated using the formula μ = np (mean = sample size × probability of success).

Step-by-step explanation:

To calculate the mean of the sampling distribution of a proportion, we should use the formula for the mean of a binomial distribution, which is μ = np. Here, n is the sample size, and p is the probability of success (in this case, the preference for texting).

From the problem, we are given:

• The sample size (n) is 300 teenagers.
• Number of teenagers who prefer texting (successes) is 180.

First, we need to find the probability of success (p):

p = number of successes / sample size

p = 180 / 300 = 0.6

Now, we can calculate the mean of the sampling distribution (which is the same as the population proportion for the sample).

μ = np = 300 × 0.6 = 180

Therefore, the mean of the sampling distribution is 180.