ASK YOUR TEACHER According to a survey conducted in a certain year by the Federal Communications...

ASK YOUR TEACHER

According to a survey conducted in a certain year by the Federal Communications Commission (FCC) of 3005 adults who were home broadband users, 31.5% of those surveyed had switched their service over the past 3 years. Of those who had switched service in the past 3 years, 53% were very satisfied, 37% were somewhat satisfied, and 10% were not satisfied with their service. Of the 68.5% who had not switched service in the past 3 years, 46% were very satisfied, 43% were somewhat satisfied, and 11% were not satisfied with their service.

(a) What is the probability that a participant chosen at random had not switched service in the past 3 years and was very satisfied with their service?

(b) What is the probability that a participant chosen at random was not satisfied with their service?

Expert Solution

We are given here the total sample size as:
n = 3005 as the broadband users.

Also for probabilities we are given here that:
P( switched service in last 3 years) = 0.315

Also for those who switched, the conditional probabilities given here as:
P( very satisfied | switched service in last 3 years) = 0.53,
P( somewhat satisfied | switched service in last 3 years) = 0.37,
P( not satisfied | switched service in last 3 years) = 0.1

For those who did not switch, we are given the probabilities here as:
P( very satisfied | not switched service in last 3 years) = 0.46,
P( somewhat satisfied | not switched service in last 3 years) = 0.43,
P( not satisfied | not switched service in last 3 years) = 0.11

A) The probability that the user had not switched service over the last 3 years and was very satisfied is computed using Bayes theorem here as:

P( very satisfied and not switched service in last 3 years)
= P(not switched service in last 3 years)P( very satisfied | not switched service in last 3 years)
= 0.685*0.46
= 0.3151

Therefore 0.3151 is the required probability here.

B) Probability that a person chosen at random was not satisfied with the service is computed using addition law of probability here as:

P( not satisfied ) = P( not satisfied | switched service in last 3 years) P(switched service in last 3 years) + P(not satisfied | not switched service in last 3 years)P(not switched service in last 3 years)

P( not satisfied ) = 0.315*0.1 + 0.685*0.11 = 0.10685

Therefore 0.10685 is the required probability here.

orchestra answered 2 years ago

A recent survey was conducted to determine how people consume their news. According to this survey,...

A recent survey was conducted to determine how people consume their news. According to this survey, 60% of men preferred getting their news from television. The survey also indicates that 42% of the sample consisted of males. Also, 42% of females prefer getting their news from television. Use this information to answer the following questions. a. Consider that you have 30000 people, given the information above, how many of them are male? b. Again considering that you have 30000...

A survey of families living in a certain city was conducted to collect information on the...

A survey of families living in a certain city was conducted to collect information on the following variables: age of the oldest person in the family, number of family members, number of males in the family, number of females in the family, whether or not they own a house, income of the family, whether or not the family took vacations during the past one year, whether or not they are happy with their financial situation, and the amount of their...

2. At a certain college, the student senate conducted a poll of 200 students to ask...

2. At a certain college, the student senate conducted a poll of 200 students to ask about using student services. In the poll, 24% of students had used tutoring services in the past week, 72% had used the library in the past week, and 14% had used both tutoring and the library in the past week. a. What percent of students used either tutoring or the library in the past week? b. What percent of students used neither tutoring nor...

In a survey of 2075 adults in a certain country conducted during a period of economic...

In a survey of 2075 adults in a certain country conducted during a period of economic uncertainty, 55% thought that wages paid to workers in industry were too low. The margin of error was 6 percentage points with 90% confidence. For parts (a) through (d) below, which represent a reasonable interpretation of the survey results? For those that are not reasonable, explain the flaw. We are 90% confident 55% (b) We are 84% to 96% confident 55% of adults in...

In a survey of 2065 adults in a certain country conducted during a period of economic...

In a survey of 2065 adults in a certain country conducted during a period of economic uncertainty, 64% thought that wages paid to workers in industry were too low. The margin of error was 4 percentage points with 95%confidence. For parts (a) through (d) below, which represent a reasonable interpretation of the survey results? For those that are not reasonable, explain the flaw. (a) We are 95% confident 64% of adults in the country during the period of economic uncertainty...

In a survey of 2085 adults in a certain country conducted during a period of economic...

In a survey of 2085 adults in a certain country conducted during a period of economic uncertainty, 67% thought that wages paid to workers in industry were too low. The margin of error was 9 percentage points with 90% confidence. For parts (a) through (d) below, which represent a reasonable interpretation of the survey results? For those that are not reasonable, explain the flaw. (a) We are 90% confident 67% of adults in the country during the period of economic...

ASK YOUR TEACHER Each of the following objects has a radius of 0.155 m and a...

ASK YOUR TEACHER Each of the following objects has a radius of 0.155 m and a mass of 2.07 kg, and each rotates about an axis through its center (as in this table) with an angular speed of 39.4 rad/s. Find the magnitude of the angular momentum of each object. (a) a hoop kg · m2/s (b) a solid cylinder kg · m2/s (c) a solid sphere kg · m2/s (d) a hollow spherical shell kg · m2/s

ASK YOUR TEACHER In this problem, assume that the distribution of differences is approximately normal. Note:...

ASK YOUR TEACHER In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer. In environmental studies, sex ratios are of great importance. Wolf society, packs, and ecology have been studied extensively at different locations in the...

5. According to a survey conducted with 132 adults by a sociology student, 73.4 % of...

5. According to a survey conducted with 132 adults by a sociology student, 73.4 % of them indicated that they were satisfied with their jobs. Test the claim that more than 70% of the people are satisfied with their jobs. Use a significance level of 0.01. For each question you need to find the following a) < 1 point > Write the given . Step 1 b) < 2 points > Write the claim and its opposite , then determine...

My Notes Ask Your Teacher The U.S. Census Bureau reported that in 2015 the proportion of...

My Notes Ask Your Teacher The U.S. Census Bureau reported that in 2015 the proportion of adult Americans, ages 25 and older, who have a bachelor's degree or higher is 0.325.† Consider the population of all adult Americans, ages 25 and over, in 2015 and define p̂ to be the proportion of people in a random sample from this population who have a bachelor's degree or higher. (a) Would p̂ based on a random sample of only 10 people from...

Question