Question

1a.)Based on data from a survey of 1,700 randomly selected Facebook users, a 95% confidence interval for the proportion of all Facebook users who say it is OK for someone to "friend" his or her boss is

(0.42, 0.48).

What is the meaning of the confidence level of 95% that is associated with this interval?

Of all possible random samples, 5% would result in an interval that includes the actual value of the population proportion

. Of all possible random samples, 95% would result in an interval that is centered at the actual value of the population proportion.    

Of all possible random samples, 95% would result in an interval that includes the actual value of the population proportion.

Of all possible random samples, 95% would result in an interval that lies below the actual value of the population proportion.

Of all possible random samples, 5% would result in an interval that lies above the actual value of the population proportion.

1b)

Many employers are concerned about employees wasting time by surfing the Internet and e-mailing friends during work hours. The article "Who Goofs Off 2 Hours a Day? Most Workers, Survey Says" summarized data from a large sample of workers.† Suppose that the CEO of a large company wants to determine whether the mean wasted time during an 8-hour workday for employees of her company is less than the mean of 120 minutes reported in the article. Each person in a random sample of 10 employees is asked about daily wasted time at work (in minutes). Participants would be guaranteed anonymity to obtain truthful responses. Suppose the resulting data are as follows.

111, 148, 140, 109, 146, 108, 103, 95, 98, 85

(a)

Calculate the point estimate (in minutes) for the population mean.

(b)

Assume that the population standard deviation is known to be σ = 54.8 minutes. We would like to estimate the population mean with 95% confidence. Calculate the margin of error (in minutes) of the point estimate. (Use a table or technology. Round your answer to three decimal places.)

(c)

Find a 95% confidence interval. (Round your answers to three decimal places.)

Answer 1

solution:-

1a.)Based on data from a survey of 1,700 randomly selected Facebook users, a 95% confidence interval for the proportion of all Facebook users who say it is OK for someone to "friend" his or her boss is

(0.42, 0.48)

What is the meaning of the confidence level of 95% that is associated with this interval?

=> Of all possible random samples, 95% would result in an interval that includes the actual value of the population proportion

1b)

given data = 111, 148, 140, 109, 146, 108, 103, 95, 98, 85

(a) point estimate = 114.3

(b) margin of error

the value of 95% confidence from z table is 1.96

margin of error formula

=> z * σ/sqrt(n)

=> 1.96 * 54.8/sqrt(10)

=> 33.965

(c) 95% confidence interval

formula

point estimate +/- margin of error

=> 114.3 +/- 33.965

=> (80.335 , 148.265)