Question

In: Statistics and Probability

A psychologist developed a survey to measure people’s feelings toward online dating. Sixty randomly selected subjects...

  1. A psychologist developed a survey to measure people’s feelings toward online dating. Sixty randomly selected subjects were given the survey, which showed a sample mean of 8.2 and a sample standard deviation of 1.6.
    1. Construct the 95% confidence interval for the population mean. Show work.
    1. If the scale of results is from 1(very negative feelings) to 10 (very positive feelings), what can you say about this population based on your confidence interval?
  3. 2. Thirty professional skiers are randomly selected to determine the proportion that are over the age of 30. Suppose that 14 of the 30 skiers were 30 or older.
    1. Find the 95% confidence interval for the population proportion.
    1. Interpret the 95% confidence interval in context to this problem.
    2. Find the 99% confidence interval for the population proportion.
    3. How does the 95% confidence interval compare to the 99% confidence interval? Explain.

3. A project requires you to determine if a population of customers are interested in a particular new product. Calculate the sample size needed to be 95% confident that the sample proportion will fall within 0.08 of the population proportion.

    1. If you have a preliminary estimate that says 81% of customers are interested in this particular new product, what is the sample size needed?
    1. Assuming there is no preliminary estimate for the proportion, what is the sample size needed?

  1. Interpret the 95% confidence interval in context to this problem.

Solutions

Expert Solution

1)

a)


b) People feel more than moderate positive feelings about online dating.

2)

We are 95% confident that the population proportion of skiers that were 30 or older lie within the interval calculated above.

b)

c)

99% confidence interval is wider than the 95% confidence interval

3) The Margin of error = ME = 0.08

for 95% confidence

a)

the proportion of customers that are interested in this particular new product p= 0.81

the sample size needed

b)

Assuming there is no preliminary estimate for the proportion p=0.5

the sample size needed

orchestra answered 1 year ago
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