Answer to Question #175454 in Statistics and Probability for Denisse Bisuña

Question

1.The mean scores of a random sample of 17 students who took a special test is 83.5. If the standard deviation of the scores is 4.1, and the sample comes from an approximately normal population, find the point and the interval estimates of the population mean adopting a confidence level of 95%.

a. point estimate

b. interval estimate

2.The mean age of 20 youth volunteers in a community project is 17.5 years with a standard deviation of 2 years. if the sample comes from an approximately normal distribution, what are the point and the interval estimates of the population mean? Use 99% confidence level.

a. point estimate

b. interval estimate

3.The average weight of 25 chocolate bars selected from a normally distributed population is 200 g with a standard deviation of 10 g. Find the point and the interval estimates using 95% confidence level.

a. point estimate

b. interval estimate

4.Explain the difference between a point estimate and an interval estimate.

Answer 1

μ = M ± Z(s_M)

1. M = 83.5

Z = 1.96

s_M = $\sqrt{(4.1^2/17)}$ = 0.99

μ = M ± Z(s_M)

μ = 83.5 ± 1.96 $\times$ 0.99

μ = 83.5 ± 1.949

2. M = 17.5

Z = 2.58

s_M = $\sqrt{(2^2/20)}$ = 0.45

μ = M ± Z(s_M)

μ = 17.5 ± 2.58 $\times$ 0.45

μ = 17.5 ± 1.152

3. M = 200

Z = 1.96

s_M = $\sqrt{(10^2/25)}$ = 2

μ = M ± Z(s_M)

μ = 200 ± 1.96 $\times$ 2

μ = 200 ± 3.92

4. A point estimate is a single value estimate of a parameter. For instance, a sample mean is a point estimate of a population mean. An interval estimate gives you a range of values where the parameter is expected to lie. A confidence interval is the most common type of interval estimate.