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FOR RYAN 1. The probability distribution shown...

FOR RYAN

1. The probability distribution shown here describes a population of measurements that can assume values of 0,2,4, and 6 each of which occurs with the same relative frequency.

X 0 2 4 6

P(x) ¼ ¼ ¼ ¼

A. Calculate the mean of all the different samples of n=2 that can be selected from this population and fill in the boxes with your choices.

2. Suppose a random sample of n=16 measurements is selected from a population with masn and standard deviation . For each of the following values of mean and s.d. give the values of mean x bar and s.d. x bar

A. Mean= 8 sd=4 B. mean =64 sd =16 C. mean =16 sd =32

A. Mean x bar = sd x bar = (type an integer or a decimal)

3.

a random sample of n=100 observations is selected from a population with mean =30 and sd=20. Approximate the possibilities shown below

a. P(x bar >= 28) b. P(22.1 <= x bar <=26.8 c. P(x bar = 27.0)

A. P(x bar>=28= round to 3 decimal places

4 The average salary for a certain professional is $65,000. Assume that the s.d. of such salaries is $28,000. Consider a random sample of 63 people in this profession and let x bar represent the mean salary for the sample.

a- What is mean x bar?

5 A random sample of 89 observations produced a mean x bar = 25.7 and a standard deviation s= 2.7

a- Find a 95% confidence interval for mu

b- Find a 90% confidence interval for mu

c- Find a 99% confidence interval for mu

A the 95 % confidence interval is _____-______

6 the mean and standard deviation of a random sample of n measurementsare equal to 34.8 and 3.7 respectively.

A find a 95 % confidence interval for mu if n=64

B find a 95 % confidence interval for mu if n=256

C find the widths of the confidence intervals found in parts a and b . what is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient fixed?

a. The 95% confidence interval for mu if n=64 is approximately _____-_____

7 the random sample shown below was selected from a normal distribution: 8,4, 10, 5, 7, 2

Complete parts a & B (b will not be shown until I enter data for a)

a. Construct a 95% confidence interval for the population mean mu round to two decimal places

b. Question to follow*****

8 for the binomial sample information summarized below, indicate whether the sample size is large enough to use the large sample approximations to construct a confidence interval for p

N= 400, p= 0.15 (there is a upside down v symbol above the p here)

Is the sample size large enough?

A no np>=15 and nq <15

B no np<15 and nq = 15 and nq>=15

D no np= 15

9 a newspaper reported that 80% of people say that some coffee shops are over priced. The source of this information was a telephone survey of 100 adults.

- ID the population of interest for this study-

- ID the sample for the study-

- ID the parameter of interest in this study-

- Find the 90% confidence interval for the parameter of interest.-

10 researchers conducted a study of variety in exercise workouts . a sample of 120 men and women were randomly divided into 3 groups with 40 people. Group 1 members varied their exercise routine in workouts , group 2 members performed the same exercise at each work out and group 3 had no set workout schedule or regulations for their workouts.

A by the end of the study17 people had dropped out of the first group. Estimate the drop out rate for exercisers who vary their workout routine. Use a 90% confidence interval

The 90% confidence interval is : (round to nearest 3 hundredths as needed)

(multi part Q)

11. if you wish to estimate a population mean with a sampling distribution error SE = 0.24 using a 95%confidence interval and you know from prior sampling that s.d squared is approx. equal to 3.4 how many observations would have to be included in your sample?

Round up to the nearest observation

12. suppose N=100,000, n = 25,000 and s = 50

a. compare the standard error of x bar using the finite population correction factor.

b. repeat part a assuming n=50,000

c. repeat part a assuming n= 100,000

d. compare parts a b and c and describe what happens to the standard error of x bar as n is increased

13 suppose you want to estimate a population proportion p and p (with upside down v above)= 0.42 ,

N=5,800 and n= 1,500. Find an approximate 95% confidence interval for p.

Round to 3 decimal places

14 a random sample size of n =20 was drawn from a pop of N=300. The measurements shown in the table were obtained.

45 18 51 25

32 21 35 21

41 38 23 51

20 36 41 43

32 38 38 50

1. The probability distribution shown here describes a population of measurements that can assume values of 0,2,4, and 6 each of which occurs with the same relative frequency.

X 0 2 4 6

P(x) ¼ ¼ ¼ ¼

A. Calculate the mean of all the different samples of n=2 that can be selected from this population and fill in the boxes with your choices.

2. Suppose a random sample of n=16 measurements is selected from a population with masn and standard deviation . For each of the following values of mean and s.d. give the values of mean x bar and s.d. x bar

A. Mean= 8 sd=4 B. mean =64 sd =16 C. mean =16 sd =32

A. Mean x bar = sd x bar = (type an integer or a decimal)

3.

a random sample of n=100 observations is selected from a population with mean =30 and sd=20. Approximate the possibilities shown below

a. P(x bar >= 28) b. P(22.1 <= x bar <=26.8 c. P(x bar = 27.0)

A. P(x bar>=28= round to 3 decimal places

4 The average salary for a certain professional is $65,000. Assume that the s.d. of such salaries is $28,000. Consider a random sample of 63 people in this profession and let x bar represent the mean salary for the sample.

a- What is mean x bar?

5 A random sample of 89 observations produced a mean x bar = 25.7 and a standard deviation s= 2.7

a- Find a 95% confidence interval for mu

b- Find a 90% confidence interval for mu

c- Find a 99% confidence interval for mu

A the 95 % confidence interval is _____-______

6 the mean and standard deviation of a random sample of n measurementsare equal to 34.8 and 3.7 respectively.

A find a 95 % confidence interval for mu if n=64

B find a 95 % confidence interval for mu if n=256

C find the widths of the confidence intervals found in parts a and b . what is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient fixed?

a. The 95% confidence interval for mu if n=64 is approximately _____-_____

7 the random sample shown below was selected from a normal distribution: 8,4, 10, 5, 7, 2

Complete parts a & B (b will not be shown until I enter data for a)

a. Construct a 95% confidence interval for the population mean mu round to two decimal places

b. Question to follow*****

8 for the binomial sample information summarized below, indicate whether the sample size is large enough to use the large sample approximations to construct a confidence interval for p

N= 400, p= 0.15 (there is a upside down v symbol above the p here)

Is the sample size large enough?

A no np>=15 and nq <15

B no np<15 and nq = 15 and nq>=15

D no np= 15

9 a newspaper reported that 80% of people say that some coffee shops are over priced. The source of this information was a telephone survey of 100 adults.

- ID the population of interest for this study-

- ID the sample for the study-

- ID the parameter of interest in this study-

- Find the 90% confidence interval for the parameter of interest.-

10 researchers conducted a study of variety in exercise workouts . a sample of 120 men and women were randomly divided into 3 groups with 40 people. Group 1 members varied their exercise routine in workouts , group 2 members performed the same exercise at each work out and group 3 had no set workout schedule or regulations for their workouts.

A by the end of the study17 people had dropped out of the first group. Estimate the drop out rate for exercisers who vary their workout routine. Use a 90% confidence interval

The 90% confidence interval is : (round to nearest 3 hundredths as needed)

(multi part Q)

11. if you wish to estimate a population mean with a sampling distribution error SE = 0.24 using a 95%confidence interval and you know from prior sampling that s.d squared is approx. equal to 3.4 how many observations would have to be included in your sample?

Round up to the nearest observation

12. suppose N=100,000, n = 25,000 and s = 50

a. compare the standard error of x bar using the finite population correction factor.

b. repeat part a assuming n=50,000

c. repeat part a assuming n= 100,000

d. compare parts a b and c and describe what happens to the standard error of x bar as n is increased

13 suppose you want to estimate a population proportion p and p (with upside down v above)= 0.42 ,

N=5,800 and n= 1,500. Find an approximate 95% confidence interval for p.

Round to 3 decimal places

14 a random sample size of n =20 was drawn from a pop of N=300. The measurements shown in the table were obtained.

45 18 51 25

32 21 35 21

41 38 23 51

20 36 41 43

32 38 38 50

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