Problems

1. The probability distribution shown here describes a population of measurements that can assume values of 3, 4, 5, and 6, each of which occurs with the same relative frequency.

x p(x)

3 0.25

4 0.25

5 0.25

6 0.25

a. Calculate the mean of all the different samples of n=2 measurements that can be selected from this population. Select the correct choice below.

A. Sample 3.3/ 3.4/ 3.5 /3.6/ 4.3/ 4.4/ 4.5/ 4.6

X ___ ___ ___ ___ ____ ___ ___ _____

Sample 5.3 / 5.4 / 5.5 / 5.6/ 6.3/ 6.4/ 6.5/ 6.6

X ___ ___ ___ ___ __ ___ ___ _____

B. Sample 3.3 / 3.4/ 3.5/ 3.6/ 4.4 / 4.5 / 4.6 / 5.5 / 5.6 /6.6

X ___ ___ ___ ___ ___ ___ ___ __ ___ ____

C. Sample 3.4 / 3.5 / 3.6 / 4.3 / 4.5 / 4.6/ 5.3/ 5.4/ 5.6/ 6.3/ 6.4 / 6.5

X ___ ___ ___ ___ ___ ___ ___ __ ___ __ ___ ___

b. If a sample of n=2 measurements is randomly selected from the population, what is the probability that a specific sample will be selected?____ (Type exact number in the simplest form)

c. Complete the sampling distribution table.

x 3 _____ 4 4.5 _____ ____ 6

Probability ____ 1/8 ____ 0.25 3/16 1/8 ____

Type exact numbers in the simplest form

2. Suppose a random sample of n=16 measurements is selected from a population with a mean ? and standard deviation ?. For each of the following values of ? and ? give the values of ux- and ?x-

a. u=12 ?=2;

b. u=144 ?=16;

c. u=24 ?=24;

d. u=12 ?=80

a.ux-= __ ?-x = ____ (type an integer or a decimal)

b.ux-= __ ?-x = ____ (type an integer or a decimal)

c.ux-= __ ?-x = ____ (type an integer or a decimal)

d. ux-= __ ?-x = ____ (type an integer or a decimal)

3. A random sample of n=100 observations is selected from a population with ? =30 and ?=22. Approximate the probabilities shown below.

Round to three decimal places

a.P(x ? 28) =

b. P(22.1 ? x ? 26.8) =

c. P(x ? 28.2) =

d. P(x ? 27.0) =

4. A random sample of 89 observations produced a mean x=26.1 and a standard deviation s=2.7.

( Use integer or decimals for any numbers in the expression. Round to 2 decimal places as needed)

a. Find a 95% confidence interval is. ___ ___

b. The 90% confidence interval for ? is. ___ ___

c. The 99% confidence interval for ?.___ ___

5. The random sample shown below was selected from a normal distribution.

5, 8, 9, 6, 4, 4

a. Construct a 99% confidence interval for the population mean u. (round to 2 decimal places)

b. Assume that sample mean x and sample standard deviation remain exactly the same as those you just calculated but they are based on the sample of n=25 observations. Repeat part a. What is the effect of increasing the sample size on the width of the confidence interval?

The confidence interval is ___ ___ (round to 2 decimal places)

What is the effect of the sample size on the width of the confidence intervals?

a. as the sample size increases the width increases

b. as the sample size increases the width decreases

c. as the sample size increases the width stays the same

6. For the binomial sample information summarized below indicate whether the sample size is large enough to use the large sample approximation to construct a confidence interval for p.

n=100, p=0.60

Is the sample size large enough?

• No because np > 15 and nq 15 and nq > 15

• No because np < 15 and nq < 15

7. A newspaper reported that 80% of people say that some coffee shops are overpriced. The source of this information was a telephone survey of 200 adults.

a. Identify the population of interest.

Coffee shops/ 200 adults/ 80% of adults/ newspapers /a telephone survey

b. Identify the sample for the study

80% of adults/ newspapers/ coffee shops/ 200 adults/ adults/ telephone survey

c. Identify the parameter of interest in the study

p, the population proportion of adults who say that some coffee shops are overpriced.

d. The 95% confidence interval for the parameter interest is ___ ___ (round to 2 decimal places)

8. If you wish to estimate a population mean with a sampling distribution error SE=0.21 using a 95% confidence interval and you know from prior sampling that ?2 (thats squared) is approximately equal to 8.1 how many observations would have to be included in your sample?

The number of observations that would have to be is____rnd to nearest obvser.

9.. Suppose N=80,000, n=20,000, and s=50.

a. What is the standard error of x?

b. What is the standard error of x if n=40,000?

c. What is the standard error of x if n=80,000?

d. What happens to the standard error of x as n is increased?

It stays the same

It increases

It decreases

There is no correlation

10. Suppose you want to estimate a population proportion , p, and p^=0.36 and N=6,400, and n=1,700. Find an approximate 95% confidence interval for p.

An appropriate 95% confidence interval for p is __ + ___

11. What is specifically observed or what participants are asked in research study is which of the following?

Management question

Investigative question

Research question

Management dilemma question

Measurement question

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