Question 3 options:

The economic dynamism, which is the index of productive growth (in dollars), for countries that are designated by the World Bank as middle-income are in following table ("SOCR data 2008," 2013).

Table: Economic Dynamism of Middle Income Countries

Countries that are considered high-income have a mean economic dynamism of 60.29. Do the data show that the mean economic dynamism of middle-income countries is less than the mean for high-income countries? Test at the 5% level.

(i) Which of the following statements correctly defines the null hypothesis H_O?

A.  μ < $60.29  

B.  p < $60.29

C.  μ = $60.29

D.  p = $60.29

(ii) Which of the following statements correctly defines the alternative hypothesis H_A?

A.  μ < $60.29  

B.  p < $60.29

C.  μ = $60.29

D.  p = $60.29

(iii) Enter the level of significance α used for this test:

Enter in decimal form. Examples of correctly entered answers:  0.01    0.02    0.05    0.10

(iv)  Determine sample mean x

Enter answer to nearest ten-thousandth, without "$" sign. Examples of correctly entered answers:

11.2385      0.0079     3.0500      7.4000

(v)  Determine sample standard deviation s :

Enter in decimal form to nearest thousandth. Do not enter "$" sign. Examples of correctly entered answers:

    0.002    9.050    11.300    210.715

(vi)  Determine degrees of freedom df

Enter answer as integer number without sign

(vii) Calculate and enter test statistic

Enter value in decimal form rounded to nearest ten-thousandth, with appropriate sign (no spaces). Examples of correctly entered answers:

–2.0140      –0.0307        +0.6000        +1.0009

(viii) Using tables, calculator, or spreadsheet: Determine and enter p-value corresponding to test statistic.

Enter value in decimal form rounded to nearest thousandth. Examples of correctly entered answers:

0.000     0.001     0.030     0.600      0.814 1.000

(ix) Comparing p-value and α value, which is the correct decision to make for this hypothesis test?

A. Reject H_o

B. Fail to reject H_o

C. Accept H_o

D. Accept H_A

(x) Select the statement that most correctly interprets the result of this test:

A. The result is statistically significant at .05 level of significance. Evidence supports the claim that the mean economic dynamism for a middle-income country is less than 60.29, the mean for high-income countries.

B. The result is statistically significant at .05 level of significance. There is not enough evidence to support the claim that the mean economic dynamism for a middle-income country is less than 60.29, the mean for high-income countries.

C. The result is not statistically significant at .05 level of significance. Evidence supports the claim that the mean economic dynamism for a middle-income country is less than 60.29, the mean for high-income countries.

D. The result is not statistically significant at .05 level of significance.   There is not enough evidence to support the claim that the mean economic dynamism for a middle-income country is less than 60.29, the mean for high-income countries.

Enter letter corresponding to most correct answer

Dr. Mack Lemore, an expert in consumer behavior, wants to estimate the average amount of money that people spend in thrift shops. He takes a small sample of 8 individuals and asks them to report how much money they had in their pockets the last time they went shopping at a thrift store. Here are the data:


19, 21, 14, 19, 20, 17, 25, 15.

Find the upper bound of a 95% confidence interval for the true mean amount of money individuals carry with them to thrift stores, to two decimal places. Take all calculations toward the final answer to three decimal places.

1. Suppose you would like to do a survey of undergraduate students on your campus to find out how much time on the average they spend studying per week. You obtain from the registrar a list of all students currently enrolled and draw your sample from this list.

a. What is your sampling frame?

b. What is your target population?

c. Explain how you would draw a simple random sample for this study.

d. Assume that the registrar’s list also contains information about each student’s major. One could then select a stratified random sample, stratifying on major. What main benefit can result from using a stratified random sample instead of a simple random sample? Would you expect this benefit to be obtained by stratifying on major? Explain.

e. How might you obtain a cluster sample? When should you consider using this type of sampling design?

f. Which type of sampling design is most appropriate for this research problem? Explain.

Design your own measure of central tendency that is:
a) unaffected by extreme scores
b)Inappropriate for use on nominal or ordinal data
demonstrate that your measure meets these requirements and contrast it with the commonly used measures of central tendency

1. How does one go about constructing a sampling frame?

2. When is stratified random sampling more efficient than simple random sampling?

3. When is it advantageous, or even necessary, to employ disproportionate stratified random sampling?

4. When is nonprobability sampling justified?

The brain volumes

​(cm cubedcm3​)

of 20 brains have a mean of

1155.11155.1

cm cubedcm3

and a standard deviation of

121.5121.5

cm cubedcm3.

Use the given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or significantly high. For such​ data, would a brain volume of

1378.11378.1

cm cubedcm3

be significantly​ high?

Significa

In 2011, when the Gallup organization polled investors, 34% rated gold the best long-term investment. In April of 2013 Gallup surveyed a random sample of U.S. adults. Respondents were asked to select the best long-term investment from a list of possibilities. Only 241 of the 1005 respondents chose gold as the best long-term investment. By contrast, only 91 chose bonds.

1. Compute the standard error for each sample proportion. Compute and describe a 95% confidence interval in the context of the question.
2. Do you think opinions about the value of gold as a long-term investment have really changed from the old 34% favorability rate, or do you think this is just sample variability? Explain.
3. Suppose we want to increase the margin of error to 3%, what is the necessary sample size?
4. Based on the sample size obtained in part c, suppose 120 respondents chose gold as the best long-term investment. Compute the standard error for choosing gold as the best long-term investment. Compute and describe a 95% confidence interval in the context of the question.
5. Based on the results of part d, do you think opinions about the value of gold as a long-term investment have really changed from the old 34% favorability rate, or do you think this is just sample variability? Explain.

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

A random sample of 5220 permanent dwellings on an entire reservation showed that 1648 were traditional hogans.

(a) Let p be the proportion of all permanent dwellings on the entire reservation that are traditional hogans. Find a point estimate for p. (Round your answer to four decimal places.)


(b) Find a 99% confidence interval for p. (Round your answer to three decimal places.)

Give a brief interpretation of the confidence interval.

1% of the confidence intervals created using this method would include the true proportion of traditional hogans.

99% of the confidence intervals created using this method would include the true proportion of traditional hogans.     

99% of all confidence intervals would include the true proportion of traditional hogans.

1% of all confidence intervals would include the true proportion of traditional hogans.

(c) Do you think that np > 5 and nq > 5 are satisfied for this problem? Explain why this would be an important consideration.

Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.

No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal.     

Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.

No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial.

The test statistic for a sign test is the smaller of the number of positive or negative signs. True False

An instructor who taught two sections of engineering statistics last term, the first with 25 students and the second with 30, decided to assign a term project. After all projects had been turned in, the instructor randomly ordered them before grading. Consider the first 15 graded projects.

(a) What is the probability that exactly 13 of these are from the second section? (Round your answer to four decimal places.)

(b) What is the probability that exactly 9 of these are from the first section? (Round your answer to four decimal places.)

(c) What is the probability that at all 15 of these are from the same section? (Round your answer to six decimal places.)

If you could please explain how to do it out on a calculator that would be much appreciated as the exam will ask us to solve this problem using a TI 84 plus CE.

Given the following data of temperature (x) and the number of times a cricket chirps in a second (y), run regression analysis and state the regression equation as long as there is a statistically significant linear relationship between the variables.

A friend who lives in Los Angeles makes frequent consulting trips to Washington, D.C.; 50% of the time she travels on airline #1, 20% of the time on airline #2, and the remaining 30%of the time on airline #3. For airline #1, flights are late into D.C. 15% of the time and late into L.A. 10% of the time. For airline #2, these percentages are 40% and 30%, whereas for airline #3 the percentages are 35% and 20%. If we learn that on a particular trip she arrived late at exactly one of the two destinations, what are the posterior probabilities of having flown on airlines #1, #2, and #3? Assume that the chance of a late arrival in L.A. is unaffected by what happens on the flight to D.C. [Hint: From the tip of each first-generation branch on a tree diagram, draw three second-generation branches labeled, respectively, 0 late, 1 late, and 2 late.] (Round your answers to four decimal places.)