A particular poll tracks daily the percentage of citizens from a certain country who approve or disapprove of the job the President is doing. Daily results are based on telephone interviews with approximately 1400 national adults. The poll reported that 50​% of adults approve of the President doing his job. A media outlet claimed the true proportion to be 52​%. Does the poll contradict this​ claim? Complete parts a through c. ​a) Test the appropriate hypothesis. Find a 95​% confidence interval for the sample proportion of adults in the country who approved of the​ President's performance. Check conditions. Which conditions for the confidence interval have been​ met? Select all that apply. A. ​Success/Failure Condition B. ​10% Condition C. Randomization Condition Let p be the proportion of adults in the country who approved of the​ President's performance. What are the null and alternative​ hypotheses? Upper H 0​: p ▼ greater than equals less than not equals nothing vs. Upper H Subscript Upper A​: p ▼ equals greater than less than not equals nothing ​(Type integers or decimals. Do not​ round.) Find the 95​% confidence interval. left parenthesis nothing comma nothing right parenthesis ​(Round to three decimal places as​ needed.) ​b) Does your confidence interval provide evidence to contradict the​ claim? Select the correct choice below and fill in the answer box to complete your choice. ​(Type an integer or a decimal. Do not​ round.) A. Since nothing is within the​ interval, the confidence interval does not provide evidence that contradicts the media​ outlet's claim. B. Since nothing is within the​ interval, the confidence interval provides evidence that contradicts the media​ outlet's claim. C. Since nothing is not within the​ interval, the confidence interval provides evidence that contradicts the media​ outlet's claim. D. Since nothing is not within the​ interval, the confidence interval does not provide evidence that contradicts the media​ outlet's claim. ​c) What is the significance level of the test in​ b? Explain. Select the correct choice below and fill in the answer box to complete your choice. ​(Type an integer or a decimal. Do not​ round.) A. The significance level is alphaequals nothing because the test is a​ two-tail test based on a 95​% confidence interval. B. The significance level is alphaequals nothing because the test is a​ one-tail test based on a 95​% confidence interval. C. The significance level is betaequals nothing because the test is a​ two-tail test based on a 95​% confidence interval. D. The significance level is betaequals nothing because the test is a​ one-tail test based on a 95​% confidence interval.

Consider the following heart disease mortality data from two hypothetical countries, including a low-income and high-income country.

A. Use these data to calculate the overall crude death rates from heart disease in the hypothetical high and low income countries.

B. Based on these data, do you think that it is better to compare the heart disease death rates in the two countries using the overall crude rate or the age-standardized rate for each country? Briefly justify your answer.

An online account password for a certain website consists of eight characters, where at least one must be a digit (i.e. a number from 0-9).

a. How many different passwords are possible if only lowercase letters and digits can be used?

b. How many different passwords are possible if a user wants to include single capital letter somewhere in their password?

c. If a computer program randomly generates eight characters (such that each could be either a digit or any lowercase letter), what is the probability that a valid password is generated?

Let ? and ? be two independent uniform random variables such that ?∼????(0,1) and ?∼????(0,1).

A) Using the convolution formula, find the pdf ??(?) of the random variable ?=?+?, and graph it.

B) What is the moment generating function of ??

A sociologist wants to know about the stress levels in the nation over the past years. In the late 2000s, the average score on the Brown's Stress Inventory (BSI) in the nation was 19 with a standard deviation of 6.6. A current day sample of 30 produces a mean BSI score of 18.4. What can the sociologist concludes with an α of 0.01?

a) What is the appropriate test statistic?
---Select--- na z-test one-sample t-test independent-samples t-test related-samples t-test

b)
Population:
---Select--- current sample the nation the years stress levels the BSI score
Sample:
---Select--- current sample the nation the years stress levels the BSI score

c) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
critical value =  ; test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0

d) If appropriate, compute the CI. If not appropriate, input "na" for both spaces below.
[  ,  ]

e) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and select "na" below.
d =  ;   ---Select--- na trivial effect small effect medium effect large effect
r² =  ;   ---Select--- na trivial effect small effect medium effect large effect

f) Make an interpretation based on the results.

There has been a significant increase in depression over the years.There has been a significant decrease in depression over the years.    There has been no significant change in depression over the years.

Imagine that you are purchasing small lots of manufactured product. If it is very costly to test a single item, it may be desirable to test a sample of items from the lot instead of testing every item in the lot. Suppose each lot contains 10 items. You decide to sample 3 items per lot and reject the lot if you observe 1 or more defectives.

a) If the lot contains 1 defective item, what is the probability that you will accept the lot?

b) What is the probability that you will accept the lot if it contains 2 defective items?

Describe what it means that your statistical analysis was statistically significant at the p-value of .05? What does this really mean

1. Among frequency distributions for physical stamina scores, the greatest variability probably would occur in the distribution for
   1. well‑trained athletes.
   2. patients at a health clinic.
   3. infants.
   4. the general population.

2. When calculating the variance, each deviation is squared in order to
   1. eliminate negative signs from deviation scores.
   2. generate squared units of measurement.
   3. emphasize the contributions of larger deviations.
   4. attain all of the above.

3. Five children are tested for IQ and their scores are: 110, 160, 100, 100, 110. What is the best way to describe the central tendency of these scores?
   1. the mode
   2. the median
   3. the mean
   4. the range

4. Knowing the standard deviation of a set of scores, it is possible to calculate
   1. range
   2. variance
   3. the mean
   4. the frequency distribution

5. When summarizing data, why is it important to report both the mean and the standard deviation?
   1. two sets of data could have the same mean but different amounts of variability
   2. this way both descriptive and inferential statistics are covered
   3. this way the null hypothesis can be evaluated
   4. this enables the researcher to avoid Type I and Type II errors

6. Indicate which one of the following sets of observations has the larger standard deviation. (Calculations aren't necessary to answer this question.)
   1. 4045, 4050, 4055
   2. 5, 20, 35
   3. 530, 540, 550
   4. 988, 1000, 1012

7. If the distribution of weekly study times reported by college students has a mean of 25 hours with a standard deviation of 10 hours, this implies that
   1. a small minority study either less than 5 hours or more than 45 hours.
   2. a majority study between 15 and 35 hours.
   3. individuals deviate, on the average, approximately 10 hours from the mean of 25 hours.
   4. all of the above

8. A key property of the interquartile range is its
   1. resistance to the distorting effect of extreme observations.   
   2. sensitivity to all observations.
   3. sensitivity to extreme observations.
   4. use of information from only two observations.

9. If the normal curve is used to describe the distribution of IQ scores for all currently enrolled students in U.S. colleges and universities, all students are identified with the
   1. smooth normal curve.
   2. total area under the normal curve.
   3. maximum height of the normal curve.
   4. horizontal axis.

10. Since the normal curve never actually touches the horizontal axis,
    1. most of the area is in its extremities.
    2. the total area is infinitely large.
    3. the normal tables are only approximate.
    4. very extreme observations are possible.           

11. Any particular normal curve is transformed into a new normal curve whenever changes occur in
    1. its mean.                   
    2. its standard deviation.          
    3. both its mean and its standard deviation.                   
    4. either its mean or its standard deviation.

12. For any z score, the corresponding proportions in columns B and C always sum to
    1. 1.0000
    2. 0.5000
    3. 0.0000
    4. the value of z.

13. If a positively skewed distribution of incomes is transformed into a distribution of z scores, the shape of the new distribution will be
    1. normal.
    2. positively skewed.
    3. intermediate between normal and positively skewed.
    4. standard normal.

14. Which of the following test scores would be the most preferable on a psychology exam?
    1. a score of 40 in a distribution with a mean of 35 and a standard deviation of 5
    2. a score of 36 in a distribution with a mean of 30 and a standard deviation of 4
    3. a score of 30 in a distribution with a mean of 24 and a standard deviation of 2
    4. a score of 25 in a distribution with a mean of 15 and a standard deviation of 4

15. Transformations from z scores to other types of standard scores
    1. change the shape of the original distribution, but not the relative standing of any test score within the distribution.
    2. change the relative standing of any test score within the original distribution, but not the shape of the distribution.
    3. change both the shape of the original distribution and the relative standing of any test score within the distribution.
    4. change neither the shape of the original distribution nor the relative standing of any test score within the distribution.

5. An important characteristic of histograms, frequency polygons, and stem and leaf displays is a. size. b. total area. c. relative area. d. shape. 6. A frequency distribution of standardized IQ scores for equal numbers of male and female grade school children probably will be a. bimodal. b. normal. c. positively skewed. d. negatively skewed. 7. When constructing a graph, you must first decide on the type of graph. This decision depends on a. the total number of observations. b. whether data are grouped or ungrouped. c. whether data are quantitative or qualitative. d. the impression that you wish to create. 8. Find the median for the following observations: a. 29, 54, 43, 38, 40, 71. b. 21 c. 40.5 d. 41.5 e. 42.5 9. You're told that the shape of the distribution of burning times for light bulbs is balanced (normally distributed), with a mean burning time of about 500 hours. Therefore you can conclude that the median burning time a. equals about 500 hours. b. is more than 500 hours. c. is fewer than 500 hours. d. could be any of the above. 10. When a distribution is skewed, report a. the median. b. both the median and mode. c. both the median and mean. d. the mean. 11. The distribution of annual incomes for U.S. households is positively skewed. If the Census Bureau reports a median annual income of $47,450, this implies that the mean annual income is a. about the same. b. larger. c. smaller. d. either larger or smaller, but it's impossible to decide on the basis of the available information. • NOTE: In Questions 12-13 Identify Which One, If Any, Of The Three Common Averages The Mode, Median Or Mean Probably Serves As The Basis For Each Statement. 12. The average college professor is a white male. a. mode b. median c. mean d. impossible to determine on the basis of available information 13. Among frequency

The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $18 and $32 per share.

What is the probability that the stock price will be:

a. More than $29 (Round your answer to 4 decimal places.)

Probability____________

b. Less than or equal to $23? (Round your answer to 4 decimal places.)

Probability____________

b1

The distribution of the number of viewers for the American Idol television show follows a normal distribution with a mean of 30 million with a standard deviation of 10 million.

What is the probability next week's show will:

a. Have between 34 and 43 million viewers? (Round your z-score computation to 2 decimal places and final answer to 4 decimal places.)

Probability____________

b. Have at least 26 million viewers? (Round your z-score computation to 2 decimal places and final answer to 4 decimal places.)

Probability____________

c. Exceed 56 million viewers? (Round your z-score computation to 2 decimal places and final answer to 4 decimal places.)

Probability____________

c1.

For the most recent year available, the mean annual cost to attend a private university in the United States was $20,132. Assume the distribution of annual costs follows the normal probability distribution and the standard deviation is $4,450.

Ninety percent of all students at private universities pay less than what amount? (Round your z value to 2 decimal places and final answer to the nearest whole dollar.)

amount ___________

d1.

Assume that the hourly cost to operate a commercial airplane follows the normal distribution with a mean of $4,230 per hour and a standard deviation of $379.

What is the operating cost for the lowest 4% of the airplanes? (Round your z value to 2 decimal places and final answer to the nearest whole dollar.)

Operating Cost________________

d2. The annual commissions earned by sales representatives of Machine Products Inc., a manufacturer of light machinery, follow the normal probability distribution. The mean yearly amount earned is $40,000 and the standard deviation is $5,000.

What percent of the sales representatives earn more than $42,000 per year? (Round z-score computation and final answer to 2 decimal places.)

Percent____________

What percent of the sales representatives earn between $32,000 and $42,000? (Round z-score computation and final answer to 2 decimal places.)

percent_____________________

What percent of the sales representatives earn between $32,000 and $35,000? (Round z-score computation and final answer to 2 decimal places.)

The sales manager wants to award the sales representatives who earn the largest commissions a bonus of $1,000. He can award a bonus to 20% of the representatives. What is the cutoff point between those who earn a bonus and those who do not? (Round your answer to the nearest dollar amount.)

Cutoff point_____________________

Scientific research on popular beverages consisted of 65 studies that were fully sponsored by the food industry, and 35 studies that were conducted with no corporate ties. Of those that were fully sponsored by the food industry, 10 % of the participants found the products unfavorable, 25 % were neutral, and 65 % found the products favorable. Of those that had no industry funding, 39 % found the products unfavorable, 13 % were neutral, and 48 % found the products favorable. What is the probability that a participant selected at random found the products favorable?

If a randomly selected participant found the product favorable, what is the probability that the study was sponsored by the food industry?

If a randomly selected participant found the product unfavorable, what is the probability that the study had no industry funding?

Discuss the advantages and disadvantages of all three measures of central tendency; mean, median, and mode. Give specific examples of situations in which you would find these measures useful.

DISCUSSION BOARD FORUM 1/PROJECT 2 INSTRUCTIONS Standard Deviation and Outliers Thread:

For this assignment, you will use the Project 2 Excel Spreadsheet to answer the questions below. In each question, use the spreadsheet to create the graphs as described and then answer the question. Put all of your answers into a thread posted in Discussion Board Forum 1/Project 2. This course utilizes the Post-First feature in all Discussion Board Forums. This means you will only be able to read and interact with your classmates’ threads after you have submitted your thread in response to the provided prompt. For additional information on Post-First, click here for a tutorial. This is intentional. You must use your own work for answers to Questions 1–5. If something happens that leads you to want to make a second post for any of your answers to Questions 1–5, you must get permission from your instructor.

1. A. Create a set of 5 points that are very close together and record the standard deviation. Next, add a sixth point that is far away from the original 5 and record the new standard deviation. What is the impact of the new point on the standard deviation? Do not just give a numerical value for the change. Explain in sentence form what happened to the standard deviation.

B. Create a data set with 8 points in it that has a mean of approximately 10 and a standard deviation of approximately 1. Use the second chart to create a second data set with 8 points that has a mean of approximately 10 and a standard deviation of approximately 4. What did you do differently to create the data set with the larger standard deviation?

2. Go back to the spreadsheet and clear the data values from Question 1 from the data column and then put values matching the following data set into the data column for the first graph. 50, 50, 50, 50, 50. Notice that the standard deviation is 0. Explain why the standard deviation for this one is zero. Do not show the calculation. Explain in words why the standard deviation is zero when all of the points are the same. If you don’t know why, try doing the calculation by hand to see what is happening. If that does not make it clear, try doing a little research on standard deviation and see what it is measuring and then look again at the data set for this question.

3. Go back to the spreadsheet one last time and put each of the following three data sets into one of the graphs. Record what the standard deviation is for each data set and answer the questions below. Data set 1: 0, 0, 0, 100, 100, 100 Data set 2: 0, 20, 40, 60, 80, 100 Data set 3: 0, 40, 45, 55, 60, 100 Note that all three data sets have a median of 50. Notice how spread out the points are in each data set and compare this to the standard deviations for the data sets. Describe the relationship you see between the amount of spread and the size of the standard deviation and explain why this connection exists. Do not give your calculations in your answer—explain in sentence form. For the last 2 questions, use the Project 1 Data Set. 4. Explain what an outlier is. Then, if there are any outliers in the Project 1 Data Set, what are they? If there are no outliers, say no outliers.

5. Which 4 states have temperatures that look to be the most questionable or the most unrealistic to you? Explain why you selected these 4 states. For each state, give both the name and the temperature. Replies: After you have submitted your thread, you will be able to see your classmates’ threads. Find 2 classmates who disagreed with at least some part of your answers to Questions 4 and 5 and explain why your answers are correct. If you change your mind about your answers for Questions 4 and 5, explain what you were thinking originally as well as what you think now and why. Replies must be at least 50 words each. Submit your thread by 11:59 p.m. (ET) on Saturday of Module/Week 3. Submit your replies to 2 classmates’ threads by 11:59 p.m. (ET) on Monday of the same module/week.

a. Name measures of spread or variability.

b. Explain the concept of error and uncertainty as it relates to decision making.

c. What are the formulas to calculate the ?̅2 (adjusted R square)?