Researchers studying children’s moral behavior have developed an altruism scale for 10-year-olds that reflects a child’s general level of helpfulness.  Scores on the altruism scale are normally distributed with mu = 95 and sigma= 14 (higher scores on the scale indicate a greater level of helpfulness).

Dr. Thornton wants to investigate whether exposing children to a videotape that shows a lost puppy in need of help will affect how helpful they are.  He selects a random sample of n = 36 10-year-olds, shows them the video, and then administers the altruism scale.  Dr. Thornton finds that the mean score for the children is M = 99.1.  

Test whether Dr. Thornton’s manipulation significantly increases altruism scores.

a. State the null and alternative hypotheses in sentence format (do not use symbol notation).

b. State the null and alternative hypotheses using statistical notation.

c. Identify the critical region(s) for an alpha = .05 level of significance for this sampling distribution.

d. Did Dr. Thornton’s manipulation significantly increase altruism scores?  Explain your answer.

Suppose that Dr. Thornton instead wants to test whether his manipulation has any effect on altruism scores.  Assume that he uses the same 36 children as noted above.  Restate the null and alternative hypotheses using symbol notation for this new test.

e. Identify the critical region(s) for an alpha = .05 level of significance for this sampling distribution.

f. Did Dr. Thornton find a significant effect of his manipulation?  Explain why the answer here is different than that for (d), above.

1. Marijuana Study: In question 2, referred to a Pew poll of 1500 adults, and 52% of the respondents said that the use of marijuana should not be made legal.

1. Among the 1500 adults who responded, what is the number of respondents who said that the use of marijuana should not be made legal?

2. In the same poll of 1500 adults, 345 of the respondents said that the use of marijuana for medical purposes should not be legal. What percentage of respondents who said that the use of marijuana for medical purposes should not be legal?

3. In this survey of 1500 adults, 727 are men and 773 are women. Find the percentage of respondents who are men, and then find the percentage of respondents who are women.

The Crown Bottling Company has just installed a new bottling process that will fill 16-ounce bottles of the popular Crown Classic Cola soft drink. Both overfilling and underfilling bottles are undesirable: Underfilling leads to customer complaints and overfilling costs the company considerable money. In order to verify that the filler is set up correctly, the company wishes to see whether the mean bottle fill, μ, is close to the target fill of 16 ounces. To this end, a random sample of 36 filled bottles is selected from the output of a test filler run. If the sample results cast a substantial amount of doubt on the hypothesis that the mean bottle fill is the desired 16 ounces, then the filler’s initial setup will be readjusted.

(a) The bottling company wants to set up a hypothesis test so that the filler will be readjusted if the null hypothesis is rejected. Set up the null and alternative hypotheses for this hypothesis test.

H₀ : μ (Click to select)=≠ 16 versus H_a : μ (Click to select)≠= 16

(b) Suppose that Crown Bottling Company decides to use a level of significance of α = 0.01, and suppose a random sample of 36 bottle fills is obtained from a test run of the filler. For each of the following four sample means— x¯x¯ = 16.06, x¯x¯ = 15.96, x¯x¯ = 16.03, and x¯x¯ = 15.90 — determine whether the filler’s initial setup should be readjusted. In each case, use a critical value, a p-value, and a confidence interval. Assume that σ equals .1. (Round your z to 2 decimal places and p-value to 4 decimal places and CI to 3 decimal places.)

x¯x¯ = 16.06

CI            [, ]   (Click to select)Do not readjustReadjust

x¯x¯⁢ = 15.96

CI              [, ]   (Click to select)Do not readjustReadjust

x¯x¯⁢ = 16.03

CI                  [, ]   (Click to select)ReadjustDo not readjust

x¯x¯⁢ = 15.90

CI              [, ] (Click to select)ReadjustDo not readjust

1. Hospitals: Currently, there are 5723 registered hospitals in the United States.

1. Are the numbers of hospitals in different states discrete or continuous?

Answer: ________________

2. What is the level of measurement for the number of hospitals in different years? Pick one (nominal, ordinal, interval, ratio)

Answer: ________________

3. A survey is conducted by randomly selecting 10 patients in every hospital, what type of sampling is used? Pick one (random, systematic, convenience, stratified, cluster)

Answer: ________________

4. If a survey is conducted by randomly selecting 20 hospitals and interviewing all of the members of each board of directors, what type of sampling is used? Pick one (random, systematic, convenience, stratified, cluster)

Answer: ________________

What are the limitations of using a dataset when data are NOT missing at random (MNAR)? Can you still publish a paper using a dataset in this condition?

Question 3. Monthly demand at A&D Electronics for flat-screen TVs are as follows:

Month Demand (units)

1 1,000

2 1,113

3 1,271

4 1,445

5 1,558

6 1,648

7 1,724

8 1,850

9 1,864

10 2,076

11 2,167

12 2,191

Estimate demand for the next two weeks using simple exponential smoothing with a = 0.3 and Holt’s model with a = 0.05 and b = 0.1. For the simple exponential smoothing model, use the level at Period 0 to be L0 =1,659 (the average demand over the 12 months). For Holt’s model, use level at Period 0 to be L0= 948 and the trend in Period 0 to be T0 = 109 (both are obtained through regression). Evaluate the MAD, MAPE, MSE, bias, and TS in each case. Which of the two methods do you prefer? Why?

Note: Please, solve the problems by using MS Excel.

A statistics teacher wants to assess whether her remedial tutoring has been effective for her five students. She decides to conduct a related samples t-test and records the following grades for students prior to and after receiving her tutoring. Tutoring Before After 2.4 3.0 2.5 2.9 3.0 3.6 2.9 3.1 2.7 3.5 (a) Test whether or not her tutoring is effective at a 0.05 level of significance. State the value of the test statistic. (Round your answer to three decimal places.) t = Incorrect: Your answer is incorrect. State the decision to retain or reject the null hypothesis. Retain the null hypothesis. Reject the null hypothesis. Correct: Your answer is correct. (b) Compute effect size using estimated Cohen's d. (Round your answer to two decimal places.) d =

You are a line manager in Super Car Part’s Eversville manufacturing facility. The company produces automotive parts, and you have responsibility for the line producing steel shafts for the gearbox manufactured in the Eversville Plant. The acceptable dimension of the shaft is 2.5±0.05 inches in diameter with the most desirable product having a diameter of exactly 2.5 inches. The current equipment is approaching the end of its useful life and needs to be replaced. Two vendors are trying to sell your company, Super Car Parts Incorporated, their machines for the shaft-machining task. You have been asked to assess the machines from each vendor, and to make a recommendation for a machine vendor supported by a justification for your decision.

You asked both vendors to supply data on the machining accuracy of their machines for the given task. Both vendors machined 100 shafts, collected data, plotted histograms, fitted the histograms with normal distributions and supplied you with their findings.

Let X= diameter in inches of the gearbox shaft

Aballo Machines Inc.: X has a normal distribution with a mean of 2.49 and a standard deviation of 0.030

Lu Equipment Corp.: X has a normal distribution with a mean of 2.53 and a standard deviation of 0.015

1. ) The Scholastic Aptitude Test (SAT) contains three sections: critical reading, mathematics and writing. Each part is scored on a 500-point scale. Information on test scores for the 2018 version of SAT is available at the College Board website. Find the sample of SAT scores for 5 students bellow.

                                                                                                                       ANOVA Table

                SAT scores - 2018

1. (9pt) Conduct a Fisher’s LSD test allowing for 1% error.

2. (4pt) The level of difficulty for all the three sections of the SAT measured by the score are supposed to be the same. Do you agree with this after the results of the LSD test? WHY? Be specific for full credit.

In the probability distribution to the​ right, the random variable X represents the number of hits a baseball player obtained in a game over the course of a season. Complete parts​ (a) through​ (f) below. x ​P(x) 0 0.1685 1 0.3358 2 0.2828 3 0.1501 4 0.0374 5 0.0254 ​

(a) Verify that this is a discrete probability distribution. This is a discrete probability distribution because all of the probabilities are at least one of the probabilities is all of the probabilities are between 0 and 1​, ​inclusive, and the sum mean sum product of the probabilities is 1. ​(Type whole numbers. Use ascending​ order.)

​(b) Draw a graph of the probability distribution. Describe the shape of the distribution. Graph the probability distribution. Choose the correct graph below. A. 0 1 2 3 4 5 0 0.1 0.2 0.3 0.4 Number of Hits Probability The graph of a probability distribution has a horizontal x-axis labeled "Number of Hits" from 0 to 5 in intervals of 1 and a vertical y-axis labeled "Probability" from 0 to 0.4 in intervals of 0.05. Vertical line segments are centered on each of the horizontal axis tick marks. The approximate heights of the vertical line segments are as follows, with the horizontal coordinate listed first and the line height listed second: 0, 0.15; 1, 0.04; 2, 0.03; 3, 0.17; 4, 0.34; 5, 0.28. B. 0 1 2 3 4 5 0 0.1 0.2 0.3 0.4 Number of Hits Probability The graph of a probability distribution has a horizontal x-axis labeled "Number of Hits" from 0 to 5 in intervals of 1 and a vertical y-axis labeled "Probability" from 0 to 0.4 in intervals of 0.05. Vertical line segments are centered on each of the horizontal axis tick marks. The approximate heights of the vertical line segments are as follows, with the horizontal coordinate listed first and the line height listed second: 0, 0.34; 1, 0.15; 2, 0.03; 3, 0.17; 4, 0.28; 5, 0.04. C. 0 1 2 3 4 5 0 0.1 0.2 0.3 0.4 Number of Hits Probability The graph of a probability distribution has a horizontal x-axis labeled "Number of Hits" from 0 to 5 in intervals of 1 and a vertical y-axis labeled "Probability" from 0 to 0.4 in intervals of 0.05. Vertical line segments are centered on each of the horizontal axis tick marks. The approximate heights of the vertical line segments are as follows, with the horizontal coordinate listed first and the line height listed second: 0, 0.03; 1, 0.04; 2, 0.15; 3, 0.28; 4, 0.34; 5, 0.17. D. 0 1 2 3 4 5 0 0.1 0.2 0.3 0.4 Number of Hits Probability The graph of a probability distribution has a horizontal x-axis labeled "Number of Hits" from 0 to 5 in intervals of 1 and a vertical y-axis labeled "Probability" from 0 to 0.4 in intervals of 0.05. Vertical line segments are centered on each of the horizontal axis tick marks. The approximate heights of the vertical line segments are as follows, with the horizontal coordinate listed first and the line height listed second: 0, 0.17; 1, 0.34; 2, 0.28; 3, 0.15; 4, 0.04; 5, 0.03. Describe the shape of the distribution. The distribution has one mode has one mode is multimodal is uniform is bimodal and is skewed right. roughly symmetric. skewed right. skewed left.

​(c) Compute and interpret the mean of the random variable X. mu Subscript xequals 0.1666 hits ​(Type an integer or a decimal. Do not​ round.) Which of the following interpretations of the mean is​ correct? A. In any number of​ games, one would expect the mean number of hits per game to be the mean of the random variable. B. Over the course of many​ games, one would expect the mean number of hits per game to be the mean of the random variable. C. The observed number of hits per game will be less than the mean number of hits per game for most games. D. The observed number of hits per game will be equal to the mean number of hits per game for most games. ​

Need help with (c) through (f) please!

(d) Compute the standard deviation of the random variable X. sigma Subscript xequals nothing hits ​(Round to three decimal places as​ needed.)

​(e) What is the probability that in a randomly selected​ game, the player got 2​ hits? nothing ​(Type an integer or a decimal. Do not​ round.)

​(f) What is the probability that in a randomly selected​ game, the player got more than 1​ hit? nothing ​(Type an integer or a decimal. Do not​ round.)

A study was designed to compare the attitudes of two groups of nursing students towards computers. Group 1 had previously taken a statistical methods course that involved significant computer interaction. Group 2 had taken a statistic methods course that did not use computers. The students' attitudes were measured by administering the Computer Anxiety Rating Scale (CARS). A random sample of 15 nursing students from Group 1 resulted in a mean score of 59.659.6 with a standard deviation of 8.1. A random sample of 12 nursing students from Group 2 resulted in a mean score of 65.5with a standard deviation of 5.2. Can you conclude that the mean score for Group 1 is significantly lower than the mean score for Group 2? Let μ1represent the mean score for Group 1 and μ2 represent the mean score for Group 2. Use a significance level of α=0.01 for the test. Assume that the population variances are equal and that the two populations are normally distributed.

Step 1 of 4: State the null and alternative hypotheses for the test.

Step 2 of 4: Compute the value of the test statistic. Round your answer to two decimal places.

Step 3 of 4: Determine the decision rule for rejecting the null hypothesis H0H0. Round the numerical portion of your answer to two decimal places.

Step 4 of 4: Make the decision for the hypothesis test.

A clinical trial is conducted to compare an experimental medication to placebo to reduce the symptoms of asthma. Two hundred participants are enrolled in the study and randomized to receive either the experimental medication or placebo. The primary outcome is self-reported reduction of symptoms. Among 100 participants who receive the experimental medication, 38 report a reduction of symptoms as compared to 21 participants of 100 assigned to placebo. When you test if there is a significant difference in the proportions of participants reporting a reduction of symptoms between the experimental and placebo groups. Use α = 0.05. What should the researcher’s conclusion be for a 5% significance level? Reject H0 because 2.64 ≥ 1.960. We have statistically significant evidence at α = 0.05 to show that there is a difference in the proportions of patients reporting a reduction in symptoms.

1. We reject H0 at the 5% level because 2.64 is greater than 1.96. We do have statistically significant evidence at α = 0.05 to show that there is a difference in the proportions of patients reporting a reduction in symptoms.

2. We fail to reject H0 at the 5% because -2.64 is less than 1.645. We do not have statistically significant evidence to show that there is a difference in the proportions of patients reporting a reduction in symptoms.

3. We fail to reject H0 at the 5% because -2.64 is less than 1.96. We do have statistically significant evidence at α = 0.05 to show that there is a difference in the proportions of patients reporting a reduction in symptoms.

4. We fail to reject H0 at the 5% because 2.64 is greater than -1.645. We do have statistically significant evidence at α = 0.05 to show that there is a difference in the proportions of patients reporting a reduction in symptoms.

The average cost of a condominium study in the Cedar Lakes development is
$ 62,000 with a standard deviation of $ 4,200 (for a n = 25).
a) What is the probability that a condominium in this development will cost at least
 $ 65,000?
b) The probability that the average cost of a sample is between $ 65,000 and
62,000?
c) With the above information, what would be the intervals for the following levels of
trust:
(1) 67%:
(2) 95%:
(3) 99%:

step by step if possible

Find an experimental study from a journal of your choice. (Provide the citation).

a.

Identify the explanatory variable

b.

Identify the dependent/response variable

c.

What were the treatments?

d.

What were the experimental units?

e.

How were the experimental units assigned to the treatments?

f.

Can you identify any source of bias? Explain

The following table shows ceremonial ranking and type of pottery sherd for a random sample of 434 sherds at an archaeological location. Ceremonial Ranking Cooking Jar Sherds Decorated Jar Sherds (Noncooking) Row Total A 91 44 135 B 89 56 145 C 75 79 154 Column Total 255 179 434 Use a chi-square test to determine if ceremonial ranking and pottery type are independent at the 0.05 level of significance. (a) What is the level of significance? State the null and alternate hypotheses. H0: Ceremonial ranking and pottery type are independent. H1: Ceremonial ranking and pottery type are independent. H0: Ceremonial ranking and pottery type are not independent. H1: Ceremonial ranking and pottery type are independent. H0: Ceremonial ranking and pottery type are independent. H1: Ceremonial ranking and pottery type are not independent. H0: Ceremonial ranking and pottery type are not independent. H1: Ceremonial ranking and pottery type are not independent. (b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.) Are all the expected frequencies greater than 5? Yes No What sampling distribution will you use? binomial uniform chi-square normal Student's t What are the degrees of freedom? (c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.) p-value > 0.100 0.050 < p-value < 0.100 0.025 < p-value < 0.050 0.010 < p-value < 0.025 0.005 < p-value < 0.010 p-value < 0.005 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence? Since the P-value > α, we fail to reject the null hypothesis. Since the P-value > α, we reject the null hypothesis. Since the P-value ≤ α, we reject the null hypothesis. Since the P-value ≤ α, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. At the 5% level of significance, there is sufficient evidence to conclude that ceremonial ranking and pottery type are not independent. At the 5% level of significance, there is insufficient evidence to conclude that ceremonial ranking and pottery type are not independent.

Show formulas in excel if used please.