A student performs an experiment in which a computer is used to simulate drawing a random sample of size p from a larger population. The proportion of the population with the characteristics of interest to the student is p. Let the random variable P represent the sample proportion observed in the experiment. If p=1/5, find the smallest integer value of the sample size such that the standard deviation of P is less than or equal to 0.01 Done, answer n>=1600. My question is from

Given “Each of 23 students in a class independently performs the experiment described and each student calculates an approximate 95% confidence interval for P using sample proportions for their sample. It is subsequently found that exactly one of the 23 confidence intervals calculated by the class does not contain the value of P”

Find “Two of the confidence intervals calculated by the class are selected at random without replacement. Find the probability that exactly one of the selected confidence intervals does not contain the value of P.

Recall in our discussion of the binomial distribution the research study that examined schoolchildren developing nausea and vomiting following holiday parties. The intent of this study was to calculate probabilities corresponding to a specified number of children becoming sick out of a given sample size. Recall also that the probability, i.e. the binomial parameter "p" defined as the probability of "success" for any individual, of a randomly selected schoolchild becoming sick was given.

Suppose you are now in a different reality, in which this binomial probability parameter p is now unknown to you but you are still interested in carrying out the original study described above, though you must first estimate p with a certain level of confidence. Furthermore, you would also like to collect data from adults to examine the difference between the proportion with nausea and vomiting following holiday parties of schoolchildren and adults, which will reflect any possible age differences in becoming sick. You obtain research funding to randomly sample 46 schoolchildren and 41 adults with an inclusion criterion that a given participant must have recently attended a holiday party, and conduct a medical evaluation by a certified pediatrician and general practitioner for the schoolchildren and adults, respectively. After anxiously awaiting your medical colleagues to complete their medical assessments, they email you data contained in the following tables.

What is the estimated 95% confidence interval (CI) of the difference in proportions between schoolchildren and adults developing nausea and vomiting following holiday parties? Assign groups 1 and 2 to be schoolchildren and adults, respectively.

Please note the following: 1) in practice, you as the analyst decide how to assign groups 1 and 2 and subsequently interpret the results appropriately in the context of the data, though for the purposes of this exercise the groups are assigned for you; 2) 0 and 1 are defined as no and yes, respectively, which is a typical coding scheme in Public Health; 3) you might calculate a CI that is different from any of the multiple choice options listed below due to rounding differences, therefore select the closest match; and 4) you may copy and paste the data into Excel to facilitate analysis.

Select one:

a. -0.5259 to -0.0712

b. -0.5423 to -0.0877

c. -0.5306 to -0.0835

d. -0.4695 to -0.0766

You are testing a treatment for a new virus. Effectiveness is judged by the percent reduction in symptoms after two weeks.It is known that if left untreated, symptoms will reduce on their own by 0.185 (18.5%) with a standard deviation of 0.123. Three trials were run simultaneously.Trial 1 involved giving the participants a sugar pill. Patients in Trial 2 were given Agent A. Patients in Trial 3 were given Agent B. Results showing the amount of symptom reduction for the various trials are summarized in the table to the left. Note that this is NOT a paired t-test.Patient 1 just means the first patient to be given the treatment in each trial. Patient 1 is a different person in each trial.

1) At the 80%, 90% and 95% confidence levels (alpha = 0.2, 0.1 and 0.05) compare Agent A, Agent B and the Sugar Pill results to the population symptom reduction. Use a one-tail hypothesis test.

When the results of a survey or a poll are published, the sample size is usually given, as well as the margin of error. For example, suppose the Honolulu Star Bulletin reported that it surveyed 385 Honolulu residents and 78% said they favor mandatory jail sentences for people convicted of driving under the influence of drugs or alcohol (with margin of error of 3 percentage points in either direction). Usually the confidence level of the interval is not given, but it is standard practice to use the margin of error for a 95% confidence interval when no other confidence level is given.

a) The paper reported a point estimate of 78%, with margin of error of ±3%. Write this information in the form of a confidence interval for p, the population proportion of residents favoring mandatory jail sentences for people convicted of driving under the influence. What is the assumed confidence level?

b) The margin of error is simply the error due to using a sample instead of the entire population. It does not take into account the bias that might be introduced by the wording of the question, by the truthfulness of the respondents, or by other factors. Suppose the question was asked in this fashion: "Considering the devastating injuries suffered by innocent victims in auto accidents caused by drunken or drugged drivers, do you favor a mandatory jail sentence for those convicted of driving under the influence of drugs or alcohol?" Do you think the wording of the question would influence the respondents? Do you think the population proportion of those favoring mandatory jail sentences would be accurately represented by a confidence interval based on responses to such a question? Explain your answer.

If the question had been "Considering the existing overcrowding of our prisons, do you favor a mandatory jail sentence for people convicted of driving under the influence of drugs or alcohol?" Do you think the population proportion of those favoring mandatory sentences would be accurately represented by a confidence interval based on responses to such a question? Explain.

find a data set of size 50 - 100 published in newspapers or journals. you also may describe and conduct a survey to have your own data set ( explain and discuss your sampling methodology and any difficulties in data collection ). Describe your data and decide on one quantitative variable ( real or interval level ) and one qualitative variable to study . Write in complete sentences and explain why you choose this data set and set of variables.

Consider the following gasoline sales time series. If needed, round your answers to two-decimal digits.

Total Snowfall and Number of Visitors at Yellowstone National Park

The table above shows the total snowfall (in inches) and the number of visitors to Yellowstone National Park during 18 randomly selected weeks. (Show all calculations)

1. Based on the variables involved in this relationship which variable do you think is the explanatory (x) variable and which is the response (y) variable?

2. Calculate the correlation between the two variables. r=

3. Interpret the full meaning of the correlation coefficient you calculated in #2, including direction, strength, and relationship between variables.

4. Calculate the average and SD for the variable you chose as the explanatory variable.

Average =

SD =

5. Calculate the average and SD for the variable you chose as the response variable.

Average=

SD=

6. Find the equation of the regression line that fits your data. Show all calculation.

7. Interpret the meaning of the slope of your regression model from question #6

8. Interpret the meaning of the y-intercept of your regression model from question #6. If there is no practical meaning, explain why.

9. Demonstrate how someone might use the regression model you found in question #6 to predict the value of a response variable. That is, plug a hypothetical x-value in your model and explain what it predicts.

For each of the following, compute the probability of randomly drawing the hand (given 5 cards from the full 52). Leave your answer numerically unsimplified but in “factorial form”

(a) Three of a Kind (that is: 3 cards of one denomination together with 2 cards of two other denominations)

(b) Two Pairs (pairs of 2 different denominations, together with a 5th card of another denomination)

Question 1

We want to conduct a statistical test to determine how a sample mean compares to a population mean. We have alpha = 0.05. We have 40 observations in the sample, and our sample is normally distributed. We do not know our population standard deviation. Which test would we use?

Group of answer choices

a) z-test

b) t-test

Question 2

I want to see if the mean midterm scores for our class (the sample) differs from a baseline average of 75. What type of one-sample t test would I conduct?

Group of answer choices

a) one-tailed

b) two-tailed

Question 3

I conduct the t-test comparing the mean midterm score of our class (the sample) to the baseline null hypothesis mean of 75. I find that the difference between the mean of our class and the null hypothesis mean is statistically significant. I calculate Cohen's d to determine the effect size, and the resulting value is 0.012. What does this tell us about the statistical and substantive significance of this result?

Group of answer choices

a) The difference is not statistically significant or substantively significant.

b) There is a statistically significant, but not substantively significant difference.

c) There is a statistically significant and substantively significant difference.

Question 4

Which of the following has greater power, a one-tailed or two-tailed one-sample t-test?

Group of answer choices

a) they're the same

b) one-tailed

c) two-tailed

Question 5

If the standard error of an estimate is increased, what is the effect to the width of the confidence interval?

Group of answer choices

a) it gets wider

b) no change

c) it narrows

Question 6

In the most recent YouGov poll 28% of respondents supported Biden for the Democratic nominee. There were 722 respondents in the poll. What is the sample standard error for preference for Biden?

You have enough information to calculate this.

Question 7

Using the SE you calculated in the previous question, determine if the 28% support for Biden in the YouGov poll is significantly different than the national support for Biden that sits at 18.1%.

Use the critical t-value of +/- 1.96.

Show your work for the calculations and explain your answer.

A politician has commissioned a survey of blue-collar and white-collar workers in her constituency. The survey asks each if they intend to vote for her. The results are presented below:

Vote     |   Blue Collar White-Collar

    For      |       448          265

  Against |       552          235     

a. Is there evidence of a significant difference in the proportions of workers that support her between the two groups of workers? Test using a .05 level of significance.

b. Find beta for the test if the true proportion voting for her among blue collar workers was 15 % less than for white collar workers.

Problem 4 (unbiased, efficient, and consistent estimators). Suppose we have n i.i.d. samples distributed according to N (µ, σ2 ). Consider two estimators for µ: X¯ = 1 n Pn i=1 Xi and Xˆ = 1 2 (X1 + Xn).

A) Calculate the mean of X¯ and Xˆ. Are they unbiased?

B) Calculate the variance of X¯ and Xˆ. Which one is more efficient?

C) If n → ∞, X¯ and Xˆ will converge to what? which one is the consistent estimator?

4. A researcher reports that performance was significantly correlated with overall engagement among nurses enrolled in an online degree program (r=0.8). You know this means:

13. A researcher is studying 378 nurses enrolled in online RN to BSN completion program and analyzing how age, level of engagement, motivation and time spent studying impact the final test score. When she enters level of engagement, motivation, and time spent studying into the regression model the R square change associated with each is significant but when she enters age into the model the R square change is not significant. You would recommend the final regression model include what variances?

19. The researcher examines the relationship between hours of sleep and average of test scores and reports an r=0.56, p=0.02. You know this means:

20. A nursing professor wishes to determine if there is an association between her students grades and three independent variables (use of online turtorials, the use of quiz review sessions and participation in study sessions). When she adds the third variable the standard error of estimate changes from 8.2 to 9.4. She knows this means:

Mr. Acosta, a sociologist, is doing a study to see if there is a relationship between the age of a young adult (18 to 35 years old) and the type of movie preferred. A random sample of 93 adults revealed the following data. Test whether age and type of movie preferred are independent at the 0.05 level. Person's Age Movie 18-23 yr 24-29 yr 30-35 yr Row Total Drama 8 15 11 34 Science Fiction 15 12 3 30 Comedy 10 10 9 29 Column Total 33 37 23 93 (a) What is the level of significance? State the null and alternate hypotheses. H0: Age and movie preference are independent. H1: Age and movie preference are independent. H0: Age and movie preference are not independent. H1: Age and movie preference are not independent. H0: Age and movie preference are not independent. H1: Age and movie preference are independent. H0: Age and movie preference are independent. H1: Age and movie preference 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 chi-square uniform Student's t normal What are the degrees of freedom? (c) Find or estimate the P-value of the sample test statistic. 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 age of young adult and movie preference are not independent. At the 5% level of significance, there is insufficient evidence to conclude that age of young adult and movie preference are not independent.

The following table shows the Myers-Briggs personality preference and area of study for a random sample of 519 college students. In the table, IN refers to introvert, intuitive; EN refers to extrovert, intuitive; IS refers to introvert, sensing; and ES refers to extrovert, sensing. Myers-Briggs Preference Arts & Science Business Allied Health Row Total IN 64 8 24 96 EN 77 38 39 154 IS 60 37 18 115 ES 76 45 33 154 Column Total 277 128 114 519 Use a chi-square test to determine if Myers-Briggs preference type is independent of area of study at the 0.05 level of significance. (a) What is the level of significance? State the null and alternate hypotheses. H0: Myers-Briggs type and area of study are independent. H1: Myers-Briggs type and area of study are independent. H0: Myers-Briggs type and area of study are not independent. H1: Myers-Briggs type and area of study are independent. H0: Myers-Briggs type and area of study are independent. H1: Myers-Briggs type and area of study are not independent. H0: Myers-Briggs type and area of study are not independent. H1: Myers-Briggs type and area of study 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? uniform binomial 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 Myers-Briggs type and area of study are not independent. At the 5% level of significance, there is insufficient evidence to conclude that Myers-Briggs type and area of study are not independent.

PrintTech, Inc. is introducing a new line of ink-jet printers and would like to promote the number of pages a user can expect from a print cartridge. A sample of 10 cartridges revealed the following number of pages printed. (Use t Distribution Table.) 2,983 3,096 2,510 2,559 2,559 2,622 2,537 2,485 3,236 2,758 picture Click here for the Excel Data File What is the point estimate of the population mean? (Round your answer to 2 decimal places.) Develop a 98% confidence interval for the population mean. (Round your answers to 2 decimal places.)

1. hat is the point estimate of the population mean? (Round your answer to 2 decimal places.)

2. Develop a 98% confidence interval for the population mean. (Round your answers to 2 decimal places.)