a sample size n =44 has sample mean =56.9 and Sample standard deviation s =9.1. a. construct a 98% confidence interval for the population mean meu b. if the sample size were n =30 would the confidence interval be narrower or wider? please show work to explain

1. Explain the difference between non-directional and directional hypotheses, and explain in which circumstances it is important to apply directional hypothesis.
2. Explain why Chi square distributions are positively skewed and what is its relationship with the degrees of freedom.
3. The objective of hypothesis testing is to reject the null hypothesis. How do we use the P-value to accomplish this goal?
4. Describe the difference between One-way versus Two-way ANOVA and provide an example of each.

1, You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion, so we assume p=.5. You would like to be 99% confident that you esimate is within 4% of the true population proportion. How large of a sample size is required?
n =

Hint: Shouldn't the answer be a WHOLE NUMBER.
Do not round mid-calculation. However, use a critical value accurate to three decimal places.

2. You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 84%. You would like to be 98% confident that your estimate is within 3.5% of the true population proportion. How large of a sample size is required?

n =

3. A political candidate has asked you to conduct a poll to determine what percentage of people support her, assume p=.5.
If the candidate only wants a 2% margin of error at a 99% confidence level, what size of sample is needed?

4. If n = 540 and ˆp (p-hat) = 0.35, construct a 99% confidence interval.

Give your answers to three decimals

< p <

Dr. Smile is interested in evaluating whether 7-year-old autistic children differ from the general population of 7-year-old children in their ability to recognize facial expressions. She develops the Facial Recognition Test, which has mean = 200 among the general population of 7-year-olds. Dr. Smile collects data on a sample of 16 children with autism. In this sample Xbar = 180 and s = 12.

A) using alpha= 0.05 and a two-tailed test, conduct a one-sample t-test evaluating the null hypothesis.

b) based on these results, should Dr Smile reject or fail to reject the null hypothesis?

c)Report the resukts of the hypothesis test you conducted in part B as if Dr Smile were writing about them in a journal article.

Biostatistics with R

- Solve the following by evaluating the test statistic and p value. Suppose that the population mean of systolic blood pressure in the US is 115. We hypothesize mean systolic blood pressure is lower than 115 among people who consume a small amount (e.g., around 3.5 ounces) of dark chocolate every day. Assume that systolic blood pressure, X, in this population has a Normal distribution. To evaluate our hypothesis, we randomly selected 100 people, who include a small amount of dark chocolate in their daily diet, and measured their blood pressure. If the sample mean is x¯ = 111 and the sample variance is s = 32, can we reject the null hypothesis at 0.1 confidence level?

- Solve the following using the Confidence Interval Hypothesis Test approah and t.test() Approach. Use the Pima.tr data set to evaluate the hypothesis that the population mean of diastolic blood pressure for Pima Indian women is not 70.

library(MASS)

data("Pima.tr")

#str(Pima.tr)

?Pima.tr

An urn contains 6 white and 10 black balls. The figure gives by
the roll of a dice balance indicates the number of balls that will be drawn without delivery of the ballot box.
Let A be the event defined by:
A: all the balls drawn from the urn are white.
What is the probability that the dice has delivered a 3 knowing that A has realized (Use Bayes' Law)?

how can i apply the concept of normal distribution in civil engineering?

Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the company’s needs. In addition, the suppliers charge different prices for the components. Component price data (in price per unit) are as follows:

Each supplier has a limited capacity in terms of the total number of components it can supply. However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1, component 2, or any combination of the two components, if the total number of units ordered is within its capacity. Supplier capacities are as follows:

If the Edwards production plan for the next period includes 1025 units of component 1 and 825 units of component 2, what purchases do you recommend? That is, how many units of each component should be ordered from each supplier? Round your answers to the nearest whole number. If your answer is zero, enter "0".

What is the total purchase cost for the components? Round your answer to the nearest dollar.

Giving a test to a group of students, the grades and gender are summarized below

If one student is chosen at random,

Find the probability that the student was NOT a female that got a "B"

12.19. A study of 300 male and female employees in two manufacturing plants was conducted to explore whether there was gender and age gap in self-esteem. The study’s participants were asked to respond to the statement "I'm happy with myself the way I am" by circling Yes or No. The study found that in in the first plant, 60% of the women and 67% of the men responded Yes. When the same statement was posed to employees in the other plant, 29% of the girls and 48% of the boys responded Yes.

To answer the research questions, two chi square tests were conducted. The first one compared the responses of men and women in the first plant, and the second one compared the responses of men and women in the second plant. The results of the analyses are summarized in the following table. Is there a difference in the responses of men and women? Explain.

Workers in a large plant are expected to complete a particular task in 60 seconds or less. The

production manager believes that the average worker is satisfying that expectation. To

examine the issue she watches eight workers perform the task and measures their times. The

times, which are assumed to be normally distributed, are 58, 53, 63, 62, 57, 55, 53, and 55.

Does this data provide sufficient evidence at the 5% significance level to support the

production manager’s belief?

a. Test statistics:

t

= 2.223

b. P-value= 1.895

c. Do not reject Ho. These data provide insufficient evidence at the 5% level of

significance to support the production manager’s belief.

d. Reject Ho. Yes, these data provide sufficient evidence at the 5% level of significance to

support the production manager’s belief.

The American Society of PeriAnesthesia Nurses (ASPAN; www.aspan.org) is a national organization serving nurses practicing in ambulatory surgery, preanesthesia, and postanesthesia care. The organization's membership is listed below.

1. Find the mean, median, and standard deviation of the number of members per component. (Round your answers to 2 decimal places.)
2. Find the coefficient of skewness, using the software method. (Round your answer to 2 decimal places.)
3. Determine the first and third quartiles. Do not use the method described by Excel. (Round your answers to 2 decimal places.)

4. What are the limits for outliers? (Round your answers to the nearest whole number. Negative amounts should be indicated by a minus sign.)

If you roll two six-sided dice, what is the probability of obtaining the following outcomes?

a)2 or 3

b) 6 and 4

c) At least one 5

d) Two of the same number (two 1s, or two 2s, or two 3s, etc.)

e) An even number on both dice

f) An even number on at least one die

Check the types of sampling methods that should be used in order to draw conclusions about a population at large from what we know about a sample we collected.

Convenience Sample

Voluntary Sample

Random Sample