1. Comparing two population proportions.

We expect that there is no difference in proportion of status of employment between male and female recent business graduates.

a) insert a frequency table and a bar chart or a pie chart labeled properly. USING EXCEL

b) Perform hypothesis test: Calculate the P-value and make the conclusion (reject or fail to reject Ho). Insert Excel software output.

C)

Calculate the corresponding confidence interval and check if the conclusion is the same

You are considering the risk-return of two mutual funds for investment. The relatively risky fund promises an expected return of 14.7% with a standard of 15.6%. The relatively less risky fund promises an expected return and standard deviation of 6.4% and 3.8%, respectively. Assume that the returns are approximately normally distributed. Using normal probability calculations and complete sentences, give your assessment of the likelihood of getting, on one hand, a negative return and on the other, a return above 10% with these funds. You may choose to use excel normal distribution formulas, but if you do, give the explicit formulas. Offer some remarks about your possible investment approach.

A random sample of 42 taxpayers claimed an average of ​$9 comma 786 in medical expenses for the year. Assume the population standard deviation for these deductions was ​$2 comma 387. Construct confidence intervals to estimate the average deduction for the population with the levels of significance shown below. a. 1 % b. 2 % c. 5 %

Stet by step in R and attach R file and R codes too - Thanks

Use one of the real-world example data sets from R (not previously used in the R practice assignment) or a dataset you have found, and at least two of the tests and R functions covered in the practice assignment to conduct a hypothesis test then report your findings and give proper conclusion(s).

Use the following supporting materials for R syntax, data sets and tools, along with other resources found in this module or that you find on your own.

• Using T-Tests in R from the Department of Statistics at UC Berkley

• Test of equal or given proportions from R Documentation

• F-Test: Compare Two Variances in R from STHDA (Statistical tools for high-throughput data analysis)

Please answer step by step with R files attached and R codes

1. For each data set below, find the following: a) The 5 Number Summary; b) The IQR c) The “Outlier Fences”; d) List any outliers e) Sketch the box plot

45,70,71,73,75,80,81,85,100

of the three men, the chances that of politician, a businessman, of an academician will be appointed as a vice-chancellor (vc) of a university are 0.5,0.3 and 0.2 respectively. Probability that the research is promoted to become vc of the university politician, businessman, and academician 0.3, 0.7, and 0.8 respectively. a) determine the probability that research is promoted. b) if reserch is promoted, what is the probability that vc is and academician?

1) Use these two confidence intervals to answer the question. 90%: (0.770, 0.808) and 99%: (0.759, 0.818)

If H_0: pi = .81 and H_a: pi not equal to .81, do we reject or fail to reject the null hypothesis at the alpha = .01 level? (reject or fail to reject)

2) Suppose you conducted a significance test with an alpha = .01 significance level. At the end of the test you concluded to reject the null hypothesis. If you had instead used alpha = .10, would you have rejected the null hypothesis, failed to reject the null hypothesis, or is there not enough information? (reject, fail to reject, or not enough)

3) Suppose you conducted a significance test with an alpha = .10 significance level. At the end of the test you concluded to reject the null hypothesis. If you had instead used alpha = .01, would you have rejected the null hypothesis, failed to reject the null hypothesis, or is there not enough information? (reject, fail to reject, or not enough)

Let n = 100, p_hat = .35, H_0: pi = .25, H_a: pi > .25, and alpha = .05. Use this information to answer 4), 5) , and 6).

4) If p_hat = .4 and everything else stayed the same, would the power increase or decrease?

5) If alpha = .01 and everything else stayed the same, would the power increase or decrease?

6) If n = 50 and everything else stayed the same, would the power increase or decrease?

7) If alpha = .01 and the p-value is .0144, what type of error is possible in this test? (type I or type II)  (Hint: you need to first think about the test decision)

8) If alpha = .05 and the p-value is .0144, what type of error is possible in this test? (type I or type II)  (Hint: you need to first think about the test decision)

Following is the average amount of money left to children by the tooth fairy in recent years, according to a  

poll of parents.  The table compares these payout amounts to the U.S. unemployment rate at the same

time.  The scatterplot for the data is also given.           

            a)  Find the value of the linear correlation coefficient .

            b)  Is there sufficient evidence to support the claim that there is a significant linear correlation between

                 the unemployment rate and the average amount left by the tooth fairy?  What do you base your conclusion on?

c)  Specify the value of the coefficient of determination .  Give a written interpretation of this value.

d)  Find the equation of the least-squares regression line.

e)  Confirm that you have examined the scatterplot with the regression line from Statdisk:

f)  What is the value of the slope of the regression equation?  Give a written interpretation of the slope in the context of this problem.

g)  What is the value of the y-intercept of the regression equation?  Give a written interpretation of the y-intercept in the context of this problem.

h)  What is the best predicted average tooth fairy payout for a year with a 4.5% unemployment rate?

A college football coach was interested in whether the college’s strength development class increased his

players’ maximum lift (in pounds) on the bench press exercise.  He asked four of his players to participate

in the study.  The amount of weight they could each lift was recorded before they took the strength

development class.  After completing the class, the amount of weight they could each lift was again

measured.  The data are as follows.  

The coach wants to know if the strength development class makes his players stronger, on average.  Use

an  significance level to test the claim that the mean amount of weight lifted increases after taking

the strength development class.  (Assume that the paired sample data are simple random samples and that

the differences have a distribution that is approximately normal.)

a)  Find the values of  and .

b)  State the hypotheses.   

c)  Calculate the test statistic and specify the critical value.

d)  Find the P-value.

e)  State the initial conclusion regarding the null hypothesis .

f)  State the final conclusion in your own words that addresses the original claim.

Question 3)The final grades in Math class of 80 students at State University are recorded in the accompanying table.

A.The given data set is in ascending order. If class interval size is 3 for the constructed 14 classes, find “m”.(Note: This section is not related with section B)

B.Construct a frequency table with 8 classes and find its frequencies.

i)Find median class

ii)Sketch the ogive curves by using either the cumulative frequency or the cumulative relative frequency.

iii)Using the ogive curve find the following probabilities:

P(x<76.5)=

P(x>88.5)=

P(x>84)=

P(x<90)=

P(74<x<92)=

P(x=78)=

iv)Find interquartile range (IQR)

v)Sketch box and whisker plot.

vi)Comment on skewness.

vii)The standard deviation and mean of another math class of 49 students from Technology University is 10.3 and 88.6, respectively. Compare the Math class in State University with Math class in Technology University, which one is more consistent? In other words which Math class has less spread of values around its mean? Show your work and explain why?Note: You can find the necessary parameters for the State University either from raw data given or from the frequency table you constructed.

          A tutoring center collected data on the number of student visits during each of the first eight weeks of the

          fall and spring semesters.  The results are given below.  (Assume that the paired sample data are simple

          random samples and that the differences have a distribution that is approximately normal.)

a)  Construct and interpret the 95% confidence interval estimate of the mean of the population of differences between the number of students visiting the tutoring center in the fall and spring semesters.   

          c)  Does there appear to be a significant difference between the number of student visits in the fall and the

               spring?  Explain.

Engineers are testing company fleet vehicle fuel economy (miles per gallon) performance by using different types of fuel. One vehicle of each size is tested. Does this sample provide sufficient evidence to conclude that there is a significant difference in treatment means?

  Click here for the Excel Data File

(a) Choose the correct statement.

• Fuel type is the blocking factor and vehicle size is the treatment.

• Fuel type is the treatment and vehicle size is the blocking factor.

(b) Fill in the boxes. (Round your SS values to 3 decimal places, F values to 2 decimal places, and other answers to 4 decimal places.)

(c) Choose the correct statement. Use α = 0.05.

• Fuel type means differ significantly and vehicle size is also a significant factor.

• Fuel type means do not differ significantly, but vehicle size is a significant factor.

• Fuel type means differ significantly, but vehicle size is not a significant factor.

• Fuel type means do not differ significantly and vehicle size is not a significant factor.

(d) Which fuel types show a significant difference in average fuel economy? Use α = 0.01. (You may select more than one answer. Click the box with a check mark for the correct answer and click to empty the box for the wrong answer.)

• Ethanol 10% and Ethanol 5%

• 89 Octane and 87 Octane

• Ethanol 5% and 91 Octane

• Ethanol 10% and 91 Octane

Given that x is a normal variable with mean μ = 108 and standard deviation σ = 14, find the following probabilities. (Round your answers to four decimal places.) (a) P(x ≤ 120) (b) P(x ≥ 80) (c) P(108 ≤ x ≤ 117)

conduct AOV test. find ss, df, MS, F,P

According to the Center for Disease Control (CDC),76 million people in the US get diarrhea and upset stomachs each year. Most of these infections can be prevented by regularly washing one’s hands. A microbiologist believes that a majority (i.e. more than 50%) of women wash their hands after using the bathroom. She collects a sample of 40 women, calculates p, and performs a hypothesis test at alpha = 0.05.

(a) Give the hypotheses which the microbiologist wants to test.

(b) Describe a Type II error in terms of this problem.