Suppose that students own an average of 4 pairs of jeans. 8 people from your class were surveyed to determine if the average for students is higher than 4.

DATA TO USE:   2, 2, 3, 4, 6, 6, 8, 9

a. Give the null and alternative hypotheses: Ho: _______________ Ha: ___________________

b. In words, CLEARLY state what your random variable or P' represents.

c. State the distribution to use for the test. If t, include the degrees of freedom. If normal, include the mean and standard deviation.

d. p-value = ______________   

e. In 1 – 2 complete sentences, explain what the p-value means for this problem.

f. Use the previous information to draw a graph of this situation. CLEARLY, label and scale the horizontal axis and shade the region(s) corresponding to the p-value. The values of your sample statistic and the hypothesized value of the population parameter should be on the axis.

g. Indicate the correct decision (“reject the null hypothesis” or “do not reject the null hypothesis”) and write an appropriate conclusion, using COMPLETE SENTENCES.

   Decision:

   Conclusion:

h. Construct a 95% Confidence Interval for the true mean or proportion.   Include a sketch of the graph of the situation. Label the point estimate and the lower and upper bounds of the Confidence Interval.

Confidence Interval: ( ___________________ , ___________________ )

i. Interpret the confidence interval in a complete sentence.

With the gasoline time series data from the given table, show the exponential smoothing forecasts using α = 0.1.

week 1 2 3 4    5 6 7 8 9 10 11 12

sales 17 21 19 23 18 16 20 18 22 20 15 22  

a.

Applying the MSE measure of forecast accuracy, would you prefer a smoothing constant of α = 0.1 or α = 0.2 for the gasoline sales time series? Do not round your interim computations and round your final answers to three decimal places.

MSE

a=0.1 --- ( )

a = 0.2 --( )

Which is Preffered?

B.Are the results the same if you apply MAE as the measure of accuracy? Do not round your interim computations and round your final answers to three decimal places.

MAE

a=0.1 --- ( )

a = 0.2 --( )

Which is preffered?

C. What are the results if MAPE is Used? Do not round your interim computations and round your final answers to two decimal places.

MAPE

a=0.1 --- ( )%

a = 0.2 -- ( )%

Which is preffered?

In many agricultural and biological experiments, one may use a two‑way model with only one observation per cell. When one of the factors is related to the grouping of experimental units into more uniform groups, the design may be called a randomized complete block design (RCBD). The analysis is similar to a two‑way analysis of variance (question B) except that the model does not include an interaction term.

            The specific leaf areas (area per unit mass) of three types of citrus each treated with one of three levels of shading are stored in Table C. The first column contains the code for the shading treatment, the second column contains the code for the citrus species, and the third column contains the specific leaf area. Assume that there is no interaction between citrus species and shading. Carry out a two‑way analysis of this data.

            The shading treatment and citrus species are coded as follows:

            Treatment        Code                Species                        Code

            Full sun           1                      Shamouti orange         1

            Half shade       2                      Marsh grapefruit          2

            Full shade        3                      Clementine mandarin 3

nCopy the treatment code, the species code, and the specific leaf area into the EXCEL worksheet, label the columns and look at the data.

                                                                                                                                       {Example 1}

nPerform a two‑way (without interaction) analysis of this data and answer the following questions. Use a 5% significance level.

{Example 26}

            Recall that the confidence interval for a difference between two means is based on a calculation of the margin of error of the estimated difference. With a common variance (Error MS) and the same number of observations in all shading treatments, the margin of error of an estimated difference will be the same whether we calculate it for treatments 1 and 2, 1 and 3, or 2 and 3. This margin of error of the difference between two means is sometimes referred as the least significant difference (LSD).

nCalculate the LSD for comparing shading treatments in this experiment.

LSD = critical tvalue ´standard error of difference.

Use the critical t value with 4 degrees of freedom is t _0.025,4= 2.776.

n is the number of times of times each treatment was tested (in this case n = 3 for the 3 species).

A student at a four-year college claims that average enrollment at four-year colleges is higher than at two-year colleges in the United States. Two surveys are conducted. Of the 35 two-year colleges surveyed, the average enrollment was 5068 with a standard deviation of 4777. Of the 35 four-year colleges surveyed, the average enrollment was 5466 with a standard deviation of 8191.† Conduct a hypothesis test at the 5% level. NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

A) State the distribution to use for the test. (Enter your answer in the form zor t_dfwhere dfis the degrees of freedom. Round your answer to two decimal places.)

B) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value. (Upload your file below.)

A study conducted by the PEW Research Center reported that 62% of cell phone owners used their phones inside a store for guidance on purchasing decisions. A random sample of 13 cell phone owners is studied to understand how cell phones are used to make purchasing decisions. Write all answers as a decimal rounded to the fourth. a) Interpret the mean using the word expect. b) Find the standard deviation c) Find the probability of exactly 7 using their phones to make purchase decisions. Do this by hand and show your work. Please reference lecture examples for the amount of work to show. d) Find the probability less than 4 use their phones to make purchasing decisions. e) Find the probability at least 8 use their phones to make purchasing decisions.

83. Suppose that the length of long distance phone calls, measured in minutes, is known to have an exponential distribution with the average length of a call equal to eight minutes.

a. Define the random variable. X= ________________.

b. Is X continuous or discrete?

c. μ= ________

d. σ= ________

e. Draw a graph of the probability distribution. Label the axes.

f. Find the probability that a phone call lasts less than nine minutes.

g. Find the probability that a phone call lasts more than nine minutes.

h. Find the probability that a phone call lasts between seven and nine minutes.

i. If 25 phone calls are made one after another, on average, what would you expect the total to be? Why?

The director of an alumni association for a small college wants to determine whether there is any type of relationship

between the amount of an alumnus's contribution (in dollars) and the years the alumnus has been out of school.

Use the Data Analysis toolpack: Correlation and Regression and answer the questions below.

Years Contribution

1 500

5 154

3 300

10 61

7 75

6 80

Give the following:

correlation coefficient:

is there a significant correlation between variables?

Equation of the Regression line

a

b

Predict the amount of contribution if the alumnus has been out of school for 4 years.

How does gender and occupational prestige affect credibility? Graduate students in a public health program are asked to rate the strength of a paper about the health risks of childhood obesity. In reality, all student raters are given the same paper, but the name and degree associated with the author are changed. The student raters are randomly assigned to one group from the following name ("John Lake", "Joan Lake") and degree (M.D., R.N., Ph.D.) combination. The raters score the paper from 1 to 5 on clarity, strength of argument, and thoroughness. The total scores (the sum of the three scores) are given in the table below. What can be concluded with an α of 0.05?

a) What is the appropriate test statistic?
---Select--- na one-way ANOVA within-subjects ANOVA two-way ANOVA

b) Compute the appropriate test statistic(s) to make a decision about H₀.
Name: p-value =  ; Decision:  ---Select--- Reject H0 Fail to reject H0
Degree: p-value =  ; Decision:  ---Select--- Reject H0 Fail to reject H0
Interaction: p-value =  ; Decision:  ---Select--- Reject H0 Fail to reject H0


c) Compute the corresponding effect size(s) and indicate magnitude(s).
Name: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Degree: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Interaction: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect


d) Make an interpretation based on the results.

There is a name difference in the total scores.There is no name difference in the total scores.    

There is a degree difference in the total scores.There is no degree difference in the total scores.    

There is a name by degree interaction in the total scores.There is no name by degree interaction in the total scores.    

The success rate of corneal transplant surgery is 90%. The surgery is performed on eight (n = 8) patients. Work on Excel

1. Construct a binomial distribution table for the above scenario; include columns for X and P(x).
2. Graph the probability histogram for this binomial distribution.
3. Extend the table with columns for x × P(x), (x – μ)², and (x – μ)² × P(x). Use this extended table to calculate the mean, variance, and standard deviation for this binomial distribution.
4. Find the probability that the surgery is successful for exactly four (X = 4) patients. Is this an unusual event? (Remember that an unusual event is one whose probability is < .05) Why or why not?
5. Find the probability that the surgery is successful for fewer than five (X < 5) patients. Is this an unusual event? Why or why not?

In a backyard vineyard in Napa Valley with 10 grape vines in a row, if the weather works well (just right), rain in the Spring and dry through summer, the yield for each vine is distributed roughly binomial with N=700, p=0.6. In a drought the yield is Binomial with N=720 and P=0.5, while if the year is too wet, the yield of useful grapes per vine is N=650, P=0.65. Under climate change the probability of just the right year is about 0.4 of a too wet year is 0.1, and a dry year is 0.5. On a just right year the wine can sell for 120 dollars/bottle, on a dry year the quality drops so it will sell for 60 dollars a bottle, on wet year it will sell for 20 dollars a bottle (For a Z score with absolute value >5 assume the probability is 0) The yield for all 10 vines was more than 4210 grapes. Given this yield:

a) What is the probability that you will be able to sell for 120 dollars a bottle?

b) What is the probability that you will be selling for 60 dollars a bottle?

c) What is the probability that you can only sell for 20 dollars a bottle?

d) What is your expected revenue per bottle?

In a survey of 1,000 people, 420 are opposed to the tax increase. Construct a 95 percent confidence interval for the proportion of those people opposed to the tax increase.

I have conducted a linear regression model to predict student scores on an exam based on the number of hours they studied. I get a coefficient (slope) of +2.5 for the variable of hours studied. The pvalue for this coefficient is 0.45 and the 95% confidence interval is [-2.5, +7]. Which of the following conclusions CANNOT be drawn from these results?

A simple random sample of 60 items resulted in a sample mean of 84. The population standard deviation is 15.

a. Compute the 95% confidence interval for the population mean (to 1 decimal).

( , )

b. Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean (to 2 decimals).

( , )

How do you find the answers? Please write legibly! Thank you!

Describe the advantages of using R to perform basic statistical analysis, as compared to using Microsoft Excel's Data Analysis add-in Descriptive Statistics tool. Provide specific examples that justify the advantages you have described.

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

A random sample of 5400 physicians in Colorado showed that 2927 provided at least some charity care (i.e., treated poor people at no cost).

(a) Let p represent the proportion of all Colorado physicians who provide some charity care. Find a point estimate for p. (Round your answer to four decimal places.)


(b) Find a 99% confidence interval for p. (Round your answers to three decimal places.)

Give a brief explanation of the meaning of your answer in the context of this problem.

99% of all confidence intervals would include the true proportion of Colorado physicians providing at least some charity care.99% of the confidence intervals created using this method would include the true proportion of Colorado physicians providing at least some charity care.    1% of all confidence intervals would include the true proportion of Colorado physicians providing at least some charity care.1% of the confidence intervals created using this method would include the true proportion of Colorado physicians providing at least some charity care.

(c) Is the normal approximation to the binomial justified in this problem? Explain.

No; np > 5 and nq < 5.No; np < 5 and nq > 5.    Yes; np < 5 and nq < 5.Yes; np > 5 and nq > 5.