Describe a correlation analysis, and provide an example of one. Provide examples of dependent and independent variables, as well.

The average number of sales at a car dealership is 24 with a standard deviation of 5. A week ago, you were promoted to manager. Over this week (seven days), the average number of sales has dipped to 20. Your boss says he is coming by tomorrow to check out how you have been doing. You know that your boss has a rule where he will fire any manager if the average number of sales is statistically lower than 24 with 99% confidence. Are you going to get fired? Complete a one sided hypothesis test.

Z =

p =

Critical Value =

Alpha =

Are you going to get fired?

No /Yes

What's the slope of this data (round to two decimal places)?

What's the Y intercept (round to two decimal places)?

What's the predicted test score for a stress level of 10 (round to two decimal places)?

What's the error of participant 5's score (round to two decimal places)?

What's the standard error of the estimate?

What is the coefficient of determination?

The following table shows the average distance, to the nearest mile, travelled per week to work by a random sample of 350 commuters.

Miles Travelled Frequency Midpoint Class Boundaries

6 - 11 43

12 - 17 32

18 – 23 80

24 - 29 120

30 - 35 75

(a) Complete the table above.

(b) What is the mean distance travelled per week by these commuters?

(c) Why is the answer for part (b) an estimate of the mean distance travelled?

(d) State one advantage and one disadvantage of using the mean as a measure of central tendency.

(e)What is the modal length of distance travelled by the commuters?

(f) Calculate the variance for the distance travelled per week by the commuters.

Question 1

The average sea surface temperature (in degree Celsius) and the coral growth (in millimetres per year) over 18 years at a particular location are observed. An excerpt of the data is shown in the table below:

Temperature (x)= 29.61 29.82 30.25 … 30.96

Growth (y)= 2.63 2.58 2.49 … 2.26

The output from R Commander appears on the next page

(c) Using the R Commander output, calculate the correlation coefficient between the two variables. [2 marks]

(d) Test the significance of the slope of the linear regression line at the 5% level of significance. State clearly the null and alternative hypotheses, the name of the test or the test statistic, decision rule, test result and conclusion in terms of the original problem. [6 marks]

(e) Write down the linear regression equation for the data. (1MARK)

(f) Interpret the slope of the linear regression equation. [1 mark]

(g) Use the equation in (e), predict the coral growth when the average sea surface temperature is 30 degree Celsius. [1 mark]

(h) Comment on the appropriateness of the prediction in (g). [2 marks]

(i) Write down three assumptions underlying the analysis. [3 marks]

> summary(RegModel.1)

Call: lm(formula = Growth ~ Temperature, data = Q1)

Residuals:

Min 1Q Median 3Q Max

-0.10279 -0.04107 -0.01688 0.04901 0.09864

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 7.81986 1.11135 7.036 2.81e-06 ***

Temperature -0.17860 0.03698 -4.830 0.000185 ***

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.06155 on 16 degrees of freedom

Multiple R-squared: 0.5931, Adjusted R-squared: 0.5677

F-statistic: 23.33 on 1 and 16 DF, p-value: 0.0001848

1. Let’s use Excel to simulate rolling two dice and finding the rolled sum.

• Open a new Excel document.

• Click on cell A1, then click on the function icon fx and select Math&Trig, then select RANDBETWEEN.

• In the dialog box, enter 1 for bottom and enter 6 for top.

• After getting the random number in the first cell, click and hold down the mouse button to drag the lower right corner of this first cell, and pull it down the column until 25 cells are highlighted. When you release the mouse button, all 25 random numbers should be present.

• Repeat these four steps for the second column, starting in cell B1.

• Put the rolled sum of two dice in the third column: Highlight the first two cells in the first row and click on AutoSum icon. Once you receive the sum of two values in the third cell, drag the lower right corner of this cell, C1, down to C25. This will copy the formula for all 25 rows. We now have 25 trials of our experiment.

• Once these steps are completed, attach a screenshot of your Excel file to your assignment.

(a) Find the probability that the rolled sum of both dice is 5.

(b) Based on the results of our experiment of 25 trials, obtain the relative frequency approximation to the probability found in (a).

(c) Repeat the simulation for 50 and 100 trials, and calculate the relative frequency approximation to the probability in (a) for each. Which approximation has the closest value to the probability?

(d) Briefly explain how these experiments demonstrate the Law of Large Numbers.

Crop rotation is a common strategy used to improve the yields of certain crops in subsequent growing seasons. An experiment was performed to assess the effects of crop rotation plant type and crop rotation plant density levels on the yield of corn, the primary crop of interest. A field was separated into 12 plots and each of the treatments was randomly applied. After 2 months of growth of the rotated crops, the plots were cleared, and corn seeds were applied evenly to each plot. After 5 months of growth of the corn, the yields were assessed. The data, in kg/m2, are shown below. Determine if crop rotation plant type and density affect the yields of corn in this field. What treatment should the farmers use to maximize the yield?

1. What kind of statistical test will you be performing?
2. Will you need to test for equal variance? If so what are your results and how does that influence the next steps in your analysis?
3. What are your null and alternative hypotheses?
4. Discuss the results of your analysis. Will you accept or reject your null hypothesis? Why? What can you specifically say about the data?

A sleep center hypothesizes that people who sleep only four hours will score lower than people who sleep for eight hours on a cognitive skills test. The center recruited 20 participants and split them into two groups, giving one group 8 hours of sleep and the other only 4 hours. The following morning, the CAT (Cognitive Ability Test) was conducted, with scores ranging from 1-9, 9 being the best score. Use this information to answer questions . CAT Scores Group X: Eight hrs sleep 4 7 9 4 3 3 8 6 3 7 Group Y: Four hrs sleep 7 8 1 4 2 3 5 2 7 4 Conduct the following hypothesis test: - A one-tail T-test for a two-sample difference in means at the 95% confidence level - with Null Hypothesis that the Group X mean CAT score is equal to the Group Y mean CAT score - and with Alternate Hypothesis that the Group X mean CAT score is greater than the Group Y mean CAT score a). Calculate the mean and standard deviation of the scores for each group. (10%)

b)Using the correct degrees of freedom (df = group X size + group Y size ̶ # of groups), the correct number of tails, and at the correct confidence level, determine the critical value of t. (10%)

c). Explain under which scenarios using a pooled variance be inadvisable, then, calculate the pooled variance (formula for S2 is on page 379) for the groups. (10%)

d). Calculate the test statistic, Ttest (formula for t is on page 380). (10%)

e). The sleep center’s statistician tells you that the p-value for the test is 0.1535. Summarize the result of the study. Compare the mean scores in each group. Compare the test statistic to the critical value. Compare the p-value to alpha. Do you find a statistically significant difference between Group X and Group Y on cognitive test performance? Is there a meaningful/practical difference? Explain your decisions and Justify your claims

The ability of a mouse to recognize the odor of a potential predator is essential to the mouse’s survival. Typically, the source of these odors are major urinary proteins (Mups). 30% of lab mice sells exposed to chemically produced cat Mups responded positively (i.e. recognized the danger of the lurking predator). Consider a sample of 100 lab mice cells, each exposed to chemically produced cat MUPS. Let X represents the number of cells that respond positively.

a) Explain why the probability distribution of X can be approximated by the binomial distribution.

b) Find E(X) and interpret its value, practically.

c) Find the variance of X.

d) Give an interval that is likely to contain the value of X (2 st. dev around the mean).

e) How likely is it that less than half of the cells respond positively to cat Mups?

Suppose the following data were collected from a sample of 1515 houses relating selling price to square footage and the architectural style of the house. Which of the following is the best equation to use relating the selling price of a house to square footage and the style of the house?

Copy Data

Twenty laboratory mice were randomly divided into two groups of 10. Each group was fed according to a prescribed diet. At the end of 3 weeks, the weight gained by each animal was recorded. Do the data in the following table justify the conclusion that the mean weight gained on diet B was greater than the mean weight gained on diet A, at the α = 0.05 level of significance? Assume normality. (Use Diet B - Diet A.)

Diet A 5 13 9 8 10 14 5 8 7 5

Diet B 15 10 11 13 16 11 20 11 10 13

(a) Find t. (Give your answer correct to two decimal places.)

(ii) Find the p-value. (Give your answer correct to four decimal places.)

Is there a way to do this problem on a TI-84 Plus calculator? If so can you please break down the steps in getting the answers on the calculator? Thank you!

Which of the following distribution-free tests has the lowest efficiency rating compared to its

parametric counterpart?

A) Kruskal-Wallis test

B) Wilcoxon rank-sum test

C) Wilcoxon signed-ranks test

D) rank correlation test

1)Assume that the service life in years of a semiconductor is a random variable that has the Weibull distribution with alpha = 5 and beta = 3. What is the probability that a semiconductor like that will still be in operational condition between 3.7 and the 5 years?

2)Assume that the service life in years of a semiconductor is a random variable that has the Weibull distribution with alpha = 2 and beta = 4. What is the probability that a semiconductor like that will still be in operational condition until 4.9 years ?

1. *The following another set of data that looking at how long it takes to get to work. Let x= commuting distance (miles) and y= commuting time (minutes)

1. Give a scatterplot of this data and comment on the direction, form and strength of this relationship.
2. Determine the least-squares estimate equation for this data set.
3. Give the r², comment on what that means.
4. Give the residual plot based on the least-squares estimate equation.
5. Test if this least-squares estimate equation specify a useful relationship between commuting distance and commuting time.

answer all questions

Suppose that independent trials, each of which is equally likely to have any of m possible outcomes, are performed until the same outcome occurs k consecutive times. If N denotes the number of trials show that, E[N]=(m^k - 1)/(m-1)