How can size of a sample hide a confounder? Is this a paradox?

Let X and Y be uniform random variables on [0, 1]. If X and Y are independent, find the probability distribution function of X + Y

Scores in the first and final rounds for a sample of 20 golfers who competed in tournaments are contained in the Excel Online file below. Construct a spreadsheet to answer the following questions.

Suppose you would like to determine if the mean score for the first round of an event is significantly different than the mean score for the final round. Does the pressure of playing in the final round cause scores to go up? Or does the increased player concentration cause scores to come down?

a. Use a = .10 to test for a statistically significantly difference between the population means for first- and final-round scores. What is the p-value?

p-value is .8904 (to 4 decimals)

What is your conclusion?

There is no significant difference between the mean scores for the first and final rounds.

b. What is the point estimate of the difference between the two population means?

.20 (to 2 decimals)

For which round is the population mean score lower?

Final round

c. What is the margin of error for a 90% confidence interval estimate for the difference between the population means?

?????? (to two decimals)

Could this confidence interval have been used to test the hypothesis in part (a)?

Yes

Explain.

Use the point of the difference between the two population means and add and subtract this margin of error. If zero is in the interval the difference is not statistically significant. If zero is not in the interval the difference is statistically significant.

A coworker claims that Skittles candy contains equal quantities of each color (purple, green, orange, yellow, and red). In other words, 1/5 of all Skittles are purple, 1/5 of all Skittles are green, etc. You, an avid consumer of Skittles, disagree with her claim. Test your coworker's claim at the α=0.10α=0.10 level of significance, using the data shown below from a random sample of 200 Skittles.

Which would be correct hypotheses for this test?

H0:H0: Red Skittles are cherry flavored; H1:H1: Red Skittles are strawberry flavored

H0:H0:Skittles candy colors come in equal quantities; H1:H1:Skittles candy colors do not come in equal quantities

H0:H0:Taste the Rainbow; H1:H1:Do not Taste the Rainbow

H0:p1=p2H0:p1=p2; H1:p1≠p2H1:p1≠p2

Sample Skittles data:

Test Statistic:



Give the P-value:



Which is the correct result:

Reject the Null Hypothesis

Do not Reject the Null Hypothesis

Which would be the appropriate conclusion?

There is not enough evidence to reject the claim that Skittles colors come in equal quantities.

There is not enough evidence to support the claim that Skittles colors come in equal quantities

2. The table below gives the list price and the number of bids received for five randomly selected items sold through online auctions. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the number of bids an item will receive based on the list price. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.

Price in Dollars 21 33 37 42 49

Number of Bids   3 5   7 9 10

Step 1 of 6: Find the estimated slope. Round your answer to three decimal places.

Step 2 of 6: Find the estimated y-intercept. Round your answer to three decimal places.

Step 3 of 6: Determine if the statement "Not all points predicted by the linear model fall on the same line" is true or false.

Step 4 of 6: Find the estimated value of y when x=37. Round your answer to three decimal places.

Step 5 of 6: Find the error prediction when x=37. Round your answer to three decimal places.

Step 6 of 6: Find the value of the coefficient of determination. Round your answer to three decimal places.

The bloodhound is the mascot of John Jay College. Suppose we weigh n=8 randomly selected bloodhounds and get the following weights in pounds

85.6, 91.6, 105.9, 83.1, 102.1, 92.5, 108.8, 81.4

Assume bloodhound weight are normally distributed with unknown mean of μ pounds and an unknown standard deviation of σ pounds.

e) Suppose W has a t distribution with 7 degrees of freedom. If P(W > t) = .03 then what is t?  

f) Suppose W has a t distribution with 7 degrees of freedom. If P(W < t) = .03 then what is t?  

g) Calculate the 97th percentile of a standard normal distribution.  

h) Compute a 94% Confidence Interval for μ using your answers above.

i) Compute a 94% Prediction Interval for a single future bloodhound weight measurement using your answers above..

3. Find the data female and male life expectancy for the 13 richest and 14 poorest countries on earth.

Test whether there is a difference of variances between male life expectancy of richest and poorest countries.

Test whether there is a difference of variances between female life expectancy of richest and poorest countries.

Among a simple random sample of 322 American adults who do not have a four-year college degree and are not currently enrolled in school, 145 said they decided not to go to college because they could not afford school.

1. Calculate a 99% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it, and interpret the interval in context. Round to 4 decimal places.

( , )

2. Suppose we wanted the margin of error for the 99% confidence level to be about 3.25%. What is the smallest sample size we could take to achieve this? Note: For consistency's sake, round your z* value to 3 decimal places before calculating the necessary sample size.

Choose n =

Given the question:

"Researchers found that 25% of the beech trees in east central Europe had been damaged by fungi. Consider a sample of 20 beech trees from this area.

How many of the sampled trees would you expect to be damaged by fungi?"

I was asked, "The question as asked is misleading, why? Nevertheless, give a numerical answer."

I don't see how this question is misleading. All I can think of it asking for is expected value, which would be µ = (0.25)(20) = 5. So my question is not what the expected value is, my question is how is the question misleading, what am I missing here?

4. In a survey sponsored by the Lindt chocolate company, 1708 women were surveyed and 85% of them said that chocolate made them happier. (a) Is there anything potentially wrong with this survey? (b) Of the 1708 women surveyed, what is the number of them who said that chocolate made them happier? (c) Use Excel to construct a 98% confidence interval estimate of the percentage of women who say that chocolate makes them happier. Insert a screenshot, write down the confidence interval and write a brief statement interpreting the result. 3 (d) Use Excel to test the claim that when asked, more than 80% of women say that chocolate makes them happier. Use a 0.02 significance level. (i.e. complete steps (a) to (e) similar to question 3) (e) Does your result from (d) contradict your result from (c)? Explain

The U-Plant’um Nursery must determine if there is a difference in the growth rate of saplings that have been treated with four different chemical formulas. The resulting growth rates over a given period are shown here. Does a difference appear to exist in the growth factor of the formulas? Set alpha = 0.01.

                                                                        FORMULA

                                                10                    8                      5                      7

                                                12                    15                    17                    14

                                                17                    16                    15                    15

5. Listed in the table below are the robbery and aggravated assault rates (occurrences per 100,000) for the 12 most populated U.S. cities in 2006: City Robbery (x) Aggravated Assault (y) New York 288 330 Los Angeles 370 377 Chicago 555 610 Houston 548 562 Phoenix 288 398 Philadelphia 749 720 Las Vegas 409 508 San Antonio 180 389 San Diego 171 301 Dallas 554 584 San Jose 112 248 Honolulu 105 169 a. Calculate the standard error of the estimate. b. Estimate the strength of the linear relationship between x and y.

A 99% CI on the difference between means will be (longer than/wider than/the same length as/shorter than/narrower than )a 95% CI on the difference between means.

In semiconductor manufacturing, wet chemical etching is often used to remove silicon from the backs of wafers prior to metalization. The etch rate is an important characteristic in this process and known to follow a normal distribution. Two different etching solutions have been compared, using two random samples of 10 wafers for each solution. Assume the variances are equal. The etch rates are as follows (in mils per minute):

(a) Calculate the sample mean for solution 1: x¯1=  Round your answer to two decimal places (e.g. 98.76).

(b) Calculate the sample standard deviation for solution 1: s₁ =  Round your answer to three decimal places (e.g. 98.765).

(c) Calculate the sample mean for solution 2: x¯2=  Round your answer to two decimal places (e.g. 98.76).

(d) Calculate the sample standard deviation for solution 2: s₁ =  Round your answer to three decimal places

(e) Test the hypothesis H0:μ1=μ2 vs H1:μ1≠μ2.
Calculate t₀ =  Round your answer to two decimal places (e.g. 98.76).

(f) Do the data support the claim that the mean etch rate is different for the two solutions? Use α=0.05.                            yesno

(g) Calculate a 95% two-sided confidence interval on the difference in mean etch rate.

(Calculate using the following order: x¯1-x¯2)
(   ≤ μ1-μ2 ≤  ) Round your answers to three decimal places (e.g. 98.765).