When traveling 40 mph (miles per hour), the distance that it takes Fred’s car to stop varies evenly between 120 and 155 feet. (This includes the reaction distance and the braking distance.) All of the questions are related to the stopping distance when Fred is traveling 40 mph.

a) Let S be the distance it takes for Fred’s car to stop at when traveling 40 mph. Find the distribution, parameter(s), and support of S.

b) What is the probability that it takes between 115 and 138 feet for the car to stop?

c) Find the expected distance it will take Fred to stop and the standard deviation of the stopping distance.

d) What values represent the middle 60% of Fred’s stopping distances?

e) Suppose a squirrel darts into the road as Fred is driving, and when Fred finally sees the squirrel and applies the brakes, the squirrel is 131 feet away. What is the probability that the squirrel survives its encounter with Fred (i.e. that Fred stops before he hits the squirrel)?

f) Fred knows that when it rains, it will take a minimum of 127 feet to stop. Fred is out driving while it is raining. If there is a stop sign that is 135 feet away, what is the probability that Fred stops in time?

Using plots and descriptive statistics is too simple for making any marketing decisions (T or F)

Median should always be preferred over mean because it is less sensitive to outliers (T or F)

If the data is largely skewed to right, median could be a better typical value than mean (T or F)

Discrete variable and continuous variable can be used at the same time for independent variables. (T or F)  

Regression analysis requires us to have at least one discrete independent variable.

USE SSPS FOR THIS APPLICATION EXERCISE!!!

A nurse at a health clinic hypothesizes that ear thermometers measure lower body temperature than oral thermometers. The nurse selects a sample of healthy staff members and took the temperature of each with both thermometers. The temperature data are below. What can the nurse conclude with α = 0.05?

a) What is the appropriate test statistic?
---Select--- na, z-test, One-Sample t-test, Independent-Samples t-test, Related-Samples t-test

b)
Condition 1:
---Select--- oral thermometer, body temperature, health clinic, staff members, ear thermometer
Condition 2:
---Select--- oral thermometer, body temperature, health clinic, staff members, ear thermometer

c) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
p-value =   ; Decision:  ---Select--- Reject H0, Fail to reject H0

d) Using the SPSS results, compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
d =   ;   ---Select--- na, trivial effect, small effect, medium effect, large effect
r² =   ;   ---Select--- na, trivial effect, small effect, medium effect, large effect

e) Make an interpretation based on the results. (select one)

-The ear thermometer measured significantly higher temperatures than the oral thermometer.

-The ear thermometer measured significantly lower temperatures than the oral thermometer.    

-There was no significant temperature difference between the ear and oral thermometer.

Let the independent random variables X1, X2, and X3 have binomial distributions with parameters n1=3, n2=5, n3=2 and the same probabilitiy of success p = 2/5.

Find P(X1=1-X3).

Find P(X1=X3).

Find P(X1+X2+X3>=1).

Find the expected value and variance for X1+X2+X3.

According to the Normal model ​N(0.052​,0.027) describing mutual fund returns in the 1st quarter of​ 2013, determine what percentage of this group of funds you would expect to have the following returns. Complete parts​ (a) through​ (d) below.

Explain the difference between a set that is well defined and one that is not. Give an example of a well-defined set. Name and describe your well-defined set using roster form and set-builder notation. Give an example of at least 1 subset. NO HANDWRITING PLEASE.

1. Listed below are attractiveness ratings made by participants in a speed dating session. Each attribute rating is the sum of the ratings of five attributes (sincerity, intelligence, fun, ambition, shared interests)

Use a 0.05 significance level to test the claim that there is a difference between female attractiveness ratings and male attractiveness rating by following the steps below:

1. (a) State the null and alternative hypotheses, indicate the significance level and the type of test (left-, right-, or two-tailed test).

2. (b) Calculate by hand the test statistic.

3. (c) Use the appropriate sheet in the Hypothesis Test and Confidence Interval template to complete all relevant computations (including the test statistic: compare with (b) to confirm your calculation is correct). Add a screenshot.

4. (d) Use the P-value obtained in (c) to explain whether or not the null hypothesis is rejected.

5. (e) Make a concluding statement.

6. (f) Comment on potential issues related to the validation of your result (Hint: the sub-

   jective nature of the measures)

4. Consider the relationship between the number of bids an item on eBay received and the item's selling price. The following is a sample of 5 items sold through an auction.

Price in Dollars 137 137 151 180 187

Number of Bids 11 12 15 16 17

Step 1 of 5: Calculate the sum of squared errors (SSE). Use the values b0= −1.8618 and b1= 0.1014 for the calculations. Round your answer to three decimal places.

Step 2 of 5: Calculate the estimated variance of errors, s2e. Round your answer to three decimal places.

Step 3 of 5: Calculate the estimated variance of slope, s2b1. Round your answer to three decimal places.

Step 4 of 5: Construct the 98% confidence interval for the slope. Round your answers to three decimal places.

Lower endpoint and Upper endpoint

Step 5 of 5: Construct the 90% confidence interval for the slope. Round your answers to three decimal places.

Lower endpoint and Upper endpoint

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.