The average rainfall during the month of April follows a normal distribution with a mean of 5 in. and a standard deviation of 0.6 in. What is the probability that the rainfall in April will be less than 4 in.?

Consider a hypergeometric probability distribution with nequals4​, Requals4​, and Nequals10. ​a) Calculate ​P(xequals0​). ​b) Calculate ​P(xgreater than​1). ​c) Calculate ​P(xless than4​). ​d) Calculate the mean and standard deviation of this distribution. ​a)​ P(xequals0​)equals nothing ​(Round to four decimal places as​ needed.) ​b)​ P(xgreater than​1)equals nothing ​(Round to four decimal places as​ needed.) ​c)​ P(xless than4​)equals nothing ​(Round to four decimal places as​ needed.) ​d) The mean of this distribution is nothing. ​(Round to three decimal places as​ needed.) The standard deviation of this distribution is nothing. ​(Round to three decimal places as​ needed.)

1. A loan officer compares the interest rates for 48-month fixed-rate auto loans and 48-month variable-rate auto loans. Two independent, random samples of auto loan rates are selected. A sample of eight 48-month fixed−rate auto loans had the following loan rates (all written as percentages): 8.75 7.63 7.26 9.43 7.86 7.20 8.09 8.60 while a sample of five 48−month variable−rate auto loans had loan rates as follows: 7.60 7.00 6.79 7.36 6.99

(a) Set up the null and alternative hypotheses needed to determine whether the mean rates for 48-month fixed-rate and variable-rate auto loans differ. H0: µf − µv = 48 versus Ha: µf − µv ≠ 48

(b) Use the data analysis tool in Excel to test the hypotheses you set up in part a. Assuming that the normality and equal variances assumptions hold, use the Excel output and critical values to test these hypotheses by setting α equal to .10, .05, .01, and .001. How much evidence is there that the mean rates for 48−month fixed and variable−rate auto loans differ? (Round your answer to 3 decimal places.) t = with 11 df Reject H0 at α = , but not at α =

(c) Use the p−value to test these hypotheses by setting α equal to .10, .05, .01, and .001. How much evidence is there that the mean rates for 48−month fixed− and variable−rate auto loans differ? (Round your answer to 4 decimal places.) p−value = Reject H0 at α = but not at α =

(d) Use a hypothesis test to establish that the difference between the mean rates for fixed− and variable−rate 48−month auto loans exceeds .4. Use α equal to .05. (Round your t answer to 3 decimal places and other answers to 1 decimal place.) H0: µf − µv versus Ha: µf − µv t = H0 with a = .05.

Why it’s important to have good randomization before introducing an intervention when conducting a randomized control trial?

A researcher compares the effectiveness of two different instructional methods for teaching physiology. A sample of 157 students using Method 1 produces a testing average of 65.9. A sample of 129 students using Method 2 produces a testing average of 80. Assume the standard deviation is known to be 12.47 for Method 1 and 12.84 for Method 2. Determine the 95% confidence interval for the true difference between testing averages for students using Method 1 and students using Method 2.

Step 1 of 2:

Find the critical value that should be used in constructing the confidence interval.

In a normal simple linear regression model you are given that the variance of the error term is 4. Four observations are taken, in which the X values are X=-2,1,2,3. Calculate the variance in the estimate for the slope coefficient.

A local statistician is interested in the proportion of high school students that drink coffee. Suppose that 20% of all high school students drink coffee. A sample of 75 high school students are asked if they drink coffee.

What is the probability that out of these 75 people, 14 or more drink coffee?

A population has a mean of 200 and a standard deviation of 60. Suppose a sample of size 100 is selected and is used to estimate . Use z-table.

What is the probability that the sample mean will be within +/- 6 of the population mean (to 4 decimals)? (Round z value in intermediate calculations to 2 decimal places.)

What is the probability that the sample mean will be within +/- 17 of the population mean (to 4 decimals)? (Round z value in intermediate calculations to 2 decimal places.)

The National Student Loan Survey asked the student loan borrowers in their sample about attitudes toward debt. Below are some of the questions they asked, with the percent who responded in a particular way. Assume that the sample size is 1253 for all these questions. Compute a 95% confidence interval for each of the questions, and write a short report about what student loan borrowers think about their debt. (Round your answers to three decimal places.)

(a) "To what extent do you feel burdened by your student loan payments?" 55.9% said they felt burdened.

(b) "If you could begin again, taking into account your current experience, what would you borrow?" 54.7% said they would borrow less.

(c) "Since leaving school, my education loans have not caused me more financial hardship than I had anticipated at the time I took out the loans." 33.2% disagreed.

(d) "Making loan payments is unpleasant but I know that the benefits of education loans are worth it." 59.9% agreed.

(e) "I am satisfied that the education I invested in with my student loan(s) was worth the investment for career opportunities." 58.2% agreed.

(f) "I am satisfied that the education I invested in with my student loan(s) was worth the investment for personal growth." 71.3% agreed.

Conclusion

While many feel that loans are a burden and wish they had borrowed less, a majority are satisfied with their education.

While a minority feel that loans are a burden and wish they had borrowed more, a minority are satisfied with their education.     

While many feel that loans are a burden and wish they had borrowed less, a minority are satisfied with their education.

While a minority feel that loans are a burden and wish they had borrowed more, a majority are satisfied with their education.

Ten randomly selected people took an IQ test A, and next day they took a very similar IQ test B. Their scores are shown in the table below. Person A B C D E F G H I J Test A 113 107 112 85 97 103 94 71 125 89 Test B 120 107 114 88 97 103 93 74 124 94 1. Consider (Test A - Test B). Use a 0.05 significance level to test the claim that people do better on the second test than they do on the first. (Note: You may wish to use software.) (a) What test method should be used? A. Two Sample t B. Two Sample z C. Matched Pairs (b) The test statistic is (c) The critical value is (d) Is there sufficient evidence to support the claim that people do better on the second test? A. No B. Yes 2. Construct a 95% confidence interval for the mean of the differences. Again, use (Test A - Test B). <μ

A professor in the School of Business wants to investigate the prices of new textbooks in the campus bookstore and the Internet. The professor randomly chooses the required texts for 12 business school courses and compares the prices in the two stores. The results are as follows:

a)At the .01 level of significance, is there any evidence of a difference in the average price of business textbooks between the campus store and the Internet? Use Excel and the classical method.

1. Hyps: H₀:  

2. H₁:

3. Test(s):
4. Decision rule:

5. analysis

6. conclusion:(1)

   (2)

   (3)

   (4)

   b) What assumptions are necessary to perform this test?

   c)Find the p-value in (a)? Using the p-value, Is there any evidence of a difference in the average price of business textbooks between the campus store and the Internet? Use Excel and the p-value method and alpha = 1%.

   1. Hyps: H₀: 2. H₁:

7. Test(s):

8. analysis

9. p- value

10. conclusion:(1)

    (2)

    (3)

    (4)

Suppose X is a normal random variable with μ = 600 and σ = 89. Find the values of the following probabilities. (Round your answers to four decimal places.)

(a) P(X < 700)

(b) P(X > 350)

(c) P(300 < X < 900)

A poker hand contains five cards. Find the mean of each of the following:

a. The number of spades in a poker hand.

b. The number of different suits in a poker hands

c. The number of aces in a poker hand.

d. The number of different face values in a poker hand.

Show steps for each part please.

In a study of binge drinking among undergraduates at Ohio University, a researcher was interested in gender differences as related to binge drinking and to drinking-related arrests. She wanted to know two things: (a) Is there a significant relationship between gender and binge drinking (as defined by 5 or more drinks at one sitting), and (b) Is there a significant relationship between gender and drinking-related arrests? A random sample of males and females were asked about their experiences with binge drinking and with drinking-related arrests. Test for a relationship in the following data:

                  Experience Alcohol-related Arrest?

  YES        NO

   Male                       38         25

   Female                   26         48


What is the calculated chi-squared value

(Minitab)

Ice Cream Sales

Answer the following questions, showing any calculations involved. Include this document along with the graphs created with Minitab in your submission.

1. Identify the independent (predictor) and dependent (response) variables. [2 pts]

Independent variable: __________________ Dependent variable: __________________

2. From the scatter diagram, does there seem to be a linear correlation? If so, is it strong or weak? Is it positive or negative? What does it say about the relationship between the 2 variables? [4 pts]

3. Use your scatter diagram to answer the following questions.
   1. If you calculated the linear correlation coefficient for this data to be r = –0.75, explain in one sentence how you know this is incorrect. [2 pts]
   2. If you calculated the linear correlation coefficient for this data to be r = 1.20, explain in one sentence how you know this is incorrect. [2 pts]

4. What is the correlation coefficient, r. Based on the correlation coefficient, how accurate do you think your regression equation is at making a prediction? Why? [2 pts]

5. What is the p-value? Is a linear relationship appropriate? How do you know? [2 pts]

6. Identify the following quantities: [3 pts]

Regression Equation: ______________________________

Slope: _______________ y-Intercept: _______________

7. Explain the meaning of the slope in terms of this problem. [5 pts]

8. Explain the meaning of the y-intercept in terms of this problem. Is it meaningful? Why or why not? [5 pts]

9. Predict the ice cream cone sales on a day where the high temperature was 75°.

10. On a 70° day, the Creamery had sales of 400 ice cream cones. Is this sales figure above or below the average for this temperature? Show your work for credit. [2 pts]

11. Answer the following questions.
    1. The high temperature on Saturday is predicted to be 75°. Would it be reasonable to use the regression equation you created to predict this day’s sales? Why or why not? [2 pts]
    2. The high temperature on Sunday is predicted to be 85°. Would it be reasonable to use the regression equation you created to predict this day’s sales? Why or why not? [2 pts]

1. 3. The high temperature on Sunday at the Creamery’s Buffalo store is predicted to be 74°. Would it be reasonable to use the regression equation you created to predict this store’s sales? Why or why not? [2 pts]

12. Compute and interpret R². [4 pts]

Ice Cream Data

Temperature F Sales

57.6        215

61.5        325

53.4        185

59.4        332

65.3        406

71.8        522

66.9        412

77.2        614

74.1        544

64.6        421

72.7        445

63.0        408

64.4        250

66.2        345

73.4        459

62.6        349

66.2        311

73.4        463

59.0        262

73.4        462

55.4        274

75.2        459

55.4        252

69.8        426

57.2        289

69.8        438

57.2        311

68.0        448

64.4        257

73.4        477

64.4        319

73.4        479

71.6        490

60.8        347

59.0        349

68.0        436