Test the given claim about the means of two populations. Assume that two dependent samples have been randomly selected from normally distributed populations. A test of abstract reasoning is given to a random sample of students before and after they completed a formal logic course. The results are given below. At the 0.05 significance level, test the claim that the mean score is not affected by the course. Include your null and alternative hypotheses, the test statistic, P-value or critical value(s), conclusion about the null hypothesis, and conclusion about the claim in your answer.

Conduct a test at the a = 0.05 level of significance by determining (a) the null and alternative hypotheses (b) the test statistic (c) the critical value, and (d) the P-value. Assume that the samples were obtained independently using simple random sampling.

1. Test whether p₁ is not equal to p₂. Sample data: x₁ = 804, n₁ = 874, x₂ = 902, n₂ = 954

An electronics company is looking to develop a regression model to predict the number of units sold for a special running watch. Data is provided below:

Compile a spreadsheet for the data and determine the predicted number of units sold if the watch is sold on a holiday for $200 while $150 is spent on advertising.

In a waiting line situation, arrivals occur at a rate of 3 per minute, and the service times average 12 seconds. Assume the Poisson and exponential distributions.

1. Based on past experience, a bank believes that 7% of the people who receive loans will not make payments on time. The bank takes a random sample of 200 recently approved loans.
   1. Find the quartiles of the sample proportions of clients who will not make timely payments.
   2. What values of sample proportions of clients who will not make timely payments would be unusual? Explain.
   3. Construct and interpret a 95% confidence interval for the true proportion of clients who will not make timely payments.
   4. Since the U.S. economy has changed, bank officials would like to do a new study to estimate the true proportion of clients who will not make timely payments. Assume you have no preconceived idea of what that proportion would be. What sample size is needed if you wish to be 99% confident that your estimate is within 2% of the true proportion.   
   5. Based on previous research, you assume the proportion of clients who will not make timely payments is 7%. What sample size is needed if you wish to be 99% confident that your estimate is within 2% of the true proportion.

The breaking strength of yarn used in the manufacture of woven carpet material is Normally distributed with 2.4 psi (pound-force per square inch). A random sample of 16 specimens of yarn from a production run were measured for breaking strength and a confidence interval for the breaking strength of yarn was found to be (128.7, 131.3).

(a) What is the confidence level, C, of this interval?

A. 90% B. 92% C. 95% D. 96% E. 97% F. 98.5% G. 99% H. None of Above

(b) What is the margin-of-error of this study?

A. 130 B. 65 C. 2.6 D. 1.3 E. None of Above F. Unable to determine with the information provided.

(c) Is it possible that the breaking strength of yarn used in the manufacture of woven carpet is 120 psi?

A. Yes B. No C. Unable to determine with the information provided.

Descriptive analysis revealed that the mean Test 3 score of all 63 students in Dr. Bills’s statistics courses was an 80. Similarly, the standard deviation for all students’ Test 3 scores was found to be 16. Assume the Test 3 scores are approximately normally distributed.

5. Determine the Test 3 score that corresponds to a z-score of -2.18. Round your solution to the nearest whole number.

6. Find the 75^th percentile. That is, find the test score such that 75% of all test scores are below it. Hint: See example on the Chapter 6 handout. Round your solution to the nearest whole number.

24)____________       An SAT prep course claims to improve the test scores of students. The

                                     table shows the scores for seven students the first two times they took                    

25)_____________     the verbal SAT. Before taking the SAT for the second time, each

                                     student took a course to try to improve his or her verbal SAT scores.  

                                     Test the claim at a = .05. List the a) null hypothesis b) average difference       

                                   between the scores        

26)______________   In a crash test at five miles per hour, the mean bumper repair cost for 14

                                    midsize cars was $547 with a standard deviation of $85. In a similar test               

                                    of 23 small cars, the mean bumper repair cost was $347 with a standard                      

27)______________ deviation of $185. At a = 0.05, can you conclude that the mean bumper

                                    repair cost is the same for midsize cars and small cars? List the

                                    26) p-value 27) accept or reject.

The distribution of GPA scores is known to be left-skewed. At a large university, the administration is interested in learning about the average GPA score of the undergraduate students. A simple random sample of 75 undergraduates results in an average GPA score of 2.97. Assume that the distribution of GPA scores of the undergraduates at this university is also left-skewed with a standard deviation of 0.62.

(a) Which of the following statements is true?

A. The sampling distribution is normal.

B. The population distribution is normal.

C. Both the sampling distribution and the population distribution are normal.

D. Neither the sampling distribution nor the population distribution is normal.

E. Unable to determine with the information provided.

(b) What is the 97% confidence interval for the mean GPA of the undergraduates?

A. (1.625, 4.315)

B. (2.835,3.105)

C. (1.73, 4.70)

D. (2.815, 3.125)

E. (1.804, 4.136)

F. (2.827, 3.113)

G. (2.830, 3.110)

H. None of Above

Experiment 2: Hematocrit In the second experiment, you will determine hematocrit for all students in the class to answer the research question: Is there a difference in hematocrit between male and female college students?

a. What basic type of study design will you use to answer the research question?

a) descriptive b) experimental c) neither

b.  More specifically, what type of study design will you use to answer the research question?

a) case study b) cross-over c) cross-sectional d) longitudinal e) pre/post f) randomized, controlled g) retrospective h) time series

c. What type of statistical test would be most appropriate to analyze these data?

a) Chi-square test b) dependent t-test c) independent t-test d) one-way ANOVA e) repeated measures ANOVA f) None of these is appropriate. g) You cannot run statistics on these data.

d. What is(are) the control(s)? Choose ANY that apply.

a) altitude of testing site b) hydration status of subjects c) sex of subjects d) training status of subjects e) There is none.

A farmer has decided to use a new additive to grow his crops. He divided his farm into 10 plots and kept records of the corn yield (in bushels) before and after using the additive. The before (first row) and after (second row) results from the 10 different plots are shown below.

Corn Yield

Before 9 9 8 7 6 8 5 9 10 11

After 10 9 9 8 7 10 6 10 10 12

You wish to test the following hypothesis at the 1 percent level of significance.

H0= µ=0 against H1: µd > 0

What decision rule would you use?

a.) Reject H0 if test statistic is less than 2.821

b.) Reject H0 if test statistic is greater than -2.821

c.) Reject H0 if test statistic is greater than 2.821

d.) Reject H0 if test statistic is greater than -2.821 or less than 2.821

（1） A study reported that 55% of Americans say parents are doing too much for their young adult children these days. The smallest sample size for which the sampling distribution of sample proportion is approximately normal is （ ） . (Your answer must be an integer.)

（2）To estimate the average income among all U.S. workers, we obtain a simple random sample of 1000 U.S. workers and calculate their average income. Then, we should

(I) conclude that the average income among all U.S. workers is the value we calculated.

(II) compute a confidence interval for the average income of all U.S. workers.

(III) perform a test of significance to see if the sample data are reliable.

A. (I) only B. (II) only C. (III) only D. (I) and (II) only E. (I) and (III) only F. (II) and (III) only

how is the interpretation of slopes in multiple regression model different from simple regression slope?

How repeated measures ANOVA control for individual differences?

write an essay in response to the merits and demerits of grading on a bell curve.

Use the following article https://cubelogger.wordpress.com/2011/07/15/the-merits-and-demerits-of-grading-on-a-bell-curve/

STRAIGHT FROM THE BOOK

Roulette In the casino game of roulette there is a wheel with 19 black slots, 19 red slots, and 2 green slots. In the game, a ball is rolled around a spinning wheel and it lands in one of the slots. It is assumed that each slot has the same probability of getting the ball. This results in the table of probabilities below.

Fair Table Probabilities

You watch the game at a particular table for 130 rounds and count the number of black, red, and green results. Your observations are summarized in the table below.

Outcomes (n = 130)

The Test: Test the claim that this roulette table is not fair. That is, test the claim that the distribution of colors for all spins of this wheel does not fit the expected distribution from a fair table. Test this claim at the 0.01 significance level.

(a) What is the null hypothesis for this test?

H₀: The probabilities are not all equal to 1/3.H₀: p₁ = 19/40, p₂ = 19/40, and p₃ = 2/40.    H₀: p₁ = p₂ = p₃ = 1/3H₀: The probabilities associated with this table do not fit those associated with a fair table.

(b) The table below is used to calculate the test statistic. Complete the missing cells.
Round your answers to the same number of decimal places as other entries for that column.

(c) What is the value for the degrees of freedom?
(d) What is the critical value of χ²? Use the answer found in the χ²-table or round to 3 decimal places.
t_α =

(e) What is the conclusion regarding the null hypothesis?

reject H₀

fail to reject H₀    

(f) Choose the appropriate concluding statement.

We have proven that this table is fair.

The results of this sample suggest the table is not fair.    

There is not enough data to conclude that this table is not fair.