In August 2003, 56% of employed adults in the United States reported that basic mathematical skills were critical or very important to their job. The supervisor of the job placement office at a 4-year college thinks this percentage has increased due to increased use of technology in the workplace. He takes a random sample of 530 employed adults and finds that 324 of them feel that basic mathematical skills are critical or very important to their job. Is there sufficient evidence to conclude that the proportion of employed adults who feel basic mathematical skills are critical or very important to their job has increased at the α = 0.01 level of significance?

The sample proportion is p^ =______- . (Round to 3 decimal places.)
The test statistic for this test is z₀=_______.  (Calculate this value in a single step in your calculator using the rounded sample proportion reported above, and report your answer rounded to 3 decimal places.)

We  (reject / fail to reject) H₀.
The given data  (does / does not) provide significant evidence that the proportion of employed adults who feel that basic mathematical skills are critical or very important to their job has increased since August 2003.

A supermarket chain analyzed data on sales of a particular brand of snack cracker

at 104 stores for a certain one week period. The analyst decided to build a regresion model to predict the sales of the snack cracker based on the total sales of all brands in the snack cracker category.

d. Make a prediction for sales in a week where sales in the entire snack

    cracker category is 1005.

CategorySales	Sales
1348	394
1110	388
1096	357
1208	385
1063	346
1097	326
1277	358
1275	359
1328	360
1281	374
1127	362
1339	406
1055	354
1263	368
1158	391
1286	370
1401	372
1085	381
1178	371
1248	353
1241	372
1320	375
1353	369
1173	353
1208	364
1280	371
1214	391
1213	381
1291	371
1230	335
1095	338
1149	320
1305	370
1134	351
1127	328
1053	295
1107	318
1054	296
1141	327
1190	313
1071	346
1147	361
1127	350
1204	367
1301	411
1184	390
1214	367
1132	341
1213	380
1173	347
1226	365
1261	352
1118	341
1096	321
1211	329
1033	336
1228	361
1241	386
1381	408
1332	359
1253	375
1043	330
1456	341
1099	340
1044	336
1230	341
1143	371
1238	378
1357	371
1150	378
1218	386
1215	357
1238	376
1196	349
1193	364
1282	361
1317	365
1157	346
1294	356
1198	343
1436	358
1278	368
1124	312
1116	315
1109	338
1285	327
1189	309
1197	330
1091	345
1251	344
1124	355
1130	346
1067	328
1150	352
1238	375
1409	370
1264	377
1151	340
1206	350
1297	375
1164	364
1108	370
1187	365
1459	396

Appraise what new statistical methods are used in the evaluation of conceptual theories outlining specific advantages these methods provide. Compare Structural Equation Modeling (SEM) techniques providing advantages of using SEM to other conventional methods outlining some of the various statistical techniques that SEM is able to perform. Evaluate sampling techniques used to conduct hypothetical studies and asses the benefits of each sampling method based on best fit to application. Critique validity and reliability methods for appropriate constructs and compare advantages and disadvantages of each method describing what methods to use with different operational techniques. Compare and evaluate factor analysis for confirmatory versus exploratory methods and assess when each is appropriate proving examples and application usages. Assess the differences of various regression analysis methods and demonstrate by examples what regression methods are most appropriate for different application. Finally discuss and recommend best statistical techniques and methods to operationally use for means comparisons, non parametric evaluation, bivariate correlation, ANOVAs, Chi Square, regression, and other techniques as appropriate. Assess the overall concept of statistical power, why it has import to statistical evaluations, and what SPSS contributes to statistical analysis in today’s research.

A supermarket chain analyzed data on sales of a particular brand of snack cracker

at 104 stores for a certain one week period. The analyst decided to build a regresion model to predict the sales of the snack cracker based on the total sales of all brands in the snack cracker category.

b. Is there sufficient evidence at 2.5% significance level to claim that linear

    relationship exists between category sales and cracker sales? Show the

   test, and make the conclusion.

CategorySales	Sales
1348	394
1110	388
1096	357
1208	385
1063	346
1097	326
1277	358
1275	359
1328	360
1281	374
1127	362
1339	406
1055	354
1263	368
1158	391
1286	370
1401	372
1085	381
1178	371
1248	353
1241	372
1320	375
1353	369
1173	353
1208	364
1280	371
1214	391
1213	381
1291	371
1230	335
1095	338
1149	320
1305	370
1134	351
1127	328
1053	295
1107	318
1054	296
1141	327
1190	313
1071	346
1147	361
1127	350
1204	367
1301	411
1184	390
1214	367
1132	341
1213	380
1173	347
1226	365
1261	352
1118	341
1096	321
1211	329
1033	336
1228	361
1241	386
1381	408
1332	359
1253	375
1043	330
1456	341
1099	340
1044	336
1230	341
1143	371
1238	378
1357	371
1150	378
1218	386
1215	357
1238	376
1196	349
1193	364
1282	361
1317	365
1157	346
1294	356
1198	343
1436	358
1278	368
1124	312
1116	315
1109	338
1285	327
1189	309
1197	330
1091	345
1251	344
1124	355
1130	346
1067	328
1150	352
1238	375
1409	370
1264	377
1151	340
1206	350
1297	375
1164	364
1108	370
1187	365
1459	396

Which probability rule would be used to determine the probability of getting into both your first choice graduate program AND getting an interview at your first choice post-graduation?

Solve for the probability of BOTH events occuring if the probability of getting into your first choice graduate program is estimated to be 25% and getting an interview at your first choice job post-graduation is estimated to be 50%.

If the robt = 0.20 and the df = 70 and the test was two-tailed, what is the rcv ?

Given the values provided in #17, should you reject or fail to reject the null hypothesis?

Significance level is 0.05

Choose the correct answer.

1. What is the percentile rank of 60 in the distribution of N(60, 100)?

a. 10

b. 50

c. 60

d. 100

1. The skewness value for a set of data is +2.75. This indicates that the distribution of scores is which one of the following?

   1. Highly negatively skewed

   2. Slightly negatively skewed

   3. Symmetrical

   4. Slightly positively skewed

   5. Highly negatively skewed

2. For a normal distribution, all percentiles above the 50th must yield positive z-scores. Is this true or false?

3. The distribution of variable X has a mean of 10 and is positively skewed. The distribution of variable Y has the same mean of 10 and is negatively skewed. Are the medians for the two variables the same or different?

A starting lineup in basketball consists of two guards, two forwards, and a center. (a) A certain college team has on its roster four centers, four guards, three forwards, and one individual (X) who can play either guard or forward. How many different starting lineups can be created? [Hint: Consider lineups without X, then lineups with X as guard, then lineups with X as forward.]

(Hypothetical) In a major national survey of crime victimization, the researchers found that 17.0% of Americans age 12 or older had been a victim of crime. The size of the sample was 6,4,00.

a) Estimate the percentage of Americans age 12 or older who were victims at the 95% confidence level. Write a sentence explaining the meaning of this confidence interval.

b) Estimate the percentage of victims at the 99% confidence level. Write a sentence explaining the meaning of this confidence interval.

Imagine that the Sample size was cut in half to 3,200, but the survey found the same value of 17.0% for the percentage of victims.

c) Would the 95% confidence interval increase or decrease? By how much?

d) Would the 99% confidence interval increase or decrease? By how much?

The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with a mean of 1262 chips and a standard deviation of 118 chips.

​(a) Determine the 27th percentile for the number of chocolate chips in a bag. ​

(b) Determine the number of chocolate chips in a bag that make up the middle 98​% of bags. ​

(c) What is the interquartile range of the number of chocolate chips in a bag of chocolate chip​ cookies?

The effectiveness of antidepressants in treating the eating disorder bulimia was examined in the article “Bulimia Treated with Imipramine: A Placebo-Controlled Double-Blind Study” (American Journal of Psychology [1983]: 554–558). A group of patients diagnosed with bulimia were randomly assigned to one of two treatment groups, one receiving imipramine and the other a placebo. One of the variables recorded was binge frequency. The authors chose to analyze the data using a rank-sum test because it makes no assumption of normality. They stated that “because of the wide range of some measures, such as frequency of binges, the rank sum is more appropriate and somewhat more conservative.” Data on number of binges during one week that are consistent with the findings of the article are given in the following table:

Placebo 8 3 15 3 4 10 6 4

Imipramine 2 1 2 7 3 12 1 5

Do these data strongly suggest that imipramine is effective in reducing the mean number of binges per week? Use a level .05 rank-sum test.

There is one 1$ bill and one 5$ bill in your left pocket and three 1$ bills in your right pocket. You move one bill from the left pocket to the right pocket. After that you take one the remaining bill from the left pocket and one of the bills at random from your right pocket. Let ? denote the amount of money that you take from the left pocket and ? denote the amount of money that you take from the right pocket.

1. ? (?=1, ? =1) is

(a) 1

(b) 3 (correct)

(c) 1

(d) 5

2. ? (?=5, ? =5) is

(a) 0 (correct)

(b) 1/8

(c) 3/8

(d) 1/2

3. ?(? ≥?)is
(a) 1/8

(b) 3/8

(c) 1/2 (correct)

(d) 1

4. Covariance between ? and ? is

(a) 0

(b) −1/2

(c) −1 (correct)

(d) 1

5. Let ? denote the total amount of money that you get from your pockets. V??(?) is

(a) 23/4

(b) 31/8

(c) 19/4

(d) 15/4 (correct)

6. Let ? denote the share of money that you get from the left pocket, i.e. ?/? . Calculate the mean of ?
(a) 1/2

(b) 2/3

(c) 11/13

(d) 5/8 (correct)

An academic department has just completed voting by secret ballot for a department head. The ballot box contains four slips with votes for candidate A and three slips with votes for candidate B. Suppose these slips are removed from the box one by one. For example, one outcome is BBBAAAA. (Enter your answers in set notation. Enter EMPTY or ∅ for the empty set.) (a) List all possible outcomes. This answer has not been graded yet. (b) Suppose a running tally is kept as slips are removed. For what outcomes does A remain ahead of B throughout the tally?

consider the following numbers: -5,-3,-1,1,3. assuming that these numbers are the sample data, use a pencil and calculator to calculate the mean, standard deviation and variance. please show work

what is the average age in the class? what is the average feeling? what is the average city?

32	Cedar Rapids	3
24	Cedar Rapids	3
34	Marion	4
23	Coralville	2
24	Iowa City	0
35	Solon	0
26	Waterloo	3
31	Marion	3
20	Marion	2
32	Cedar Rapids	3
30	Cedar Rapids	4
34	Cedar Rapids	2
26	Cedar Falls	3
47	Cedar Rapids	-3
31	Cedar Rapids	3
29	Coralville	0
29	North Liberty	0
33	North Liberty	2
44	Cedar Rapids	3
40	Williamsburg	3
40	Cedar Rapids	2
31	Marion	1
28	Cedar Rapids	0
28	Robins	3
26	Cedar Rapids	4
27	Marion	3
48	Solon	1
22	Wever	2
35	Marion	3
27	Cedar Rapids	3
27	Dubuque	3
38	Riverside	-1
27	Center Point	0
28	Center Point	2
27	Cedar Falls	3
26	Cedar Rapids	1
24	Iowa City	2
54	Iowa City	2
25	Cedar Rapids	0
26	North Liberty	1
27	Dubuque	2
25	Dubuque	2
26	North Liberty	5
27	Cedar Rapids	0
24	Cedar Falls	2
30	North Liberty	1
24	Cedar Rapids	0
24	Waterloo	2
26	North Liberty	5
27	Cedar Rapids	0
25	Cedar Rapids	4
26	Cedar Rapids	3
24	Coralville	3
24	Cedar Rapids	3
31	Marion	-3

Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi. Suppose the actual air pressure in each tire is a random variable. X for the right tire and Y for the left tire, with joint pdf.

f(x,y) = k(x² + y²), when 20 ≤ x ≤ 30, 20 ≤ y ≤ 30, and

f(x,y) = 0 (otherwise)

A. What is the value of k.

B. what is the probability that both tires are underfilled?

C. What is the marginal distribution of air pressure in the right tire?