A high school is examining whether or not a certain college admissions test prep course is helpful. To evaluate this, 15 students took the college admissions test. Afterwards, they went through the prep course and then took the admissions test again. Their before and after scores are shown below. With a significance level of 0.90, is the admissions test prep course effective?

Student Before After

1 27 29

2 28 29

3 30 31

4 32 31

5 16 20

6 25 27

7 27 27

8 25 26

9 27 30

10 23 28

11 25 26

12 24 24

13 22 25

14 31 32

15 25 25

The U.S. Department of Transportation, National Highway Traffic Safety Administration, reported that 77% of all fatally injured automobile drivers were intoxicated. A random sample of 51 records of automobile driver fatalities in Kit Carson County, Colorado, showed that 37 involved an intoxicated driver. Do these data indicate that the population proportion of driver fatalities related to alcohol is less than 77% in Kit Carson County? Use α = 0.10. (a)

What is the level of significance?

State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

Ho: p = 0.77; H1: p > 0.77; right-tailed

Ho: p = 0.77; H1: p < 0.77; left-tailed

Ho: p = 0.77; H1: p ≠ 0.77; two-tailed

Ho: p < 0.77; H1: p = 0.77; left-tailed

(b) What sampling distribution will you use? Do you think the sample size is sufficiently large?

The normal distribution, since the sample size is large.

The t distribution, since the sample size is large.

What is the value of the sample test statistic? (Use 2 decimal places.)

(c) Find the P-value of the test statistic. (Use 4 decimal places.)

Sketch the sampling distribution and show the area corresponding to the P-value.

d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant.

At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

At the α = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(e) State your conclusion in the context of the application.

Reject the null hypothesis, there is sufficient evidence that the true proportion of driver fatalities related to alcohol is less than 0.77 in Kit Carson County.

Fail to reject the null hypothesis, there is insufficient evidence that the true proportion of driver fatalities related to alcohol is less than 0.77 in Kit Carson County.

Fail to reject the null hypothesis, there is sufficient evidence that the true proportion of driver fatalities related to alcohol is less than 0.77 in Kit Carson County.

Reject the null hypothesis, there is insufficient evidence that the true proportion of driver fatalities related to alcohol is less than 0.77 in Kit Carson County.

You are part of a team investigating the identifying motor vehicle accidents. A multiple regression model is to be constructed to predict the number of motor vehicle accidents in a town per year based upon the population of the town, the number of recorded traffic offenses per year and the average annual temperature in the town.

Data has been collected on 30 randomly selected towns:

Number of motor vehicle accidents per year	Population (× 1000)	No. of recorded traffic offences (× 100)	Average temperature °F
355	181	29	78
490	257	56	82
597	441	34	81
475	50	95	81
922	495	102	82
736	38	165	81
305	167	25	84
1,128	378	191	78
745	369	86	76
476	237	63	84
143	100	4	84
203	118	21	79
909	489	106	78
410	210	39	77
642	138	131	81
847	308	138	82
604	418	40	77
719	194	132	78
350	319	8	84
327	70	61	76
1,038	259	192	78
756	299	115	81
635	440	40	79
796	283	131	85
301	64	56	81
135	26	26	79
639	31	150	81
325	210	13	77
441	43	98	79
522	370	26	82

a)Find the multiple regression equation using all three explanatory variables. Assume that X₁ is population, X₂ is number of recorded traffic offenses per year and X₃ is average annual temperature. Give your answers to 3 decimal places.

y^ =  + population + no. traffic offences + average temp

b)At a level of significance of 0.05, the result of the F test for this model is that the null hypothesis isis not rejected.

For parts c) and d), using the data, separately calculate the correlations between the response variable and each of the three explanatory variables.

c)The explanatory variable that is most correlated with number of motor vehicle accidents per year is:

population
number of traffic offenses
average annual temperature

d)The explanatory variable that is least correlated with number of motor vehicle accidents per year is:

population
number of traffic offenses
average annual temperature

e)The value of R² for this model, to 2 decimal places, is equal to

f)The value of s_e for this model, to 3 decimal places, is equal to

g)Construct a new multiple regression model by removing the variable average annual temperature. Give your answers to 3 decimal places.

The new regression model equation is:

y^ =  + population + no. traffic offences

h)In the new model compared to the previous one, the value of R² (to 2 decimal places) is:

increased
decreased
unchanged

i)In the new model compared to the previous one, the value of s_e (to 3 decimal places) is:

increased
decreased
unchanged

5). Finally, which of the following would you use to write out the results in an APA formatted results section? Note that this one is tricky – some answer options differ in only a single number or word! Pay close attention to details here.

A. We ran a One Way ANOVA with condition (FITD vs. DITF vs. Control) as our dependent variable and willingness to participate in the 30 minute study as our independent variable. The One Way ANOVA was significant, F(2, 87) = 4.05, p < .05. Tukey post hoc tests showed that participants were significantly less willing to participate in the 30 minute study in the control condition (M = 6.63, SD = 1.30) than in both the FITD condition (M = 7.40, SD = 1.00) and the DITF condition (M = 7.37, SD = 1.22), though the DITF and FITD conditions did not differ from each other.

B. We ran a One Way ANOVA with condition (FITD vs. DITF vs. Control) as our independent variable and willingness to participate in the 30 minute study as our dependent variable. The One Way ANOVA was significant, F(2, 87) = 4.05, p < .05. Tukey post hoc tests showed that participants were significantly less willing to participate in the 30 minute study in the control condition (M = 6.63, SD = 1.30) than in both the FITD condition (M = 7.40, SD = 1.00) and the DITF condition (M = 7.37, SD = 1.22), though the DITF and FITD conditions did not differ from each other.

C. We ran a One Way ANOVA with condition (FITD vs. DITF vs. Control) as our independent variable and willingness to participate in the 30 minute study as our dependent variable. The One Way ANOVA was significant, F(2, 87) = 4.05, p < .001. Tukey post hoc tests showed that participants were significantly less willing to participate in the 30 minute study in the control condition (M = 6.63, SD = 1.30) than in both the FITD condition (M = 7.40, SD = 1.00) and the DITF condition (M = 7.37, SD = 1.22), though the DITF and FITD conditions did not differ from each other.

D. We ran a One Way ANOVA with condition (FITD vs. DITF vs. Control) as our independent variable and willingness to participate in the 30 minute study as our dependent variable. The One Way ANOVA was not significant, F(2, 89) = 4.05, p > .05. Since p was greater than .05, there was no need to conduct post hoc tests.

E. We ran a One Way ANOVA with condition (FITD vs. DITF vs. Control) as our independent variable and willingness to participate in the 30 minute study as our dependent variable. The One Way ANOVA was significant, F(2, 87) = 4.05, p < .05. Tukey post hoc tests showed that participants were significantly less willing to do the study in the control condition (M = 6.63, SD = 1.30) than in both the FITD condition (M = 7.40, SD = 1.00) and the DITF condition (M = 7.37, SD = 1.22). In addition, those in the DITF condition were significantly less willing to participate in the 30 minute study than those in the FITD condition.

A coin will be tossed 5 times.

The chance of getting exactly 2 heads among 5 tosses is %.

The chance of getting exactly 4 heads among 5 tosses is %.

A coin will now be tossed 10 times.

The chance of getting exactly 2 heads in the first five tosses and exactly 4 heads in the last 5 tosses is BLANK %.

All answers must have three numbers following the decimal.

I just need the answer to the bolded on (where I put "BLANK" just provided the whole question in case it is needed)

Banking fees have received much attention during the recent economic recession as banks look for ways to recover from the crisis. A sample of 32 customers paid an average fee of ​$12.33 per month on their​ interest-bearing checking accounts. Assume the population standard deviation is ​$1.75. Complete parts a and b below. a. Construct a 95​% confidence interval to estimate the average fee for the population. The 95​% confidence interval has a lower limit of ​$ nothing and an upper limit of ​$ nothing. ​(Round to the nearest cent as​ needed.) b. What is the margin of error for this​ interval? ​$ nothing ​(Round to the nearest cent as​ needed.)

9) (CH. 9-2) Is there a difference between the average NBA Championship Final game winning scores of the 1970’s versus the average of the winning scores of the 2000’s? Use a 0.01 significance level to test the claim that there is a difference.

	1970’s	2000’s
	97	99
	105	131
	109	83
	87	95
	96	81
	102	100
	102	88
	114	113
	118	108
	113	116

Use the data from problem #9 to construct a 99% confidence interval estimate for the mean of the differences. Does this interval contain zero? Do the results of this problem support the results of problem #9?

• What is the Confidence Interval Estimate:

• Does the interval indicate a difference or not? Explain your answer.

• Do the results of the hypothesis test (from problem #9) and the confidence interval estimate support each other?

A study of undergraduate computer science students examined changes in major after the first year. The study examined the fates of 256 students who enrolled as first-year students in the same fall semester. The students were classified according to gender and their declared major at the beginning of the second year. The students studied were enrolled at a large Midwestern university several years ago. Discuss how you would conduct a similar study at a college or university of your choice today. Include a description of all the variables that you would collect for your study.

How is variation within categories and between categories relevant to ANOVA? What is dfw? dfb?

In ANOVA, if the null is false, the means of the sample should be very (different? Similar? zero?) and the standard deviation of the different samples should be (very large? Low?)

ANOVA proceeds by developing two separate estimates of what?

The population variance is a measure of what? What assumptions are required for ANOVA? When will ANOVA tolerate some violation of model assumptions?

You test a new drug to reduce blood pressure. A group of 15 patients with high blood pressure report the following systolic pressures (measured in mm Hg): before medication: after medication: change: ̄y s 187 120 151 143 160 168 181 197 133 128 130 195 130 147 193 187 118 147 145 158 166 177 196 134 124 133 196 130 146 189 156.40 0 2 4 -2 2 2 4 1 -1 4 -3 -1 0 1 4 1.133 27.409 27.060 2.295 a) Calculate a 90% CI for the change in blood pressure. b) Calculate a 99% CI for the change in blood pressure. c) Does either interval (the one you calculated in (a) or (b)) include 0? Why is this important? d) Now conduct a one sample t-test using μ = 0, and α = .10. Are the results consistent with (a)? e) Finally, conduct a one sample t-test using μ = 0, and α = .01. Are the results consistent with (b)?

What distribution is used for ANOVA? What are limitations of ANOVA?

How do you calculate various portions of the ANOVA process (ex. SST, SSB, SSW)? What do they measure?

What is MSB? MSW? What is the F ratio equal to? What is a computational shortcut for anova (consider how you can calculate SSW)?

How do you calculate degrees of freedom in anova?

Baseball's World Series is a maximum of seven games, with the winner being the first team to win four games. Assume that the Atlanta Braves are playing the Minnesota Twins in the World Series and that the first two games are to be played in Atlanta, the next three games at the Twins' ballpark, and the last two games, if necessary, back in Atlanta. Taking into account the projected starting pitchers for each game and the home field advantage, the probabilities of Atlanta winning each game are as follows:

Game	1	2	3	4	5	6	7
Probability of Win	0.4	0.55	0.42	0.56	0.55	0.39	0.52

a. Set up a spreadsheet simulation model in whether Atlanta wins each game is a random variable. What is the probability that the Atlanta Braves win the World Series? If required, round your answer to two decimal places.

b. What is the average number of games played regardless of winner? If required, round your answer to one decimal place.

Suppose that M&M claims that each bag of Peanut M&Ms should be 18 grams and Plain M&Ms should be 13.5 grams.

a. Test the claim that M&M is shorting its customers in bags of Plain M&Ms.

b. Test the claim that M&M is overfilling Peanut bag bags of M&Ms.

c. Discuss your choice of ?.

i. Why did you choose the ? you did?

ii. If you had chosen a different ?, would it have affected your conclusion?

Total Plain M&Ms: 665

Total Peanut M&Ms: 356

Sum Total Weight of All the Bags of Peanut M&Ms: 921 grams

(18g, 21g, 19g, 17g, 18g, 21g, 18g, 18g, 21g, 17g, 19g, 16g, 20g, 20g, 17g, 17g, 18g, 16g, 20g, 18g, 19g, 20g, 20g, 18g, 21g, 19g, 17g, 18g, 17g, 19g, 16g, 19g, 19g, 19g, 17g, 20g, 18g, 18g, 17g, 19g, 19g, 18g, 18g, 18g, 17g, 17g, 19g, 20g, 18g, 18g)

Sum Total Weight of All the Bags of Plain M&Ms: 601 grams

(13g, 13g, 12g, 14g, 14g, 14g, 13g, 13g, 12g, 12g, 13g, 13g, 13g, 14g, 13g, 14g, 12g, 11g, 12g, 12g, 13g, 10g, 15g, 14g, 16g, 14g, 15g, 13g, 12g, 13g, 14g, 13g, 13g, 13g, 11g, 12g, 12g, 14g, 13g, 13g, 14g, 14g, 12g, 13g, 13g, 15g)

The following data represent the calories and​ sugar, in​ grams, of various breakfast cereals.

Product	Calories	Sugar
A	270	10.0
B	280	3.8
C	290	21.2
D	410	23.4
E	520	19.8
F	530	23.9
G	550	17.7

Use the data above to complete parts​ (a) through​ (d).

Compute the covariance.

b. Compute the coefficient of correlation.

c. Which do you think is more valuable in expressing the relationship between calories and

sugarlong dash—the

covariance or the coefficient of correlation? Explain.

d. What conclusions can you reach about the relationship between calories and sugar?

1) You want to construct a 92% confidence interval. The correct z* to use is

A) 1.645

B) 1.41

C) 1.75

2) Suppose the average Math SAT score for all students taking the exam this year is 480 with standard deviation 100. Assume the distribution of scores is normal. The senator of a particular state notices that the mean score for students in his state who took the Math SAT is 500. His state recently adopted a new mathematics curriculum, and he wonders if the improved scores are evidence that the new curriculum has been successful. Since over 10,000 students in his state took the Math SAT, he can show that the P-value for testing whether the mean score in his state is more than the national average of 480 is less than 0.0001. We may correctly conclude that

A) these results are not good evidence that the new curriculum has improved Math SAT scores.

B) there is strong statistical evidence that the new curriculum has improved Math SAT scores in his state.

C) although the results are statistically significant, they are not practically significant, since an increase of 20 points is fairly small.

3) Suppose the average Math SAT score for all students taking the exam this year is 480 with standard deviation 100. Assume the distribution of scores is normal. A SRS of four students is selected and given special training to prepare for the Math SAT. The mean Math SAT score of these students is found to be 560, 80 points higher than the national average. We may correctly conclude

A) the results are statistically significant at level α = 0.05, but they are not practically significant.

B) the results are not statistically significant at level α = 0.05, but they are practically significant.

C) the results are neither statistically significant at level α = 0.05 nor practically significant.