In March 1999, the Gallup Organization conducted a survey among 535 adults and asked them if they believed there is some form of life on other planets in the universe. In another survey conducted three years earlier, among 535 adults the same questions was asked. The results appear below:

Calculate the 95% confidence interval for the difference in response. Interpret your confidence interval.

3. In the information below: two variables are defined, a regression equation is given, and one data point is given.

Variable:  Weight = Maximum weight capable of bench pressing (pounds)

Variable:  Training = Number of hours spent lifting weights a week

Regression: Weight= 95 + 11.7(Training)

Data point:  An individual who trains 5 hours a week and can bench 152 pounds

Give the value of the slope and interpret the value of the slope in context. Clearly label answer below.

Give the value of the y-intercept and interpret the value of the intercept in context. If the intercept makes no sense in this context, briefly explain why or why not. Clearly label answer below.

14. A sample of size 144 is taken from a population with an unknown distribution. It is known that the population distribution has mean 32 and standard deviation 15.

(A)What is the distribution of the sample means x̄ ? Justify your reasoning and be sure to completely specific the distribution by stating values of the appropriate parameters.

(B) Compute P( x̄ ≥ 34). You may only use the z-score approach and the probabilities provided in Table A.

(C) How large does the sample size need to be in order to reduce the standard deviation of x̄ to 0.75?

20. Run the same data from question 19 (and the same criteria) using a repeated measures t test.
a. Perform the test and report results (show ALL work)
b. Explain what the difference in results is due to.

19. A teacher wanted to test that if telling students that a test would be curved to the highest grade would help them perform better on quizzes. She gave quizzes to two groups of 5 students each and told one that there would be a curve and the other group was told there would be no curve given. Following are the scores on the quizzes for the two groups:

Yes curve: 75, 80, 78, 87, 90
No curve: 76, 83, 72, 80, 70
Run an independent t test on the data and report the test results using an alpha level of .05. Show ALL work.

A poll asked for​ people's opinion on whether closing local newspapers would hurt civic​ life;428 of 1002 respondents said it would hurt civic life a lot. Complete parts a through d below.

a. Find the proportion of the respondents who said that closing local papers would hurt civic life a lot. Answer ______ ​(Round to three decimal places as​ needed.)

b. Find a​ 95% confidence interval for the population proportion who believed closing newspapers would hurt civic life a lot. Assume the poll used a simple random sample​ (SRS). (In​ fact, it used random​ sampling, but a more complex method than​ SRS.) Answer (______, and _____) ​(Round to three decimal places as​ needed.)

c. Find an​ 80% confidence interval for the population proportion who believed closing newspapers would hurt civic life a lot. Answer (______, and _____) ​(Round to three decimal places as​ needed.)

d. Which interval is wider A,B,C or D?

A.The​ 95% interval is wider. To get a higher degree of​ certainty, the interval needs to be widened just on the right side.

B.The​ 95% interval is wider. To get a higher degree of​ certainty, the interval needs to be widened just on the left side.

C.The​ 80% interval is wider. To get a higher degree of​ certainty, the interval needs to be widened.

D. The​ 95% interval is wider. To get a higher degree of​ certainty, the interval needs to be widened.

Suppose that Motorola uses the normal distribution to determine the probability of defects and the number of defects in a particular production process. Assume that the production process manufactures items with a mean weight of 10 ounces. Calculate the probability of a defect and the suspected number of defects for a 1,000-unit production run in the following situations. (a) The process standard deviation is 0.30, and the process control is set at plus or minus one standard deviation. Units with weights less than 9.85 or greater than 10.15 ounces will be classified as defects. If required, round your answer to four decimal places. (b) Through process design improvements, the process standard deviation can be reduced to 0.10. Assume that the process control remains the same, with weights less than 9.85 or greater than 10.15 ounces being classified as defects. If required, round your answer to four decimal places. (c) What is the advantage of reducing process variation, thereby causing process control limits to be at a greater number of standard deviations from the mean? Reducing the proces standard deviation causes a in the number of defects.

Please use the p value approach to conduct a hypothesis test for the following problem. Please provide detailed solutions in the four steps to hypothesis testing.

The security department of a factory wants to know whether the true average time required by night guard to walk his round is 30 minutes. If, in a random sample of 45 rounds, the night guard averaged 30.9 minutes with a`standard deviation of 1.8 minutes, determined whether this is sufficient evidence to reject the null hypothesis Mu=30 minutes in favor of the alternative hypothesis Mu is not equal to 30 minutes. Use the four steps for testing and 0.05 level of significance.

SurveyUSA conducted a poll from March 4, 2020 to March 6, 2020 regarding how concerned people were about the Wuhan Coronavirus. One of the questions asked, "As a result of the coronavirus, have you bought anti-bacterial surface wipes?" The results are summarized in the table below.

Using your tools from the probability chapter, does it appear that buying anti-bacterial wipes is independent of gender?

• Yes, it does appear that buying anti-bacterial wipes is independent of gender.
• No, it appears that buying anti-bacterial wipes and gender are dependent.

Explain.

Are female and purchasing anti-bacterial wipes mutually exclusive (disjoint)?

• Yes, being female and purchasing anti-bacterial wipes are mutually exclusive.
• No, being female and purchasing anti-bacterial wipes are not mutually exclusive.

Explain.

RESEARCH SCENERIO A researcher conducts an independent-measures study examining the effectiveness of a group exercise program at an assisted living facility for elderly adults. One group of residents is selected to participate in the program, and a second group serves as a control. After 6 weeks, the researcher records a combined score measuring balance and strength for each individual. The data are as follows:

                                                Control               Exercise

                                                 n = 12                 n = 15

                                                M = 12                M = 15.5

                                               SS = 120.5        SS = 190.0

1. Show all four steps of hypothesis testing with an α = .05

2. write up your “statistical results” as they would appear in an APA journal

3. In the research scenario: Is there a chance of a Type I error?

4.   What is the independent variable?

5. What is the dependent variable?

Question 1: A researcher is testing 4 different blood coagulation drugs. The drugs are labeled A,B,C and D. He is interested in how the drugs affect the blood coagulation rates of mice. The coagulation rate is the time in seconds that it takes for a cut to stop bleeding. He has 16 mice available for the experiment, so he will use 4 on each drug, randomized.

A                     B                     C                     D

62                    63                    68                    56

60                    67                    66                    62

63                    71                    71                    60

59                    64                                            61

64

a. Perform CRD (completely randomized design) manually as we did in the lectures. You need to write the STEPS clearly.

b. Watch the video on, CRD & CRBD on how to perform EXCEL calculation for CRD

c. Use the attached EXCEL sheet to perform the same calculation.

PART 2:   Three different washing solutions are being compared to study their effectiveness in retarding bacteria growth in 5-gallon milk containers. The analysis is done in a laboratory, and only three trials can be run on any day. Because days could represent a potential source of variability, the experimenter decides to use a randomized block design. Observations are taken for four days, and the data are shown here.

a. Watch the video on, CRD & CRBD on how to perform EXCEL calculation

b. Use the attached EXCEL sheet to perform the calculation for CRBD

PART 3: Explosive manufacturer conducts an experiment to study the explosive force of 4 different mixtures. It is planned to run five replicates (5 runs with each mixture).. The experiment is conducted outdoors which meant only 4 runs cam be made in a given day. Because conditions on each day and can affect the test results, a randomized block design is used, blocking against each day.

                Data on next sheet

Mixture                Day1                  Day2                     Day3                     Day4                         Day5

1                             72                           68                           74                           71                           67

2                              73                           67                           75                           72                           70

3                              75                           68                           78                           73                           68

4                              73                          71                           75                           75                           69

Determine if mixture affects explosive force.

a. Watch the video on, CRD & CRBD on how to perform EXCEL calculation

b. Use the attached EXCEL sheet to perform the calculation for CRBD

Each year the Hershey company reviews candy bar sales records to compare current consumer preferences to sales records of previous years. Previous sales suggest that 30% of consumers prefer Kit Kats, 15% prefer PayDays, 5% prefer the Whatchamacallit, and 50% prefer the traditional Hershey’s chocolate bar. Market analysts collect a sample of consumers from a random day 2018 and found that 50 people preferred Kit Kat, 45 people prefer PayDay, 12 people prefer Whatchamacallits, and 93 people prefer the traditional Hershey chocolate bars. Have current preferences changed from the historical preferences?

(please also specify null and alternative hypothesis)

a toll road with three tolls booths has an arrival rate of 1000 veh/h and vehicle are processed at the rate of 8 veh/min . if the arrival rate and departure times are exponentially distribution ,how would the probability of waiting in a queue change if a fourth toll booth were opened

1) Please find the partially completed multiple regression analysis below, which explores the relationship between the sales (in hundreds) and the independent variables price(in dollars), promotional expenditure(in hundreds of dollars) and the quality score ( 0-100) for a very popular Christmas season toy.

The regression equation is

Sales = 343.2 - 0.23* Price + 2.7* Promotional exp + 0.22* Quality

Predictor Coef Standard Error/ SE Coef    VIF

Constant 343.20 / 62.59 / 0

Price -0.23358 / 0.0373 / 2.415

Promotional exp 2.704 / 1.4 / 1.047

Quality 0.2204 / 0.1429 / 10.387

R-Sq =

Analysis of Variance

Source DF SS   

Regression 0 / 2847.78

Residual Error   

Total 15 / 3933.40

Answer questions A - F based on the above analysis

A) Is the factor Promotional Exp significant at α=0.05 ? Perform the test of hypothesis and show all the relevant calculations.

B) Construct a 95% confidence interval estimate of the population slope of sales with Quality showing all the relevant calculations and also state whether 'Quality' is a significant factor in predicting sales.

C) What is the value of the partial F test statistic (F_STAT) for the independent variable 'Price' (show all the relevant calculations)?

D) Is there a problem with multi-collinearity  among independent variables in this analysis? Explain.

E) What is the adjusted R² value?(show all the relevant calculations)

F) Based on the ANOVA presented, perform the overall F- test showing all the relevant calculations and also state if the regression is significant? (α=0.05)

3) Please answer questions A and B based on the following information:

The director of transportation of a large company is interested in the usage of her van pool. She considers her routes to be divided into local and non-local. She is particularly interested in learning if there is a difference in the proportion of males and females who use the local routes. She takes a sample of a day's riders and finds the following:

She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.

A) Please develop the Expected frequencies table based on the above information showing all the relevant calculations.

B) Given that π₁ represents the proportion of males who use local routes and π₂ represents the proportion of females who use local routes; perform the Chi-square test of hypothesis for the following and also show all the relevant calculations.

H₀:π₁ = π₂

H₁:π₁ ≠ π₂

2) Please answer questions A and B based on the following Best Subsets Regression.

Best Subsets Regression: Sales versus Price, Promotional exp, Quality

Response is Sales

P

r

o

m

o

t

i

o

n Q

a u

P l a

r l

i e i

Mallows c x t

Vars R-Sq R-Sq(adj)       Cp S e p y

   1 81.3       79.8 6.1 7.8239 X

   1 58.0       54.5 26.2 11.734 X

   1   9.5        2.0 68.1 17.221 X

   2 85.7       83.0 4.4 7.1630 X X

   2 82.9       79.8 6.8 7.8193 X X

   2 69.2       63.6 18.6 10.499 X X

   3 88.4       84.9 4.0 6.7523 X X X

A) If you want to consider regression models with just one independent variable, which variable would you consider to include into the model based on S criterion?

B) If you want to consider regression models with just two independent variables, which variables would you include according to R-Sq(adj) criterion?