A research lab has developed a new instructional technique for statistics. They chose five class topics and completed five separate studies. For each study, they selected a new sample of students, used the new technique to teach the specific topic, then gave the sample of students a test on that topic. Below are the mean test scores for each of the five studies, along with the population means for students taking the test after the 'traditional' instructional technique. For each of the five studies:

• carry out a z-test using the expanded hypothesis testing steps, using a two-tailed test and .05 significance level
• explain the decision the research lab should make for each topic (that is, should the new technique be used to teach the topic covered by the study or not)
• make a drawing of each distribution
• calculate the 95% confidence interval for each study

Ten years ago the mean Math SAT score of all high school students who took the test in a small high school was 490, with a standard deviation of 80. This year, a researcher took the scores of a random sample of 16 students in the high school who took the SAT.
The mean score of these 16 students is (X bar) = 530. In addition, the researcher assumes that the population standard deviation continues to be σ = 80. The researcher will test if there is evidence that the scores in the district have changed with two approaches: (i) test of significance; and (ii) confidence interval.

1. Find H0 and Ha

2.z statistics

3.p value

4.What are your statistical conclusion and its interpretation? Use significance level, α = 0.05 (or 5%).

5.Find a 95% confidence interval for µ and interpret it. ( lower and upper bound)

6.Based on the hypotheses obtained in (a) and your 95% confidence interval for µ in (e), what is your conclusion? Is it the same as the conclusion of the test, i.e., (d)? Explain.

7.The researcher feels that the confidence interval for µ is too wide. So the researcher wonders how to increase of precision by decreasing the size of the confidence interval for µ. If the researcher can control only its sample size, what should be the researcher’s choice? How does it work? Explain.

Kay is the nurse supervisor of a small clinic located on the campus of a Midwestern college. In a single week, she treated fifteen students (ages 19-24) with similar symptoms. They each appeared at the student clinic in various stages of the development of a red macular rash. It seemed to start on the face and spread to the trunk and extremities. Each complained of having had a severe cold, including sore throat, headache, and cough, for a few days previously.

After observing tiny red patches with white centers on the oral mucosa, next to the molars, Kay made her diagnosis. She warned each student that their infection was extremely contagious and placed them in isolation. She also warned them of the need for strict bed rest because of the dangerous complications of this infection. Chemotherapy was limited to acetaminophen for comfort. Kay checked each student’s immunization record and found it complete and up-to-date.

QUESTION 1

Which of these is likely to be Kay’s diagnosis?

The following case is for Questions 1-4:

A study considers whether the mean score of a college entrance exam for students in 2019 (Group 1) was higher than the mean score in 2018 (Group 2). A random sample of 25 students who took the exam in 2019 and a random sample of 25 students who took the exam in 2018 were selected. Assume α=0.1.

                                                              Sample Size                     Mean                       Standard Deviation

                           2019:                       n = 25                          = 497                            s= 102

                           2018:                       n = 25                          = 485                            s= 98

                           Difference:              n = 25                          = 12                              s= 20

Question 1:

Frame the null hypothesis and alternative hypothesis:

(a) Ho: µ1=µ2          Ha: µ1>µ2

(b) Ho: µ1=µ2          Ha: µ1<µ2

(c) Ho: µ1=µ2          Ha: µ1≠µ2

(d) Ho: µ1>µ2          Ha: µ1=µ2

Question 2:

What is the case of this question?

(a) Large Independent Sample Mean

(b) Small Independent Sample Mean

(c) Paired Difference Case

(d) Large Independent Sample Proportion

Question 3:

What is the degree of freedom?

(a) 24

(b) 25

(c) 48

(d) 49

Question 4:

What is the test statistic?

(a) 4.16

(b) 3.0

(c) 0.42

(d)24.36

1. What is the response rate of an online survey sent to 650 email recipients, where 100 email addresses were ineligible, 400 recipients responded to the survey, and 150 refused to participate? (Show all your work)

2.  A department store manager believes that at least half of the households in a test market city contain at least one adult who has visited the store since the new layout was introduced. To conduct online surveys, a researcher working with this manager has purchased access to a 1,100 online panel with members located in the target area. The researcher asked the following question to the contacted respondent "Has any adult in this household visit XYZ department store in the previous month?". Here are the final results of the online panel surveys.

Completed surveys 426

Refusals 260

No Contact 0

Ineligible surveys 292

Nonworking emails 122

What is the response rate with eligibility requirements? Show all your work.

3. Knowing that you need a sample pool of 1019 students to ultimately get about 500 students in your sample, you are in a position to draw a systematic sample from the student directory at your university. Further, 9,500 students are listed in the directory. What is the sampling interval? Interpret your results. Show all your work

The school district recently adopted the use of e-textbooks, and the superintendent is interested in determining the level of satisfaction with e-textbooks among students and if there is a relationship between the level of satisfaction and student classification. The superintendent selected a sample of students from one high school and asked them how satisfied they were with the use of e-textbooks. The data that were collected are presented in the following table.

Table 1: Student Classification (N=128)

Questions

1. Of the students that were satisfied, what percent were Freshmen, Sophomore, Junior, and Senior? (Round your final answer to 1 decimal place).

2. State an appropriate null hypothesis for this analysis.

3. What is the value of the chi-square statistic?

4. What are the reported degrees of freedom?

5. What is the reported level of significance?

6. Based on the results of the chi-square test of independence, is there an association between e-textbook satisfaction and academic classification?

7. Present the results as they might appear in an article.

This must include a table and narrative statement that reports and interprets the results of the analysis. Note: The table must be created using your word processing program. Tables that are copied and pasted from SPSS are not acceptable.

Poverty is more likely to be viewed as a result of laziness by _______ and a result of situational influences by _______.

A)evolutionary psychologists; social psychologists

B)the actor-observer bias; the fundamental attribution error

C)collectivists; individualists

D)wealthy people; people living in poverty

The Stanford prison experiment revealed that

A)few college students are vulnerable to artificially created social roles.

B)only individuals with personality problems are vulnerable to social roles.

C)trained professionals are less susceptible to social roles than college students.

D)ordinary college students will quickly become cruel to innocent people.

Which is true of social stereotypes?

A)Stereotypes are always negative.

B)Most stereotypes are rational.

C)We are consciously aware of all of our stereotypes.

D)Stereotypes increase prejudice.

piano student mastered a difficult piece of music after many hours of practice at home. At his next lesson, he played the piece for his piano teacher. He then performed it in front of an enthusiastic audience, and finally, in front of a critical panel of judges. According to the theory of social facilitation, which of these was likely to be his worst performance?

A)Playing at home after mastering the piece

B)Performing for an enthusiastic audience

C)Playing for his piano teacher

D)Performing for a panel of judges

A bank teller can handle 40 customers an hour and customers arrive every six minutes. What is the average time a customer spends waiting in line?

a. 15 seconds b. 0.40 minutes c. 1.25 minutes d. 30 seconds

Customers arrive at a bakery at an average rate of 18 per hour on week day mornings. Each clerk can serve a customer in an average of three minutes. How long does each customer wait in the system?

a. 1 hour b. 0.33 hour c.0.45 hour d. 0.5 hour e. 1.5 hour

Students arrive at a class registration booth at the rate of 4 per hour. The administrators serve students in a first-come, first-serve priority with the average service time of 10 minutes. What is the mean number of students in the system?

a. 1.0 b. 1.33 c. 0.67 d. 2. 0 e. 15

Customers arrive at an ice cream store at the rate of 15 per hour. The owner attempts to serve in a first come, first-serve priority. The mean time to serve a customer is 3 minutes. Whatis the probability of walking into the store and not having to wait?

a. 75% b. 100% c. 133% d. 25% e. 50%

A high school physics teacher wondered if his students in the senior class this year will be more likely to go into STEM (Science, Technology, Engineering, Mathematics) majors than Social Science and Liberal Arts majors. He asked each of his 65 students about their first choice for major on their college applications and conducted a Chi-square test for goodness of fit with an alpha level of .05 to see if the number of students choosing each category differs significantly.

35 – STEM

20 – Social Sciences

10 – Liberal Arts

a. What is the variable in this test? What type of variable is it (nominal, ordinal, or continuous)? (1 point total: .5 for each question)

b. State the null and alternative hypotheses in words (1 point total: .5 for each hypothesis)

c. Calculate X² statistic (2 points total: 1 for final answer, 1 for the process of calculating it)

d. Calculate the degree of freedom and then identify the critical value (1 point total: .5 for df, .5 for critical value)

e. Compare the X² statistic with the critical value, then report the hypothesis test result, using “reject” or “fail to reject” the null hypothesis in the answer (1 point total, .5 for each answer)

f. Explain the conclusion in a sentence or two, to answer the research question. (1 point)

Question 12 Unsaved A sample of University of Colorado students each viewed one of two simulated news reports about a terrorist bombing against the United States by a fictitious country. One report showed the bombing attack on a military target and the other on a cultural/educational site. Additionally, before viewing the news report, each student read one of two "primes." The first was a prime for forgiveness based on the biblical saying "Love thy enemy," while the second was a retaliatory prime based on the biblical saying "An eye for an eye, and a tooth for a tooth." After viewing the news report, the students were asked to rate on a scale of 1 to 12 what the U.S. reaction should be, with the lowest score (1) corresponding to the United States sending a special ambassador to the country and the highest score (12) corresponding to an all-out nuclear attack against the country.6 (Use a diagram like Figure 9.2 from the text to display the factors and treatments.) Identify the following in this experiment:

_____ eye-for-an-eye prime

_____ the students

_____ love thy neighbor prime

_____ rating of U.S. reaction to attack

_____ prime used

_____ cultural/educational target

_____ military target

_____ type of attack

Options:

1. Subjects

2. Factors

3. Treatments for the prime

4. Treatments for the type of attack

5. Response variable