A university wants to study the experience of students enrolled in its big classes, defined asclasses with enrollments of 500 or more. There are 20 such classes. From each of these classes,one enrolled student is chosen uniformly at random to take part in the university’s survey. Youcan assume that the selection from each class is performed independently of the selections inthe other classes. In this scenario: (T / F)

1. The method of sampling produces a probability sample of students enrolled in the big classes. (T / F)

2. The method of sampling produces a simple random sample of students enrolled in the big classes. (T / F)

3. Because a student is chosen from each class, all students in the big classes have the same chance of being selected. (T / F)

4. Because a student is chosen from each of 20 big classes, there will be 20 students in the sample. (T / F)

Consider the following hypothesis test:

H ₀:   50

H _a:  > 50

A sample of 65 is used and the population standard deviation is 7. Use the critical value approach to state your conclusion for each of the following sample results. Use  = .05.

a. With  = 52.5, what is the value of the test statistic (to 2 decimals)?


Can it be concluded that the population mean is greater than 50?
SelectYesNoItem 2

b. With  = 51, what is the value of the test statistic (to 2 decimals)?


Can it be concluded that the population mean is greater than 50?
SelectYesNoItem 4

c. With  = 51.8, what is the value of the test statistic (to 2 decimals)?


Can it be concluded that the population mean is greater than 50?
SelectYesNoItem 6

You want to estimate the difference between the average grades on a certain math exam before the students take the associated math class and after they take the associated math class. You take the random samples of 5 students who have taken the class and 5 students who have not taken the class. You get the following results:

A) Determine the population(s) and parameter(s) being discussed.

B) Determine which tool will help us find what we need (one sample z test, one sample t test, two sample t test, one sample z interval, one sample t interval, two sample t interval).

C) Check if the conditions for this tool hold.

D) Whether or not the conditions hold, use the tool you choose in part B. Use C=95% for all confidence intervals and alpha=5% for all significance tests.

* Be sure that all methods end with a sentence describing the results *

You want to know if, on average, households have more cats or more dogs. You take an SRS of 8 households and find the data below:

A) Determine the population(s) and parameter(s) being discussed.

B) Determine which tool will help us find what we need (one sample z test, one sample t test, two sample t test, one sample z interval, one sample t interval, two sample t interval).

C) Check if the conditions for this tool hold.

D) Whether or not the conditions hold, use the tool you choose in part B. Use C=95% for all confidence intervals and alpha=5% for all significance tests.

* Be sure that all methods end with a sentence describing the results *

Independent samples t-test: An experimenter is interested in how the “foot-in-the-door” tactic could increase compliance in college students. The “foot-in-the-door” tactic involves asking first for a small request to butter someone up for a larger (originally intended) request. Typically, the “foot-in-the-door” tactic increases compliance because people do not like to appear inconsistent and since they originally agreed to the small request, they feel compelled to also agree with the large request.

Our experimenter was seeking to increase the number of students who volunteer for research in the department of psychological sciences. One group of students were subject to the “foot-in- the-door” tactic and these students were first asked to wear a sticker promoting research participation (small request) around campus. Later, these same students were asked to participate in a research project. The second group of students were simply asked to participate in research with no initial, small request.

This study was conducted across multiple semesters, and the value below represents how many students agreed to participate in research each semester.

“foot-in-the-door” (FITD): 11 8 10 6 5

Large request only (Large): 6 6 9 10 8

Now we’ll use this information for hypothesis testing....

3. What are your degrees of freedom for this independent samples t-test? 2pts.

4. What is your critical t-value (t-crit) for this hypothesis test? 2pts.

Next we calculate the t-value for our sample to compare to this critical value (see table below for reminders)......

5. What is the pooled variance for our sample? 4 pts. Pooled Variance: ??1+ ??2 =

   ?? 1+ ?? 2

6. What is the standard error of the mean difference (??1−?2)for our sample? 4 pts.

7. What is the value for t-observed? 4 pts.

8. Is there a statistically significant difference between these groups? 3pts.

1. A simple linear regression model relating a bank lending interest rate and investment in physical capital by companies is stated as:

Which variable (lending interest rate or investment in physical capital) do you think should be the dependent variable in this regression model? Please justify your answer.                                                        [2 points]

2. What sign would you expect for the slope of this regression model for interest rate and investment in physical capita? Please justify your answer.                    
3. What is the role of the error term in the simple linear regression model like the one stated above? Please state at least three examples of the factors that you think belong in the error term of the simple linear regression model stated above briefly justifying each example.                                                                                           [3 points]
4. Please explain how you would estimate the relationship between interest rate and investment specified above. [note: you do not need to write any formulas as an answer to this question. Just explain what you will need and the reasoning behind the method you would use to estimate the relationship].                               [3 points]
5. For what purpose could you use the estimated simple linear regression model for lending interest rate and investment in physical capital? Why could the simple linear regression model stated above be inadequate for the purpose?            [2 points]                       
6. Using an example, please explain why a statistically significant relationship in a regression model for two variables does not necessarily imply “cause” and “effect” relationship between the two variables.   

5 Two different fish attractors were compared during 16 time periods spanning 4 years. (Wilbur, R. L. (1978). Two types of fish attractors compared in Lake Tohopekaliga, Florida. Transactions of the American Fisheries Society, 107(5), 689-695.) I present the data as a set of ordered pairs where in each case the first entry is the “pipe attractor” and the second entry is the “brush attractor”

{(6.64,9.73), (7.89,8.21),(1.83,2.17),(.42,.75),(.85,1.61),(.29,.75),(.57,.83),(.63,.56),(.32,.76),(.37,.32),(.00,.48),(.11.,.52),(4.86,5.38),(1.80,2.33),(.23,.91,),(.58,.79)}

(a)(4 pts) Perform the appropriate paired parameteric t-based test to compare the means.

(b)(6 pts) What happens if the two independent samples t-test is used? Make sure to perform all appropriate tests.

Is it possible to answer this questions with the code in Rstudio codes? If not the regular answer will be appreciated.

Case Study 1 - Data Visualization and Descriptive Statistics The data file Home_Values.xlsx contains median home values (Home Value), median household income (HH Inc), median per capita (Per Cap Inc) and percent of homes that are owner occupied (Pct Owner Occ) for each state and the District of Columbia. Prior to a more detailed analysis of the data, a company wants to get a good understanding of the 4 variables (e.g. central tendency, variability, shape of the distribution, pattern of relationship between the variables). A company representative contracts with you to help with this process. To help the company get a better understanding of the data, you are asked to perform the following analysis steps:

From public records, individuals were identified as having been charged with drunken driving not less than 6 months or more than 12 months from the starting date of the study. Two random samples from this group were studied. In the first sample of 35 individuals, the respondents were asked in a face-to-face interview if they had been charged with drunken driving in the last 12 months. Of these 35 people interviewed face to face, 15 answered the question accurately. The second random sample consisted of 50 people who had been charged with drunken driving. During a telephone interview, 28 of these responded accurately to the question asking if they had been charged with drunken driving during the past 12 months. Assume the samples are representative of all people recently charged with drunken driving.

(a) Categorize the problem below according to parameter being estimated, proportion p, mean μ, difference of means μ₁ – μ₂, or difference of proportions p₁ – p₂. Then solve the problem.

μp    p₁ – p₂μ₁ – μ₂

(b) Let p₁ represent the population proportion of all people with recent charges of drunken driving who respond accurately to a face-to-face interview asking if they have been charged with drunken driving during the past 12 months. Let p₂ represent the population proportion of all people who respond accurately to the question when it is asked in a telephone interview. Find a 95% confidence interval for p₁ – p₂. (Use 3 decimal places.)

(c) Does the interval found in part (a) contain numbers that are all positive? all negative? mixed? Comment on the meaning of the confidence interval in the context of this problem. At the 95% level, do you detect any differences in the proportion of accurate responses to the question from face-to- face interviews as compared with the proportion of accurate responses from telephone interviews?

Because the interval contains only positive numbers, we can say that there is a higher proportion of accurate responses in face-to-face interviews.Because the interval contains both positive and negative numbers, we can not say that there is a higher proportion of accurate responses in face-to-face interviews.    We can not make any conclusions using this confidence interval.Because the interval contains only negative numbers, we can say that there is a higher proportion of accurate responses in telephone interviews.

How profitable are different sectors of the stock market? One way to answer such a question is to examine profit as a percentage of stockholder equity. A random sample of 25 retail stocks such as Toys 'R' Us, Best Buy, and Gap was studied for x₁, profit as a percentage of stockholder equity. The result was x₁ = 14.8. A random sample of 30 utility (gas and electric) stocks such as Boston Edison, Wisconsin Energy, and Texas Utilities was studied for x₂, profit as a percentage of stockholder equity. The result was x₂ = 10.0. Assume that σ₁ = 4.9 and σ₂ = 2.3.

Categorize the problem below according to parameter being estimated, proportion p, mean μ, difference of means μ₁ – μ₂, or difference of proportions p₁ – p₂. Then solve the problem.

pμ₁ – μ₂    p₁ – p₂μ

(b) Let μ₁ represent the population mean profit as a percentage of stockholder equity for retail stocks, and let μ₂ represent the population mean profit as a percentage of stockholder equity for utility stocks. Find a 95% confidence interval for μ₁ – μ₂. (Use 1 decimal place.)

(c) Examine the confidence interval and explain what it means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the 95% level of confidence, does it appear that the profit as a percentage of stockholder equity for retail stocks is higher than that for utility stocks?

A researcher wanted to test the theory that people who live in urban environments are more liberal compared to people who live in suburban environments. To test this, they gave a group of people from the suburbs and a group of people from the city a measure of liberalness (the higher the score, the more liberal-minded you are). The data are given below.

Suburban: ?=15, n=60, ?$ = 3.81 $# Urban: ?=20, n=60, ?$ = 3.39

Run the appropriate hypothesis test (all 4 steps) to test the hypothesis people in urban and suburban environments have significantly different levels of liberalness. Use an alpha of α=0.01, two-tailed test. (Use the back of your sheet to complete this problem). Are you surprised at all with your results? Why/Why not?

What is the probability that you would get heads-up when flipping a coin ONE time?

What is the probability that you would get heads-up when flipping a coin TEN times?

What is the probability that you would get heads-up on two coins flipped at the same time?

What is the probability that you would roll a 5 on a single dice if you rolled it five times?

What is the probability that you would roll a 3 on a single dice if you rolled it five times?

1. A recent study of seat belt use found that for a random sample of 117 female Hispanic drivers in Boston; 68 were wearing seat belts. Is this sufficient evidence to claim that the proportion of all female Hispanic drivers in Boston who wear seat belts is greater than 50%. Use a significance level of 5%.
   1. This problem is about (circle the correct one):

One population proportion                      Two population proportions        

One population mean                             Two populations means (Independent samples)

One population standard deviation        Two populations means (paired samples)

Two population standard deviations

2. State the null and alternate hypotheses.

3. What is the level of significance?

4. List the requirements and show the numbers or information given to meet each requirement.

5. Circle which of the following Statcrunch methods you would use to test the hypothesis stated in part (b).

Proportion Stats – One sample         Proportion Stats-Two samples

Variance Stats – One sample           Variance Stats – Two samples

T Stats - One sample                 T Stats-Two samples (Independent)

T Stats - Paired

6. If the P-value = 0.0395, show details of determining if Ho is rejected or not.

7. Write the interpretation of the results of the hypothesis test.

You wish to test the following claim (HaHa) at a significance level of α=0.05α=0.05.

      Ho:μ=87.9Ho:μ=87.9
      Ha:μ≠87.9Ha:μ≠87.9

You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data:

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

The p-value is...

• less than (or equal to) αα
• greater than αα

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 87.9.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 87.9.
• The sample data support the claim that the population mean is not equal to 87.9.
• There is not sufficient sample evidence to support the claim that the population mean is not equal to 87.9.