The big idea behind hypothesis testing is that we have an assumption about reality, and we see if the data fits that assumption. The whole process gets complicated by all the notation and calculations, but essentially we’re deciding if the assumption is possible, or if the data leads us to reject it.

1. Your friend Hamad claims to be exceptional at basketball and can make 90% of free throws. You watch him at the gym for a week and find out that he makes 64 shots out of 176 attempts.

Don’t do any calculations here. Just give a quick look at his results and claim, and then a statement about whether it backs up Hamad’s claim. Please write a complete sentence (or more).

2. In each situation, determine whether you should reject or fail to reject H₀.

a.         p-value = 0.15, α = 0.10                      b.         p-value = 0.015, α = 0.02

c.         z = 2.345, critical value = 1.645          d.         test statistic = -2.56, critical value = 1.96

3. Yolanda thinks she can roll a 1 on a 6-sided die more often than chance would predict. Write hypotheses to test this. Be sure to define p in words (p = the proportion of…).

4. Test 2: The Japanese harvester beetle has infected several forests in the Northwest. Official estimates are that 17% of trees are infected. You are a park ranger who has been seeing a lot of these beetles lately, and you think the rate is higher in your area. You check 400 trees around your cabin and find that 79 of them are infected.

• Go through the steps on the Hypothesis Test Guide (D2L). List each step like Step 1, Step 2, etc.
• Please check the conditions using complete sentences.
• Please do the calculations out the long way, but definitely use GeoGebra or a calculator stats package to check.
• Even if the conditions aren’t met, do the rest anyway.
• Use α = 0.03

Given the following pairs of scores from dependent samples: Pair: 1 2 3 4 5 X: 4 4 6 5 9 Y: 5 2 3 1 6 (a) State formally the hypotheses necessary to conduct a non-directional test of no difference between the two population means. (b) Calculate t using Formula 15.5. t=Dbar-ud/square root sum of D squared - (sum of d)2/n / n(n-1) (c) Calculate t using formula 15.3. t= (xbar -ybar) - (ux-uy)hyp/ square root s2x + s2y - 2rsbarsybar (d) Complete the test at the .05 and .01 levels of significance and state your conclusion.

R Questions Question 2

In an experiment of rolling 10 dice simultaneously. Use the binomial distribution to calculate the followings:

a) The probability of getting six 6's ```{r} #INSERT YOUR ANSWER HERE ```

b) The probability of getting six, seven, or eight 3's ```{r} #INSERT YOUR ANSWER HERE ```

c) The probability of getting six even numbers ```{r} #INSERT YOUR ANSWER HERE ``` ****** ##

Question 3 In a shipment of 20 engines, history shows that the probability of any one engine proving unsatisfactory is 0.1

a) Use the Binomial approximation to calculate the probability that at least three engines are defective? ```{r} #INSERT YOUR ANSWER HERE ```

b) Use the Poisson approximation to calculate the probability that at least three engines are defective? ```{r} #INSERT YOUR ANSWER HERE ```

c) Compare the results of parts a and b, then illustrate on how well the Poisson probability distribution approximates the Binomial probability distribution. ```{r} #INSERT YOUR ANSWER HERE ``` ******

if R code can't be provided that is fine, but will need the answer in simple form if possible with explanation

1. Solve the problem using the employment information in the table on Alpha Corporation

1. The mean of a set of data is 5.07 and its standard deviation is 3.39. Find the z-score for a value of 9.65. _______________________
2. Which is better and corresponds to the higher relative position, a score of 92 on a test with a mean of 71 and a standard deviation of 15, or a score of 688 on a test with a mean of 493 and a standard deviation of 150? ____________________________________
3. On a given registration day, 45 CJ majors and 25 CIS majors arrive. What is the empirical probability that the next student to arrive will be a CJ major? ______________________________

No Hand Writing please, Type your answer.

4. Compare the preceding four simple linear regression models to determine which model is the preferred model. Use the Significance F values, p-values for independent variable coefficients, R-squared or Adjusted R-squared values (as appropriate), and standard errors to explain your selection.

5.. Calculate the predicted income of a 45 year old, with 18 years of education, 2 children, and works 40 hours per week using your preferred regression model from part 4.

1. 2.194 Comparing Global Internet Connections. In Exercise 2.120 we discuss a study in which the Nielsen Company measured connection speeds on home computers in nine different countries in order to determine whether connection speed affects the amount of time consumers spend online. Table 2.29 (by exercise 2.194 in the textbook) shows the percent of Internet users with a “fast” connection (defined as 2Mb or faster) and the average amount of time spent online, defined as total hours connected to the Web from a home computer during the month of February 2011. The data are also available in the dataset GlobalInternet. We are interested in looking at whether the percent of Internet users with a fast internet connection predicts the number of hours spent online.
   
   1. What is the explanatory variable? What is the response variable? Is each categorical or quantitative?
      
      
      
      
      
   2. What would a positive association mean between these two variables? Briefly explain why a positive relationship might make sense in this context.
      
      
      
      
      
      
      
      
      
   3. What would a negative association mean between these two variables? Briefly explain why a negative relationship might make sense in this context.
      
      
      
      
      
      
      
   4. Make a scatterplot with regression line, using connection speed as the explanatory variable and time online as the response variable. Include a screen shot of your Statkey output with your homework submission. What is the correlation?
      
      
   5. Are there any outliers? If so, indicate the country associated with each outlier and describe the characteristics that make it an outlier for the scatterplot.
      
   6. Eliminate the outliers you identified, and generate another scatterplot with regression line. Is the correlation strongly affected by the outliers?
      
      
      
      
   7. Find the regression equation for these variables with the outliers removed. Include a screen shot of your Statkey scatterplot with regression line with your homework submission, and write the regression equation here.
   8. Interpret the slope of the regression line in context. Remember that an interpretation must include a number and units, in a sentence that explains the meaning.
   9. Use the regression line to predict the number of hours spent online in Febrary 2011 in a country in which 65% of Internet users have a fast connection. Show your calculations.

Sampling Distribution. To commemorate Facebook’s 10-year milestone, Pew Research reported several facts about Facebook obtained from its Internet Project survey. One was that the average adult user of Facebook has 338 friends. This population distribution takes only integer values, so it is certainly not Normal. It is also highly skewed to the right, with a reported median of 200 friends.

Suppose that σ = 380 and you take an SRS of 80 adult Facebook users.

a. For your sample, what are the mean and standard deviation of ̅ (xbar), the mean number of friends per adult user?

b. Use the central limit theorem to find the probability that the average number of friends for 80 Facebook users is greater than 350.

Five cigarette manufacturers claim that their product has low tar content. Independent random samples of cigarettes are taken from each manufacturer and the following tar levels (in milligrams) are recorded.

Brand Tar Level (mg)

A 4.2, 4.8, 4.6, 4.0, 4.4

B 4.9, 4.8, 4.7, 5.0, 4.9, 5.2

C 5.4, 5.3, 5.4, 5.2, 5.5

D 5.8, 5.6, 5.5, 5.4, 5.6, 5.8

E 5.9, 6.2, 6.2, 6.8, 6.4, 6.3

Can the differences among the sample means be attributed to chance?

A regular six-sided die and a regular eight-sided die are rolled to find the sum. Determine the probability distribution for the sum of the two dice. Create a frequency histogram for the probability distribution and determine the expected sum of the two dice.

A study was conducted to see if students’ writing skills continue to improve as the academic year progresses. English 101 students were asked to write essays throughout the year in September, December, March and June. The scores were compared to see if there is any improvement in this one-year course. Was there a significant improvement?

a. The appropriate test for this problem is:

b. The obtained statistic is:

c. The associated p value is:

Decision is:

Conclusion is:

Consider the following. (Give your answers correct to two decimal places.)

(a) Calculate the value for the test statistic, χ², for H_o: σ² = 20.5, n = 16, s² = 16.5.
χ²* =

(b) Calculate the value for the test statistic, χ², for H_o: σ² = 30.1, n = 22, s = 6.2.
χ²* =

(c) Calculate the value for the test statistic, χ², for H_o: σ = 44, n = 22, s = 37.6.
χ²* =

(d) Calculate the value for the test statistic, χ², for H_o: σ = 14, n = 19, s² = 163.
χ²* =

For the following four questions, a group of residents were asked about their support for a homeless shelter being opened in their neighborhood. They were also asked about how long they had lived in the neighborhood, with short term residency defined as less than three years and long-term as three years or more. Resident Neighborhood Tenure Supports Shelter 1 Short term Yes 2 Short term No 3 Long term Yes 4 Long term No 5 Short term Yes 6 Short term Yes 7 Long term No 8 Short term Yes 9 Short term Yes 10 Short term No Flag this Question Question 1 4 pts What is the probability of selecting a short term resident at random from this group? Flag this Question Question 2 4 pts What is the probability of selecting a resident who does not support the homeless shelter at random from this group? Flag this Question Question 3 4 pts What is the probability of selecting a long term resident who supports the homeless shelter at random from this group? Flag this Question Question 4 4 pts What is the probability of selecting a short term resident who does not support the homeless shelter at random from this group? Flag this Question For the following two questions, research has shown that nearly 25% of homeless adults are veterans. Flag this Question Question 5 4 pts What is the probability of selecting a particular homeless person who is not a veteran? Flag this Question Question 6 4 pts What is the probability of selecting two random homeless people who are both veterans? Flag this Question For the following seven questions, you are drawing one card at random from a standard deck of 52 cards. Flag this Question Question 7 4 pts What is the probability of drawing the eight of diamonds? Flag this Question Question 8 4 pts What is the probability of drawing a diamond card? Flag this Question Question 9 4 pts What is the probability of drawing an eight? Flag this Question Question 10 4 pts What is the probability of drawing a red car

A Study of recent graduates from BSCC revealed that for a sample of 10 recently graduated Accounting Technology majors the mean salary was $32,000 per year with a sample standard deviation of $1,800. A sample of 8 business Administration majors revealed a mean salary of $29,000 per year with a sample standard deviation of $2,000. At the .05 significance level, can we conclude there is a difference in the starting salaries?

1. State the Null and Alternate Hypothesis(H0, H1).

2. Determine the level of significance.

3. Determine the test statistic. (z or t)

4. State the decision rule.(Reject H0 if)

5. Conduct the test and make a decision.(Include Formula and show all work)

6. Interpret the results.

"PLEASE SHOW ALL WORK WITH THE CORRECT ANSWERS"

Thanks!

my question is about 3.2.13 which is

A loan of amount L is to be repaid by n payments, starting one period after the loan is made, with interest at rate I per period. Two repayment schemes are considered:

i) level payments for the lifetime of the loan;

ii) each payment consists of principal repaid of L/n plus interest on the previous outstanding balance.

Find the total interest repaid under each scheme and show algebraically that the interest paid under scheme (i) is larger than that paid under scheme (ii).

Show that for each t = 1, 2, . . . , n − 1, OBt is larger under scheme (i) than under scheme (ii).

Verify algebraically that L is the present value at the time of the loan, at rate of interest i per payment period, of all payments made under scheme (ii).

Sophia who took the Graduate Record Examination (GRE) scored 157 on the Verbal Reasoning section and 162 on the Quantitative Reasoning section. The mean score for Verbal Reasoning section for all test takers was 150 with a standard deviation of 7.2, and the mean score for the Quantitative Reasoning was 153 with a standard deviation of 7.64. Suppose that both distributions are nearly normal.

(a) What is Sophias Z-score on the Verbal Reasoning section?
On the Quantitative Reasoning section?
(b) Relative to others, which section did she do better on? .
(c) Find her percentile scores for the two exams.
Verbal Reasoning percentile: th
Quantitative Reasoning percentile: th
(d) What percent of the test takers did better than her on the Verbal Reasoning section? .
On the Quantitative Reasoning section? .

Find the following:
(e) The score of a student who scored in the 75th percentile on the Quantitative Reasoning section.
(f) The score of a student who scored worse than 85% of the test takers in the Verbal Reasoning section.