A mortgage company performs reviews of its closing documents prior to the closing dates. This review may prompt changes or document additions that should have been in the closing package. Any closing package found with inaccuracies or known to be incomplete are deemed defective and require rework prior to closing. In the prior calendar year, the defective rate for these reviews was 17.99% (783 defective packages out of 4,352 reviewed). During the current year, the year-to-date defective rate is 20.69% (180 of 870). Use the information provided to perform a 2-sample proportion test to determine if there is a difference between the current satisfaction rate and the prior year.

Makers of generic drugs must show that they do not differ significantly from the "reference" drugs that they imitate. One aspect in which drugs might differ is their extent of absorption in the blood. The table gives data taken from 20 healthy nonsmoking male subjects for one pair of drugs. This is a matched pairs design. Numbers 1 to 20 were assigned at random to the subjects. Subjects 1 to 10 received the generic drug first, and Subjects 11 to 20 received the reference drug first. In all cases, a washout period separated the two drugs so that the first had disappeared from the blood before the subject took the second drug. Absorption extent for two versions of a drug Subject Reference Generic Subject Reference Generic 15 4108 1755 4 2344 2738 3 2526 1138 16 1864 2302 9 2779 1613 6 1022 1284 13 3852 2254 10 2256 3056 12 1833 1310 5 938 1287 8 2463 2120 7 1339 1930 18 2059 1851 14 1262 1964 20 1709 1878 11 1438 2549 17 1829 1682 1 1735 3340 2 2594 2613 19 1020 3050 To access the complete data set, click the link for your preferred software format: Excel Minitab JMP SPSS TI R Mac-TXT PC-TXT CSV CrunchIt!

Do the drugs differ significantly in absorption?

STATE: Do the generic and reference drugs differ in mean absorption level? PLAN: We test H 0 : μ = 0 versus H a : μ ≠ 0 , where μ is the mean difference in absorption (Generic minus Reference). The alternative is two‑sided because we have no prior expectation of a direction for the difference. SOLVE: Find ¯ x , s , and the t statistic. (Enter your answers rounded to two decimal places.) ¯ x = s = t = Find the degrees of freedom. (Enter your answer as a whole number.) df = Obtain the P ‑value. (Enter your answer rounded to two decimal places.) P ‑value = CONCLUDE: Do the drugs differ significantly in absorption? No, the drugs don't differ significantly in absorption ( 0.05 < P < 0.1 ) . Yes, the drugs differ significantly in absorption ( P < 0.01 ) . Yes, the drugs differ significantly in absorption ( 0.01 < P < 0.05 ) . No, the drugs don't differ significantly in absorption ( P > 0.5 ) .

The probability that a patient with a heart attack dies of the attack is 4%. Suppose we have 4 patients who suffer a heart attack

a) what is the probability that 2 will survive?

b) what is the probability that all will die?

c) what is the probability that less than 3 will survive?

d) what is the probability that all will survive?

Problem 2

A consumer products firm has recently introduced a new brand. The firm would like to estimate the proportion of people in its target market segment who are aware of the new brand. As part of a larger market research study, it was found that in a sample of 125 randomly selected individuals from the target market segment, 84 individuals were aware of the firm's new brand.

1.    Construct a 95% confidence interval for the proportion of individuals in the target market segment who are aware of the firm's new brand. If you use Excel and/or StatTools, please specify any functions you use and all the inputs.

2.    The manager in charge of the new brand has stated that the brand awareness is greater than .75, meaning that more than 75% of the population is aware of the brand. He would like to use hypothesis testing to prove his claim. At the 5% significance level, conduct a hypothesis test with the goal of proving his claim. In particular i) specify the null hypothesis and the alternative hypothesis, ii) state whether you are using a one- or two-tailed test, iii) specify the p-value of the test, and iv) provide the results of the test in "plain English".

Hints: 1) Think carefully about what is the null hypothesis, and what is the alternative. 2) If you want to use StatTools for the analysis, you need to create the survey data in Excel first; then you can run the analysis.

For future polls, the firm is interested in minimizing their marketing-research costs. The margin of error (MOE) in their pools should be no larger than B (i.e., ± 100B percentage points). To simplify the analysis, we will assume their marketing study only has a single question that is used to estimate p, at the 5% significance level.

3.    If the firm had no prior knowledge of p, how large would the sample size have to be to ensure MOE ≤ B? (Hint: your answer will be a formula containing B).

4.    The firm has prior knowledge that p will likely be somewhere between .10 and .20 (that is between 10% and 20%). How large should the sample be if they would like to ensure that MOE (=B) is no larger than 0.01 or 1%?

The national average of college students on a test of sports trivia is 50 with a standard deviation of 5. A sportscaster is interested in whether BC students know less about sports than the national average. The sportscaster tests a random sample of 25 BC students and obtains a mean of 48 Use an alpha level of 0.05.

1. State the z score(s) that form the boundaries of the critical region. Use an alpha level of 0.05.

2. Calculate the standard error

3. Calculate the z score

4. What decision would you make? Fail to reject the null hypothesis or Reject the null hypothesis

5. What can the researcher conclude? Let’s say in the above example that the BC average on the sports trivia test was 52 resulting in a z score of +2.0. What decision would the researcher make? Fail to reject the null hypothesis? or reject the null hypothesis?

6. Why did you make that decision in Question 5?

In this problem, we explore the effect on the standard deviation of adding the same constant to each data value in a data set. Consider the following data set.

12, 6, 11, 10, 15

(a) Use the defining formula, the computation formula, or a calculator to compute s. (Enter your answer to one decimal place.)


(b) Add 3 to each data value to get the new data set 15, 9, 14, 13, 18. Compute s. (Enter your answer to one decimal place.)

(c) Compare the results of parts (a) and (b). In general, how do you think the standard deviation of a data set changes if the same constant is added to each data value?

Adding the same constant c to each data value results in the standard deviation remaining the same.

Adding the same constant c to each data value results in the standard deviation increasing by c units.

   Adding the same constant c to each data value results in the standard deviation decreasing by c units.

There is no distinct pattern when the same constant is added to each data value in a set.

Math & Music (Raw Data, Software Required): There is a lot of interest in the relationship between studying music and studying math. We will look at some sample data that investigates this relationship. Below are the Math SAT scores from 8 students who studied music through high school and 11 students who did not. Test the claim that students who study music in high school have a higher average Math SAT score than those who do not. Test this claim at the 0.05 significance level.

You should be able copy and paste the data directly into your software program.

(a) The claim is that the difference in population means is positive (μ1 − μ2 > 0). What type of test is this?

This is a right-tailed test.

This is a left-tailed test.

This is a two-tailed test.

(b) Use software to calculate the test statistic. Do not 'pool' the variance. This means you do not assume equal variances. Round your answer to 2 decimal places.

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.

(d) What is the conclusion regarding the null hypothesis?

reject H0

fail to reject H0

(e) Choose the appropriate concluding statement.

The data supports the claim that students who study music in high school have a higher average Math SAT score than those who do not.

There is not enough data to support the claim that students who study music in high school have a higher average Math SAT score than those who do not.

We reject the claim that students who study music in high school have a higher average Math SAT score than those who do not.

We have proven that students who study music in high school have a higher average Math SAT score than those who do not.

Suppose we think that listening to classical music will affect the amount of time it takes a person to fall asleep; we conduct a study to test this idea. Answer all of the following questions:

Assume that the amount of time it takes people in the population to fall asleep is normally distributed. In the study, we have a sample of people listen to classical music and then we measure how long it takes them to fall asleep. Supposed the sample of 36 people fall asleep in 12 minutes. What is the probability of obtaining a sample mean of 12 minutes or smaller? Assuming alpha equals 0.05, is your calculated p value in the critical region? (Hint: Remember to consider two critical regions.)

Let X~Geometric(p), with parameter p unknown, 0<p<1.

a) Find I(p), the Fisher Information in X about p.

b) Suppose that pˆ is some unbiased estimator of p. Determine the Cramér-Rao Lower Bound for Var p[ ]ˆ based on one observation from this distribution.

c) Show that p= I _{1}(X) is an unbiased estimator of p. Does its variance achieve the Cramer-Rao Lower Bound?

Statistics is its own language. In fact, it is often called the language of science. Why do you think it is called the language of science? What does it mean to be statistically literate? Why is it important to be statistically literate?

Please don't copy from chegg or anywhere

Technician           Technician

A B

1.45                        1.54

1.37                       1.41

1.21                        1.56

1.54                        1.37

1.48                        1.2

1.29                        1.31

1.34                        1.27

1.35

Technician           Technician

1                              2

1.45                        1.54

1.37                       1.41

1.21                        1.56

1.54                        1.37

1.48                        1.2

1.29                        1.31

1.34                        1.27

1.35

a. Test the hypothesis that the mean surface finish measurements made by the two technicians are equal. Use α = 0.05 and assume equal variances. b. What are the practical implications of the test in part (a)? Discuss what practical conclusions you would draw if the null hypothesis were rejected. c. Assuming that the variances are equal, construct a 95% confidence interval on the mean difference in surface-finish measurements d. Test the hypothesis that the variances of the measurements made by the two technicians are equal. Use α = 0.05. What are the practical implications if the null hypothesis is rejected? e. Construct a 95% confidence interval estimate of the ratio of the variances of technician measurement error.Please solve urgent

Consider the following time series.

1. Trying to improve the techniques I use in the classroom and reduce the anxiety of the students, I decided to try an experiment. I decided that I would incorporate more relaxation techniques prior to exams. For a comparison, I subjected the students to twice the exams (evil, I know). In essence, I did a pre- and post-test. The scores are below. At α = 0.05, can it be concluded that the relaxation techniques helped improve test scores?

(For each of the problems you must state: the hypotheses and identify the claim, state the test value, p-value, make a decision and summarize the results.)

Round all your answers to 4 decimal places. Let μ=E(X), σ=stanard deviation of X. Find the probability P(μ-σ ≤ X ≤ μ+σ) if X has...

a. ... a Binomial distribution with n=6 and p=1/3.

b. ... a Geometric distribution with p = 0.63.

c. ... a Poisson distribution with λ = 7.2.

The American Community Survey is a survey that uses U.S. census data to compile information on various characteristics of the U.S. population. Here are statistics that I would like you to analyze from a sample of states.

The independent variable (x-variable) is the percent of the state population living below the poverty level. The dependent variable (y-variable) is the state infant mortality rate in deaths per 1000 births. The data is displayed in the following table:

Create a scatterplot of the x-values vs. the Residuals. The Residual plot shows two unusual values (values with the largest deviations).

Of the following statements, choose the two statements that correctly describe these unusual values.

    1. New Mexico has an actual infant mortality rate that is much higher than the

        predicted infant mortality rate.

    2. New Mexico has an actual infant mortality rate that is much lower than the

        predicted infant mortality rate.

    3. Louisiana has an actual infant mortality rate that is much higher than the

        predicted infant mortality rate.

    4. Louisiana has an actual infant mortality rate that is much lower than the

        predicted infant mortality rate.

    5. Mississippi has an actual infant mortality rate that is much higher than the

        predicted infant mortality rate.

    6. Mississippi has an actual infant mortality rate that is much lower than the

        predicted infant mortality rate.