A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before​ treatment, 19 subjects had a mean wake time of 105.0 min. After​ treatment, the 19 subjects had a mean wake time of 99.4 min and a standard deviation of 21.9 min. Assume that the 19 sample values appear to be from a normally distributed population and construct a 95​% confidence interval estimate of the mean wake time for a population with drug treatments. What does the result suggest about the mean wake time of 105.0 min before the​ treatment? Does the drug appear to be​ effective?

PART 2:

What does the result suggest about the mean wake time of 105.0 min before the​ treatment? Does the drug appear to be​ effective? The confidence interval_____ includes

does not include the mean wake time of 105.0 min before the​ treatment, so the means before and after the treatment _______ are different. could be the same. This result suggests that the drug treatment ________. does not have has a significant effect.

Assignment Problem:

Matt Profitt, an MBA student, is studying companies that are going public for the first time. He is curious about whether or not there is a significant relationship between the size of the offering (in millions of dollars) and the price per share.

Size    108     4.4      3.5      8.6      139     228     47.5    5.5      175     12        51        66

Price   12        4          5          6          13        19        8.5      5          15        6          12        12        

a. Develop the appropriate scatterplot for the two variables in the Excel spreadsheet.

b. Based upon the visual inspection of the plot, what type (directional) of relationship do you anticipate between the dependent and independent variables? Offer a brief explanation why that makes theoretical sense.

Please use the example illustrated Tables 12.2 and 12.3 for guidance on the EXCEL steps appropriate to generate the information needed to address the remaining sections.

c. Calculate SS_XX,SS_YY, and SS_XY.

d. Calculate the estimated y intercept (b₀) and the estimated slope coefficient (b₁).

e. Interpret the estimate slope coefficient.

f. Construct the ANOVA appropriate for this regression model.

g. Calculate r².

h. Interpret the coefficient of determination.

i. Calculate s sub b1.

j. Calculate the correlation coefficient.

k. Test whether or not the population correlation coefficient (rho) differs from zero. Use alpha = 0.05.

Could you please just help me with J and K? Thank you so much!

Discuss how choosing a significance level of 90%, 95%, or 99% might influence the results of our analysis as well as the factors you might consider in making your choice. Consider and discuss how doing the wrong thing (alpha risk, implementing when the improvements aren’t significant) might be perceived differently than choosing to do nothing yet (beta risk, going back for more design when the improvements are significant). How might you approach this analysis of your two data samples

A barber shop has two barbers, both of whom average 15 minutes/haircut (exponentially distributed). The first customer Joe arrives when both barbers are free and starts his haircut. A second customer Jack arrives 10 minutes later while Joe is still getting his haircut. Finally, a third customer John arrives another 20 minutes later, while both Joe and Jack are still having their haircuts. Assuming that no other customers arrive in this 30-minute interval:

a. What is the probability that Joe will be done before Jack?

b. What is the chance that John will be done before Joe?

c. What is the probability that John will be done before Jack?

An advertising executive wants to estimate the mean amount of time that consumers spend with digital media daily. From past​ studies, the standard deviation is estimated as 42 minutes.

A. What sample size is needed if the executive wants to be 90% confident of being correct to within plus or minus 4 minutes?

B. If 99% confidence is desired, how many consumers need to be selected?

The University of Cincinnati Center for Business Analytics is an outreach center that collaborates with industry partners on applied research and continuing education in business analytics. One of the programs offered by the center is a quarterly Business Intelligence Symposium. Each symposium features three speakers on the real-world use of analytics. Each of the corporate members of the center (there are currently 10) receives six free seats to each symposium. Nonmembers wishing to attend must pay $75 per person. Each attendee receives breakfast, lunch, and free parking. The following are the costs incurred for putting on this event:

1. Motivational speakers want to be perceived as trustworthy. One hypothesis is that speakers who exhibit immediacy behaviors such as making eye contact, smiling and leaning forward might be perceived as more trustworthy than those who do not engage in these behaviors. To test this hypothesis, a psychologist obtained data from 26 participants. For people in a nonimmediacy group, the speaker did not engage in any immediacy behaviors. For the immediacy group, however, the speaker made eye contact, smiled and leaned forward while giving a speech. After the speech, participants rated the speaker on a scale of trustworthiness ranging from 1 (not at all trustworthy) to 9 (highly trustworthy). The following data were obtained. Test whether the immediacy behaviors of the speaker affect trustworthiness rating.

1. Identify IV(s) and DV(s) of the experiment.
2. What is the researcher's question(s)?
3. State the null and alternative hypotheses
4. Compute the t-statistic.
5. Draw a conclusion by comparing the t-values (i.e., the t-obtained value and the t-critical valu.
6. The z-table provides the exact p-value for a given z-statistic. However, because the t-table does not provide the exact p-value for a given t-statistic, we will infer the approximate p-value based on the answer in 1-e. What is the approximate p-value? Also, draw a conclusion using the approximate p-value. Did you reach the same conclusion as the one you draw in 1-e?
7. Construct a 95% confidence interval and explain the meaning of the computed interval.
8. Compute the effect size.

Conceptual questions (Use the numbers that you obtained above if necessary):

1. Assume that you decide to reject the null hypothesis. Whenever you reject the null hypothesis, you commit certain amount of a Type I error. How much a Type I error approximately would you commit if you decide to reject the null? How does it differ from the alpha level that you set above?

10. Write a brief report that describes the result of this hypothesis testing. For this, you have to specify what test you applied, what was the purpose of the hypothesis testing, and what you found. Report the test value with df, the p-value, and the effect size (if you found one). Also, report the mean and SD of each group. (Read the SPSS book).
11. Which test did you apply? Why did you apply this test?

The manager of the commercial mortgage department of a large bank has collected data during the past two years concerning the number of commercial mortgages approved per week. The results from these two years ​(104 weeks) are shown to the right.

a. Compute the expected number of mortgages approved per week.

b. Compute the standard deviation.

c. What is the probability that there will be more than one commercial mortgage approved in a given​ week?

Number_Approved   Frequency
0   12
1   25
2   32
3   18
4   9
5   5
6   2
7   1

The expected number of mortgages approved per week is

​(Round to three decimal places as​ needed.)

b. The standard deviation is

​(Round to three decimal places as​ needed.)

c. The probability that there will be more than one commercial mortgage approved in a given week is

​(Round to three decimal places as​ needed.)

7. Suppose P(Z > z) = 0.9656. What is the value of z? Round your answer to 2 decimal places.

8. Let X be the number of shoppers in a supermarket line in an hour. Assume each person is independent. What type of probability distribution does X follow?

9. At a walk-in clinic, 60 patients arrive per hour on average. What is the probability that the receptionist needs to wait at least 2 minutes for the next patient to walk in? Round your answer to 4 decimal places.

10.Which of the following statements about discrete random variables and discrete probability distributions is/are TRUE?

I. If X is a Binomial random variable, then X could take the value 1

II. The Poisson distribution is right skewed.

III. The mean and the standard deviation of a Poisson random variable are equal.

IV. The probability that a discrete random variable X takes the value 8.4 may not be 0.

11.Suppose people arrive at a hospital’s emergency department at a rate of 1 every 9.5 minutes. What is the probability that a person arrives within the next 3.5 minutes? Round your answer to 4 decimal places.

1. A tire company produces a tire that has an average life span of 500 miles with a standard deviation of 250. The distribution of the life spans of the tires is normal. What is the probability that the tires lasts between 530 and 375 miles? (Round three decimal places)

2. A tire company produces a tire that has an average life span of 480 miles with a standard deviation of 30. The distribution of the life spans of the tires is normal. What is the probability that the tires lasts less than 430 miles? Round your answer to three decimal places

3. A tire company produces a tire that has an average life span of 480 miles with a standard deviation of 25. The distribution of the life spans of the tires is normal. What is the probability that the tires lasts greater than 498 miles? (Round three decimal places)

We wish to estimate what percent of adult residents in a certain county are parents. Out of 400 adult residents sampled, 128 had kids. Based on this, construct a 90% confidence interval for the proportion pp of adult residents who are parents in this county.

Give your answers as decimals, to 4 places.

What percentage of cases are lower than those with each Z score: -1, -2, -1.75, 1, 2, 1.75

For a data set with Mean = 20, SD = 3 find the Z scores for each of the following raw scores:

23, 17, 15, 22, 30. Would you consider any of these cases an outlier? Explain your reasoning.

Assume that you want to play a game called “who is the murderer?” with a total of seven suspects including Angelina, Boris, Chris, Dillon, Eve, Frank, and Gunther. Among them, Angelina and Eve are girls and all the other five suspects are boys. According to the polygraph and some other technology tools, you are sure about the following clues. • The number of murders is either one or two; • All the murderer(s) must be among them; • If Angelina is the murderer, the number of murderers is two; • If Chris is a murderer, so is Frank; • At least one of the girls is innocent; • If Frank is a murderer, so is Eve; • If both Gunther and Boris are innocent, Angelina is a murderer; • If Dillon is innocent, so is Gunther; • If both Chris and Dillon are innocent, so is Boris; • Angelina and Dillon cannot be both murderers; • If Dillon is a murderer, either Boris is a murderer or Gunther is innocent; • If Eve is murderer, either Chris is a murderer or Boris is innocent. Now, who did it? Why?

From the 2016 General Social Survey, when we cross-classify political ideology
(with 1 being most liberal and 7 being most conservative) by political party affiliation
for subjects of ages 18–27, we get:
-------------------------------------------------------------
1 2 3 4 5 6 7
Democrat 5 18 19 25 7 7 2
Republican 1 3 1 11 10 11 1
-------------------------------------------------------------
When we use R to model the effect of political ideology on the probability of being
a Democrat, we get the results:
-------------------------------------------------------------
> y <- c(5,18,19,25,7,7,2); n <- c(6,21,20,36,17,18,3)
> x <- c(1,2,3,4,5,6,7)
> fit <- glm(y/n ~ x, family=binomial(link=logit), weights=n)
> summary(fit)
Estimate Std. Error z value Pr(>|z|)
(Intercept) 3.1870 0.7002 4.552 5.33e-06
x -0.5901 0.1564 -3.772 0.000162
---
Null deviance: 24.7983 on 6 degrees of freedom
Residual deviance: 7.7894 on 5 degrees of freedom
Number of Fisher Scoring iterations: 4
> confint(fit)
2.5 % 97.5 %
(Intercept) 1.90180 4.66484
x -0.91587 -0.29832
-------------------------------------------------------------
a. Report the prediction equation and interpret the direction of the estimated effect.
b. Construct the 95% Wald confidence interval for the effect of political ideology.
Interpret and compare to the profile likelihood interval shown.
c. Conduct the Wald test for the effect of x. Report the test statistic, P-value, and
interpret.
d. Conduct the likelihood-ratio test for the effect of x. Report the test statistic, find
the P-value, and interpret.
e. Explain the output about the number of Fisher scoring iterations