The following table provides summary statistics for the DurationSurgery based on whether or not patients contracted an SSI from the Seasonal Effect data set. One of the researchers is curious whether there is evidence to suggest that surgery duration was longer in patients who contracted SSIs. Use the following information to conduct the following hypothesis test:

• A one-tail T-test for a two-sample difference in means at the 99% confidence level
• with Null Hypothesis that the average surgery duration in patients that did contract SSIs is equal to the average surgery duration in patients that did not contract SSIs
• and with Alternate Hypothesis that the average surgery duration in patients that did contract SSIs is greater than the average surgery duration in patients that did not contract SSIs

a. Calculate the standard error of the mean for each group. (10%)

b. Using the correct degrees of freedom (df = group X size + group Y size ̶ # of groups), the correct number of tails, and at the correct confidence level, determine the critical value of t. (10%)

c. Explain under which scenarios using a pooled variance be inadvisable, then, calculate the pooled variance (formula for S² is onpage 379) for the groups. (10%)

d. Calculate the test statistic, T_test (formula for t is on page 380). (10%)

e. The sleep center’s statistician tells you that the p-value for the test is less than 0.0001. Summarize the result of the study. Compare the mean scores in each group. Compare the test statistic to the critical value. Compare the p-value to alpha. Do you find a statistically significant difference? Is there a meaningful/practical difference? Explain your decisions and Justify your claims. (15%)

A car wash has two stations, 1 and 2. The service time at station 1 is exponentially distributed with parameter λ1, and the service time at station 2 is exponentially distributed with parameter λ2.When a car arrives at the car wash, it begins service at station 1, provided station 1 is free; otherwise, the car waits until station 1 is available. Upon completing service at station 1, the car then proceeds to station 2, provided station 2 is free; otherwise, the car has to wait at station 1, blocking other cars from receiving service at station 1. The car exits thecarwash after service at station 2 is completed. Different cars are independent of each other, and for any car, the service time at station 1 is independent of the service time at station 2.When you arrive, there is only one car at the car wash, and it is receiving service at station 1.Compute the expected time from your arrival until your exit from the car wash.

variable1   variable2
-1.60263   6.66630
5.13511   22.39796
6.36533   48.04439
5.62218   33.73949
-2.19935   13.13368
6.44037   34.07411
7.53576   57.43268
6.84911   46.18391
-0.96507   2.31758
-7.97987   66.45126
7.71148   60.12220
8.00414   69.34776
-1.84249   -8.58487
-6.64529   35.44469
3.52281   15.81326
6.12823   42.51683
-8.02429   63.53322
1.93739   10.39306
1.60250   -1.67370
9.59542   92.44574
0.97873   -2.22144
7.61991   66.59948
6.35683   35.62167
4.60624   15.37388

Correlation is used to discover relationships between variables. Evaluate the correlation between the variables in DATA. What is the correlation?

A) 0.984

B) -0.991

C) 0.310

D) -0.008

E) None of the answers are correct.

Bardi Trucking Co., located in Cleveland, Ohio, makes deliveries in the Great Lakes region, the Southeast, and the Northeast. Jim Bardi, the president, is studying the relationship between the distance a shipment must travel and the length of time, in days, it takes the shipment to arrive at its destination. To investigate, Mr. Bardi selected a random sample of 20 shipments made last month. Shipping distance is the independent variable and shipping time is the dependent variable. The results are as follows:

Draw a scatter diagram. Based on these data, does it appear that there is a relationship between how many miles a shipment has to go and the time it takes to arrive at its destination?

Fill in the blanks. (Round your answers to 3 decimal places. Negative values should be indicated by minus sign.)

State the decision rule for 0.10 significance level: H₀: ρ ≤ 0; H₁: ρ > 0.

Compute the value of the test statistic.

Determine the coefficient of determination.

Fill in the blank below. (Round your answer to 1 decimal places.)

___% of the variation in shipping time is explained in by shipping distance

Determine the standard error of estimate.

What is the probability, given a 52 card deck, of being dealt an Ace of spades, an Ace of hearts, and Ace of clubs, in that order.

The lengths of pregnancies are normally distributed with a mean of

267 days and a standard deviation of 15 days. a. Find the probability of a pregnancy lasting

308 days or longer. b. If the length of pregnancy is in the lowest 3%, then the baby is premature. Find the length that separates premature babies from those who are not premature.

A nutritionist wants to determine how much time nationally people spend eating and drinking. Suppose for a random sample of
1062 people age 15 or​ older, the mean amount of time spent eating or drinking per day is
1.07 hours with a standard deviation of 0.65 hour. Complete parts ​(a) through ​(d) below.

​(a) A histogram of time spent eating and drinking each day is skewed right. Use this result to explain why a large sample size is needed to construct a confidence interval for the mean time spent eating and drinking each day.

A. The distribution of the sample mean will never be approximately normal.

B. Since the distribution of time spent eating and drinking each day is not normally distributed​ (skewed right), the sample must be large so that the distribution of the sample mean will be approximately normal.

C. The distribution of the sample mean will always be approximately normal.

D. Since the distribution of time spent eating and drinking each day is normally​ distributed, the sample must be large so that the distribution of the sample mean will be approximately normal.

​(b) In​ 2010, there were over 200 million people nationally age 15 or older. Explain why​ this, along with the fact that the data were obtained using a random​ sample, satisfies the requirements for constructing a confidence interval.

A. The sample size is less than​ 5% of the population.

B. The sample size is greater than​ 10% of the population.

C. The sample size is less than​ 10% of the population.

D. The sample size is greater than​ 5% of the population.

​(c) Determine and interpret a 90​% confidence interval for the mean amount of time Americans age 15 or older spend eating and drinking each day.

Select the correct choice below and fill in the answer​ boxes, if​ applicable, in your choice.
​(Type integers or decimals rounded to three decimal places as needed. Use ascending​ order.)

A.The nutritionist is 90​% confident that the amount of time spent eating or drinking per day for any individual is between ____ and ____hours.

B.There is a 90​% probability that the mean amount of time spent eating or drinking per day is between ____ and ____ hours.

C.The nutritionist is 90​% confident that the mean amount of time spent eating or drinking per day is between ____ and ____ hours.

D.The requirements for constructing a confidence interval are not satisfied.

(d) Could the interval be used to estimate the mean amount of time a​ 9-year-old spends eating and drinking each​ day? Explain.

A. No; the interval is about individual time spent eating or drinking per day and cannot be used to find the mean time spent eating or drinking per day for specific age.

B. No; the interval is about people age 15 or older. The mean amount of time spent eating or drinking per day for​ 9-year-olds may differ.

C. ​Yes; the interval is about the mean amount of time spent eating or drinking per day for people people age 15 or older and can be used to find the mean amount of time spent eating or drinking per day for​ 9-year-olds.

D. Yes; the interval is about individual time spent eating or drinking per day and can be used to find the mean amount of time a​ 9-year-old spends eating and drinking each day.

E. A confidence interval could not be constructed in part ​(c).

When only two treatments are involved, ANOVA and the Student’s t test (Chapter 11) result in the same conclusions. Also, for computed test statistics, t^₂ = F. To demonstrate this relationship, use the following example. Fourteen randomly selected students enrolled in a history course were divided into two groups, one consisting of 6 students who took the course in the normal lecture format. The other group of 8 students took the course as a distance course format. At the end of the course, each group was examined with a 50-item test. The following is a list of the number correct for each of the two groups.

1= Complete the ANOVA table. (Round your SS, MS, and F values to 2 decimal places and p value to 4 decimal places.)?

2=a-2. Use a α = 0.01 level of significance. (Round your answer to 2 decimal places.)

2. Using the t test from Chapter 11, compute t. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

3. There is any difference in the mean test scores.

1. Suppose we have the following data on variable X (independent) and variable Y (dependent):

(SOLVE ALL BY HAND, NOT BY USING EXCEL)

1. By hand, determine the simple regression equation relating Y and X.
2. Calculate the R-Square measure and interpret the result.
3. Calculate the adjusted R-Square.
4. Test to see whether X and Y are significantly related using a test on the population correlation. Test this at the 0.05 level.
5. Test to see whether X and Y are significantly related using a t-test on the slope of X. Test this at the 0.05 level.
6. Test to see whether X and Y are significantly related using an F-test on the slope of X. Test this at the 0.05 level.

1. 3 e) Of course the number of years smoked and longevity do not follow a normal distribution. That being the case, we have to use a nonparametric test to test if there is a correlation between these two variables. So using the Spearman correlation approach, test the claim at 95% confidence that there is a negative correlation between these two variables.
   1. State the Null and Alternative Hypothesis (1)
   2. Draw the appropriate probability density curve setting up the problem and state the Decision Rule. (1)
   3. Determine the Spearman Correlation Coefficient (2)
   4. Perform the test (2)
   5. State your decision (1)
      
      (Note, to help you out, I have started your Spearman calculation)
      

A researcher collected data from a small random sample of ten students by asking them individually how much time (y) they spent studying and how much time (x) they spent on social media, on one day during an exam week. Both times were given in hours, rounded to the nearest half hour. They shown in the table below.

The researcher wishes to find a simple linear regression model Yi ∼ N(a + bxi , σ2 ).

(i) Find data summaries for this data and use them to calculate estimates for the slope and intercept parameters (b and a) for this linear regression. (ii) Construct the ANOVA table for this regression. (iii) Calculate the coefficient of Determination, R2 and comment on how well the regression line fits the data. (iv) Find a 90% confidence interval for the mean expected number of hours of studying in a day, for an individual who spends 1.5 hours on social media.

The number of letters arriving each day at a residential address is assumed to be Poisson distributed with mean 1.8. The numbers of letters arriving on different days are independent random variables. (i) Calculate the probability that exactly two letters arrive at the address in one day. (ii) Calculate the probability that no more than 5 letters arrive at this address in a 5 day period. (iii) On a particular day, there are no letters at this address. Find the probability that exactly 6 days go by before this happens again. (iv) Use a suitable approximation to calculate the probability that during a 30 day period, more than 65 letters are received at this address, with mean rate λ = 1.8 for each day

HOW DO YOU DETERMINE IF ITS TRUE OR FALSE WHEN DEALING WITH BINOMINAL VARIABLES

a) If sample data are such that the null hypothesis is rejected at the alpha=5% level of significance based upon a 2 tailed test, is H0 also rejected at the alpha=1% level of significance ? Explain. b) If a 2 tailed hypothesis test leads to rejection of the null hypothesis at a certain level of significance, would the corresponding 1 tailed test lead to rejection of the null hypothesis ? Explain.