Background: Despite their antimicrobial potential, vaginal lactobacilli often fail to retain dominance, resulting in overgrowth of the vgna by other bacteria, as observed with bacterial vaginosis. It remains elusive however to what extent interindividual differences in vaginal Lactobacillus community composition determine the stability of this microflora. In a prospective cohort of pregnant women we studied the stability of the normal vaginal microflora (VMF) (assessed on Gram stain) as a function of the presence of the vaginal Lactobacillus index species (determined through culture and molecular analysis with tRFLP).

Results: From 100 consecutive Caucasian women vaginal swabs were obtained at mean gestational ages of 8.6 (SD 1.4), 21.2 (SD 1.3), and 32.4 (SD 1.7) weeks, respectively. Based on Gram stain, 77 women had normal or Lactobacillus-dominated vaginal microflora (VMF) during the first trimester of which 56 remained normail in the third trimester. Th3 remaining 23 women tested abnormal in the first trimester and 13 of them converted in the second or third trimester.

Test the null hypothesis that having an abnormal result in the first trimester is related to having an abnormal result in the third trimester (Hint: What type of chi-square test is this?). (5 pts).

1,

Which one of the following statement explains the definition of Type I error:

Pick one

		Reject the null hypothesis when the null hypothesis is true
		Reject the null hypothesis when the null hypothesis is false
		Fail to reject the null hypothesis when the null hypothesis is true
		Fail to reject the null hypothesis when the null hypothesis is false
		none of the above

2,

You test a hypothesis and you get a t-score = 2.87. If the p-value is 0.054 and the significance level alpha=0.05, you will be able to reject the null hypothesis. Pick one

True

False

3,

If the null hypothesis is µ = 0, which one of the following statements is a two-tailed alternative hypothesis? Pick One

		H1: µ < 0
		H1: µ ≠ 0
		H1: µ > 0
		H1: µ = 0
		none of the above

4,

Suppose we divide the states into two groups. Let population H be states with high levels of state funding and population L be states with low levels of state funding.

If we want to examine whether state funding changes education performance, how would you state the null hypothesis and alternative hypothesis?

Note: you may use != to stand for "not equal to".

find p (-1.20< z< 2.03)

1. in a study conducted recently 675 out of 1070 people surveyed expressesed preference for choclate ice cream over other flavors. Let p be the proportion of the population surveyed that prefers choclate ice cream to other flavors.

a. at 5% significance level does the data presents evidence that more than 60% or people from the surveyed population prefer choclate ice cream to other flavors? show both your critical values and p-value hypothesis tests.

b. at 10% significance level does the data presents evidence that the percent of the popluation who prefers choclate ice cream differs from 60%? show both the critical values and p-value hypothesis test.

c. obtain a 90% confidence interval for p

d. based on your Confidence interval, do you think p>.60? explain why or why not

e. what sample size is needed to cut margin or error in your interval from part (c) to at most 1.5%? use 63% as a best guess for p̂

hypothetically data on weekly family consumption expenditure Y and weekly family income X. Y = 70 ,65, 90, 95, 110, 115, 120, 140, 155, 150. AND X = 80, 100, 120, 140, 160, 180, 200, 220, 240, 260. from the data given above ,you are required to obtain the estimates of the regression coefficients,their variances and standard errors, the correlation and coefficient of determination

Consider three students taking an examination. Their respective probabilities of obtaining the different available grades are shown in Table 1. (a) What is the probability that each will obtain a grade of A? (b) If two students were to receive an A, what is the probability that Jim would be among them?

Table 1. Probabilities of Individual Student Exam Grades*

Student    Grade   

                 A   B     C     D      F

Terry         0.5 0.3 0.1 0.06 0.04

Jim           0.4 0.4 0.1 0.07 0.03

Sam         0.3 0.3 0.3 0.05 0.05

* Assume each examination outcome to be independent.

5	Assume that the heights of U.S. residents are normally distributed with mean 65 inches and
	standard deviation of 5 inches.
a	What is the probability that a randomly selected resident is over 70 inches tall?
b	What is the probability that a randomly selected resident will be between 62 and 72 inches tall?
c	What is the probability that a randomly selected resident will be less than 58 inches tall?

Do a two-sample test for equality of means assuming unequal variances. Calculate the p-value using Excel.

(a-1) Comparison of GPA for randomly chosen college juniors and seniors:

x¯1x¯1 = 4, s₁ = .20, n₁ = 15, x¯2x¯2 = 4.25, s₂ = .30, n₂ = 15, α = .025, left-tailed test.
(Negative values should be indicated by a minus sign. Round down your d.f. answer to the nearest whole number and other answers to 4 decimal places. Do not use "quick" rules for degrees of freedom.)

d.f.
t-calculated
p-value
t-critical

(b-1) Comparison of average commute miles for randomly chosen students at two community colleges:

x¯1x¯1 = 17, s₁ = 5, n₁ = 22, x¯2x¯2 = 21, s₂ = 7, n₂ = 19, α = .05, two-tailed test.
(Negative values should be indicated by a minus sign. Round down your d.f. answer to the nearest whole number and other answers to 4 decimal places. Do not use "quick" rules for degrees of freedom.)
  

d.f.
t-calculated
p-value
t-critical	+/-

(c-1) Comparison of credits at time of graduation for randomly chosen accounting and economics students:
x¯1x¯1 = 141, s₁ = 2.8, n₁ = 12, x¯2x¯2 = 138, s₂ = 2.7, n₂ = 17, α = .05, right-tailed test.
(Negative values should be indicated by a minus sign. Round down your d.f. answer to the nearest whole number and other answers to 4 decimal places. Do not use "quick" rules for degrees of freedom.)

d.f.
t-calculated
p-value
t-critical

Suppose a research team is interested in the behavioral ramifications that may develop from women and young girls receiving the HPV vaccine at an early age. The research hypothesis is that women and girls that receive the vaccine are less likely to follow federal recommendations that mandate these women to undergo regular screening for cervical cancer. The research team decides to investigate this relationship by following a group of women and girls aged 12-21 for up to 10 years and observing their behaviors in relation to cervical screening. The team receives a list of women and girls in this age range from their local legislators, and divides the group into 4 different age ranges. The team then sampled 100 women and girls from each age range and followed them for the full study period. What type of study design is this? Is there a sampling methodology use and if so what kind? What are the exploratory and response variables?

Can you please answer the questions as well as checking my previous answers to see if ti correct

You love the new elliptical machines your gym added several months ago, but because they are so popular with other members too, you usually have to wait for a machine to become available. Out of curiosity, each day you write down how many minutes you have to wait for an elliptical machine. Using a confidence level of 80%, is the average wait time for an elliptical machine less than 5 minutes?

2	0	5	7	5	8	5	5
10	5	2	0	2	4	0	4
0	7	3	5	8	2	5	10
7	0	6	4	4	4	8	3

Step 1) What type of hypothesis test is required here?                                                                                                  

                               

How would you run this test in MINITAB (Menus, Functions used)?   Stat>BASIC STAT>1-Sample t                                              

Is this a left-tailed, right-tailed, or two-tailed test?   Two Tailed                                                                                   

Step 2) Verify all assumptions required for this test:                                                                                                       

                                                                                                                                                                                                                Step 3) State the null and alternate hypotheses for this test: (use correct symbols and format!)

                   Null hypothesis                 u = 5                                                                                                                     

                   Alternate hypothesis      u < 5                                                                                                                     

Step 4) Run the correct test in MINITAB and provide the information below. Use correct symbols and round answers to 3 decimal places.

               

Test Statistic                       =            1.24                        Degrees of freedom                        =            31          

               

Critical Value                     = 0.8533                                              p-value                                                 = 0.111                

               

Step 5) State your statistical decision (and justify it!)       I would have to say that T value is greater Critical Value and it is Rejected to the null hypothesis accept alternate.                                                                                                                                                                                                                                                                                          

Step 6) Interpret your decision within the context of the problem: what is your conclusion?

                I would have to say that the population mean of the wait time < 5 minutes is 80 percent Con.

Data from n = 113 hospitals in the United States are used to assess factors related to the likelihood that a hospital patients acquires an infection while hospitalized. The variables here are y = infection risk, x₁ = average length of patient stay, x₂ = average patient age, x₃ = measure of how many x-rays are given in the hospital. The Minitab output is as follows:

Regression Analysis: InfctRsk versus Stay, Age, Xray

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Regression	3	73.099	24.366	20.70	0.000
Stay	1	31.684	31.684	26.92	0.000
Age	1	1.126	1.126	0.96	0.330
Xray	1	13.719	13.719	11.66	0.001
Error	109	128.281	1.177
Total	112	201.380

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
1.08484	36.30%	34.55%	30.64%

Coefficients

Term	Coef	SE Coef	T-Value	P-Value	VIF
Constant	1.00	1.31	0.76	0.448
Stay	0.3082	0.0594	5.19	0.000	1.23
Age	-0.0230	0.0235	-0.98	0.330	1.05
Xray	0.01966	0.00576	3.41	0.001	1.18

Regression Equation

InfctRsk

=

1.00 + 0.3082 Stay - 0.0230 Age + 0.01966 Xray

1. Set up the hypothesis test to decide whether there is a connection between the infection risk and the group of predictors.
2. Then, decide, using tests, which of the predictors and constant should be in the final relationship.
3. Give the value of the coefficient of determination and tell what it means.

the table below shows the price quantity of demanded of packaged of pure water in nigeria. price in # = 0.5, 0.6, 0.7, 0.8, 0.8, 0.9. Quantity Demand = 160, 140, 120, 110, 90, 80. Let Xi represent the price change per unit and Yi represent the quantity demand at that price. The demand function may be postulated as; Yi =a+bXi + ei . FIND THE OLS ESTIMATE OF THE DEMAND FUNCTION AND var(a), var(b) and their respective standard error , Compute the value of the coefficient of determination (r^2) and f-statistic of the model

1-For random variable X~N(3,0.75²), what is P(X < 2.5)? Find the nearest answer.

2-For random variable X~N(3,0.75), what is the probability that X takes on a value within two standard deviations on either side of the mean?

3-For standard normal random variable Z, what is P(Z<0)? Answer to two decimal places.

A package delivery service wants to compare the proportion of on-time deliveries for two of its major service areas. In City A, 377 out of a random sample of 449 deliveries were on time. A random sample of 282 deliveries in City B showed that 220 were on time.

Compute a 99% confidence interval for the difference ?̂ ?????−?̂ ?????

Q1. Consider a pot containing balls. Each ball has a number painted on it with the number ranging from 1 to 9. For 1<=n<=9 there are n balls with the number n painted on it. For each number i where i lies between 1 and 9, write down the probability that a ball drawn at random from the pot has the number i painted on it.

Q2) Put 3 balls into 3 boxes randomly. Find 1) Probability that there is just one ball in each box. 2) The Probability that there is one empty box