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 Lactobacillusdominated 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 chisquare test is this?). (5 pts).
In: Statistics and Probability
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 tscore = 2.87. If the pvalue 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 twotailed 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".
In: Statistics and Probability
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 pvalue 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 pvalue 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
In: Statistics and Probability
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
In: Statistics and Probability
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.
In: Statistics and Probability
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? 
In: Statistics and Probability
Do a twosample test for equality of means assuming unequal
variances. Calculate the pvalue using Excel.
(a1) Comparison of GPA for randomly chosen
college juniors and seniors:
x¯1x¯1 = 4, s_{1} = .20, n_{1} =
15, x¯2x¯2 = 4.25, s_{2} = .30,
n_{2} = 15, α = .025, lefttailed
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.  
tcalculated  
pvalue  
tcritical  
(b1) Comparison of average commute miles for
randomly chosen students at two community colleges:
x¯1x¯1 = 17, s_{1} = 5, n_{1} =
22, x¯2x¯2 = 21, s_{2} = 7, n_{2}
= 19, α = .05, twotailed 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.  
tcalculated  
pvalue  
tcritical  +/ 
(c1) Comparison of credits at time of graduation
for randomly chosen accounting and economics students:
x¯1x¯1 = 141, s_{1} = 2.8, n_{1}
= 12, x¯2x¯2 = 138, s_{2} = 2.7,
n_{2} = 17, α = .05, righttailed
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.  
tcalculated  
pvalue  
tcritical  
In: Statistics and Probability
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 1221 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?
In: Statistics and Probability
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>1Sample t
Is this a lefttailed, righttailed, or twotailed 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 pvalue = 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.
In: Statistics and Probability
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, x_{1} = average length of patient stay, x_{2} = average patient age, x_{3} = measure of how many xrays 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 
FValue 
PValue 
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 
Rsq 
Rsq(adj) 
Rsq(pred) 
1.08484 
36.30% 
34.55% 
30.64% 
Coefficients
Term 
Coef 
SE Coef 
TValue 
PValue 
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 
In: Statistics and Probability
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 fstatistic of the model
In: Statistics and Probability
1For random variable X~N(3,0.75^{2}), what is P(X < 2.5)? Find the nearest answer.
2For 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?
3For standard normal random variable Z, what is P(Z<0)? Answer to two decimal places.
In: Statistics and Probability
A package delivery service wants to compare the proportion of ontime 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 ?̂ ?????−?̂ ?????
In: Statistics and Probability
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
In: Statistics and Probability