A study might compare the rates of microbiologic cure of three different antibiotics used for urinary tract infection, as shown in the following table:

1. Are the variables quantitative or qualitative?
2. Which statistical test is appropriate to use on these data?
3. What are the null & the alternative hypotheses, here? Use 10% level of significance
4. Carry out the hypothesis test(s) in question in above c.

Is there is a relationship between which antibiotic the patient took and achieving microbiologic cure?                

For the problems 1 -6

Consider the data set   

16, 26, 31, 32, 32, 32, 42, 47, 47, 47, 50, 50 (already put in increasing order)

Compute the following:

1/   The mode:

A/ 47       B/ 32           C/ Bimodal       D/ 42  

2/   The median:

A/ 42       B/ 37           C/ 32           D/ 47  

3/   The mean:

       A/ 37.7       B/ 37           C/ 36           D/ 36.2

4/   The standard deviation:

       A/ 10.5       B/ 12          C/ 14           D/ 11  

5/   The mid-range:

A./ 17       B/ 20.5         C/ 33           D/ 34      
6/   If x = 42 , the standard deviation s = 12 and the mean = 67, then the z-score ( the standard score) of x is

A./ 2.28       B/ - 1.00       C/ 3.52       D/ -2.08
  
7/   In the set of data : 2, 3, 35, 5, 8, 9,10, 10,12,14,16, is the value 35 outlier?

A/ No, upper limit for outlier is 27.5       B/ Yes, upper limit for outlier is 27.5
C/ No, upper limit for outlier is 24.5       D/ Yes, upper limit for outlier is 32.1
  

For the problems 8 -13: Consider the set of 15 data ( in increasing order )

   10, 15, 19, 20, 21, 21, 29, 29, 30, 30, 33, 39, 40, 50, 50.

( It is better to enter this data set into a calculator to find the needed values to answering the following questions )

8/   Find ( the value x which separates the bottom 30th percentile )      

A./ 70       B/ 21           C/ 29.5         D/ 53      

9/   Find the percentile ( kth percentile ) of the value x = 30.

A/ 53 percentile   B/ 82 percentile C/ 38 percentile   D/ 60 percentile  

10/   The third quartile () is:

   A./ 39       B/ 17           C/ 40         D/ 18      

11/   The inter-quartile range ( IQR) is:          

A./ 17       B/ 21           C/ 19         D/ 59  

12/   The sample variance is approximate to ( round to whole number )

A./ 11       B/ 148       C/ 12         D/ 142
      

13/   Approximate the value of x if its z-score is 0.83 ( Use the formula )

  
A./ 35       B/ 39           C/ 19         D/ 25      
14/   For the data set 8, 6, 29, 3, 9, 23, 15, 18, 5, 3, 22, 27, 4, 2 and 22 the midrange is

  
A./ 16       B/ 11           C/ 15         D/ 18      

15/   By the Empirical Rule, in a city of 62,000 people, the number of people below the mean by more than 1 standard deviation is:

A./ 41,160      B/ 9, 920       C/ 21,080        D/ 6,200      
Questions 16-18 : Use the distribution in the form of the stem-leaf plot

         
Stem   Leaves   

1478   
01237888  
189   

16/   The mid-point of the third class is

   A./ 32       B/ 36           C/ 34.5         D/ 35      

17/   The median is

   A./ 24       B/ 23           C/ 25           D/ 5
      
18/   The relative frequency for the third class is:

A./ 20%       B/ 50%        C/ 66%         D/ 40%

19/   The heights of a group of professional basketball players are summarized in the frequency distribution below. Find the mean height from this frequency table.

           Height s ( in)   Frequency
  
4
6
8
79-81       2

A./ 75.2 in       B/ 76.8 in       C/ 74.0 in       D/ 77.5 in

20/   The temperatures ( in ºF ) in a room is recorded at the top of hours are

   67, 68, 70 , 5, 77, 77, 78, 80, 78, 79, 74, 74. Choose best answer:
  
   a/ It is a typo
   b/ highest temperature is probably 95
   c/ 5 is not an outlier
   d/ 5 is an outlier

21/   The variance of 6 washing machines with prices: $ 800, $784, $ 1,235, $860, $1,036 and $770 is

A/ 196.4       B/ 34,295.3       C/ 26,002.7       D/ 185.2

22/   The coefficient of variation ( round to closest %) for the set of data :

1, 3, 3, 5, 5, 6, 7, 8, 9 ,12, 15, 24 is

A 74%       B/ 67%       C/ 24%       D/ 78 %

23/   Human body temperatures have the mean of 98.2º and a standard deviation of 0.6º.
   Amy’s temperature can be described by z = 0.9. What is her temperature?

   A/   98.2º       B/ 97.8º       C/ 98.7º       D/ 99.3º

24/   The upper bound for the outlier for the data set
-11, 14, 22, 22, 22, 23, 31, 31, 42, 44, 44, 75 is

A/ 74.5           B/ 75           C/ 84       D/ 68
                                  
25/   The box-plot of a data with 5- point summary 2, 6, 8, 11, 18
  

   A/is positive skewed.       B/ is negative skewed.
   C/ is symmetric       D/ perfect skewed

Let X ~ N(196; 19). Find:

(a) P(X </= 223)

(b) P(143 < X < 206)

(c)  P(|X-196|> 30)

Background

The 2016 US Presidential Election brought considerable attention to the phenomenon of “fake news”: entirely fabricated and often partisan content that is presented as factual. Researchers evaluated one mechanism that may contribute to the believability of fake news: fluency via prior exposure. Using an actual fake news headline presented as it was seen on Facebook (Kid Rock launches campaign to run for U.S. Senate in 2018), the researchers hypothesized that previous exposure to the fake news story would increase perceptions of accuracy. Subjects were pre-screened to determine in which of 3 groups they belonged: 1) no previous exposure to the fake news story, 2) previous exposure to the fake news story and had not heard that the story was, in fact, fake, or 3) previous exposure to the fake news story but had heard that the story was, in fact, fake. They recorded perception of the accuracy of the news story (ranging from 1 (definitely false) to 6 (definitely true)).

Please complete all empty boxes in the tables below.

Data

One-way ANOVA (please show your work!)

Post-hoc results using the Tukey test

Full interpretation of the results

A parabolic satellite dish reflects signals to the dish’s focal point. An antenna designer analyzed signals transmitted to a satellite dish and obtained the probability density function

f(x)=cæ1- 1 x2öfor 0<x<2,whereXisthedistance(inmeters)fromthecentroidofthe ç 16 ÷

èø

dish surface to a reflection point at which a signal arrives. Determine the following:

1. Value of c that makes f (x) a valid probability density function

2. ?(? < 0.4

3. ?(0.1<?<0.4

4. ?(?)

5. ?(?)

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

A random sample of 5260 permanent dwellings on an entire reservation showed that 1585 were traditional hogans.

(a) Let p be the proportion of all permanent dwellings on the entire reservation that are traditional hogans. Find a point estimate for p. (Round your answer to four decimal places.)


(b) Find a 99% confidence interval for p. (Round your answer to three decimal places.)

Give a brief interpretation of the confidence interval.

1% of the confidence intervals created using this method would include the true proportion of traditional hogans.99% of the confidence intervals created using this method would include the true proportion of traditional hogans.    99% of all confidence intervals would include the true proportion of traditional hogans.1% of all confidence intervals would include the true proportion of traditional hogans.

(c) Do you think that np > 5 and nq > 5 are satisfied for this problem? Explain why this would be an important consideration.

No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial.No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal.    Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.

The two data sets in the table below are dependent random samples. The population of (x−y)(x-y) differences is approximately normally distributed. A claim is made that the mean difference (x−y)(x-y) is greater than 17.9.

For each part below, enter only a numeric value in the answer box. For example, do not type "z =" or "t =" before your answers. Round each of your answers to 3 places after the decimal point.

(a) Calculate the value of the test statistic used in this test.

     Test statistic's value =

(b) Use your calculator to find the P-value of this test.

     P-value =

(c) Use your calculator to find the critical value(s) used to test this claim at the 0.04 significance level. If there are two critical values, then list them both with a comma between them.

     Critical value(s) =

(d) What is the correct conclusion of this hypothesis test at the 0.04 significance level?     

• There is sufficient evidence to warrant rejection the claim that the mean difference is greater than 17.9
• There is not sufficient evidence to support the claim that the mean difference is greater than 17.9
• There is not sufficient evidence to warrant rejection the claim that the mean difference is greater than 17.9
• There is sufficient evidence to support the claim that the mean difference is greater than 17.9

A survey is conducted using 2000 registered voters who are asked to choose between candidate A and candidate B. Let p denote the fraction of voters in the population who prefer candidate A and let ˆp denote the fraction of voters who prefer Candidate B.

i You are interested in performing the following hypothesis test H0 : p = 0.4 (1) H1 : p 6= 0.4

(2) Determine the size of the test and compute the power of the test if the true value is p = 0.45

ii Assuming that in the survey ˆp = 0.44. Test H0 : p = 0 − 4 vs H1 : p 6= 0.4 using a 10% significance level

iii Assuming that in the survey ˆp = 0.44. Test H0 : p = 0 − 4 vs H1 : p < 0.4 using a 10% significance level

iv Construct a 90% confidence interval for p

iv Construct a 95% confidence interval for p iv Construct a 99% confidence interval for p

In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. Consider the data set 11, 9, 4, 6, 6. (a) Use the defining formula, the computation formula, or a calculator to compute s. (Round your answer to one decimal place.) s = (b) Multiply each data value by 7 to obtain the new data set 77, 63, 28, 42, 42. Compute s. (Round your answer to one decimal place.) s =

For this discussion, comment on any programming errors you encountered.

Did the same issues keep recurring?

A corporation only recruits applications who attended one of three schools: College A, B and C. The director HR knows that 10% of the job applicants attended A, 30% attended B and the rest attended C. However 60% of all applicants from A, are offered positions in the Corporation, whereas only 35% of applicants from B and 25% of applicants from C are given offers.

i) What percentage of offer letters go to applicants from College A?

ii) What percentage of offer letters go to applicants from College B?

iii) What percentage of offer letters go to applicants from College C?

The following data are the ages (in years) at diagnosis for 20 patients under treatment for meningitis: 18 18 25 19 23 20 69 18 21 18

20 18 18 20 18 19 28 17 18 18

(a) . Calculate and interpret the values of the sample mean, variance, and standard deviation.

(b) . Compute the sample median. Why might you recommend it as a measure of centre rather than the sample mean? 2

(c) . Compute the upper fourth, the lower fourth, and the fourth spread. (d) . Illustrate the center, spread, and symmetry or skewness of this data using a horizontal modified boxplot.

Anyone who has studied statistics or research has heard the saying "Correlation does not imply causation." What factors must an analyst consider to decide whether the correlation is meaningful enough to investigate further?

annual income for Americans in 2012. Use the data set to answer the following questions: Hint: Use Excel

Data set

income (in dollars)

1. Formulate the null and alternative hypotheses that can be used to test the assumption that the average American annual income is $42,500.

Ho = 42500

Ha ≠ 42500

2. Compute the value of the test statistic.
3. What is the p-value?
4. At α = .05, what is the critical value?
5. At α = .05, what is your conclusion? Briefly justify your answer.
6. Compute a 95% confidence interval for the population mean. Does it support your conclusion?