Question

1. What is the difference between descriptive analytics and descriptive statistics? (1pt)
2. Consider a sample with a mean of 500 and a standard deviation of 100.What are the z scores for the following data values: 520,650,500,450, and 280 (5pts)
3. What do you understand by the following terminologies:

• Normal probability distribution (0.5pt)
• Probability density function(0.5pt)
• Sampling distribution(0.5pt)
• Systematic sampling(0.5pt)

4. Medical tests were conducted to learn about drug resistant tuberculosis. Of 142 cases tested in New Jersey, 9 were found to be drug resistant.Of 268 cases tested in Texas , 5 were found to be drug resistant. Do these data suggest a statistically significant difference between the proportions of drug resistant cases in two states? Use 0.02 level of significance. What is the p-value, and what is your conclusion? (2pts)

Answer 1

With descriptive statistics you are simply describing what is or what the data shows. With inferential statistics, you are trying to reach conclusions that extend beyond the immediate data alone. For instance, we use inferential statistics to try to infer from the sample data what the population might think

...........................

µ=   500
σ=   100
X=   520
Z=(X-µ)/σ=   (520-500)/100)=       0.2
...........

x = 650

Z=(X-µ)/σ=   (650-500)/100)=       1.5

.....

x=500

Z=(X-µ)/σ=   (500-500)/100)=       0
......

x = 450

Z=(X-µ)/σ=   (450-500)/100)=       -0.5  
.........

x = 280

Z=(X-µ)/σ=   (280-500)/100)=       -2.2
.....................

normal probaility distribution :

is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is

A normal distribution is sometimes informally called a bell curve

....................

In probability theory, a probability density function (PDF),of a continuous random variable, is a function whose value at any given point in the sample space can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample

...................

In statistics, a sampling distribution or finite-sample distribution is the probability distribution of a given random-sample-based statistic.

........................

Systematic sampling is a type of probability sampling method in which sample members from a larger population are selected according to a random starting point but with a fixed, periodic interval. This interval, called the sampling interval, is calculated by dividing the population size by the desired sample size

..................

Ho:   p1 - p2 =   0          
Ha:   p1 - p2 ╪   0          
                  
sample #1   ----->   experimental          
first sample size,     n1=   142          
number of successes, sample 1 =     x1=   9          
proportion success of sample 1 , p̂1=   x1/n1=   0.0634          
                  
sample #2   ----->   standard          
second sample size,     n2 =    268          
number of successes, sample 2 =     x2 =    5          
proportion success of sample 1 , p̂ 2=   x2/n2 =    0.019          
                  
difference in sample proportions, p̂1 - p̂2 =     0.0634   -   0.0187   =   0.0447
                  
pooled proportion , p =   (x1+x2)/(n1+n2)=   0.0341          
                  
std error ,SE =    =SQRT(p*(1-p)*(1/n1+ 1/n2)=   0.0188          
Z-statistic = (p̂1 - p̂2)/SE = (   0.045   /   0.0188   ) =   2.3726
                        
p-value =        0.0177   [excel formula =2*NORMSDIST(z)]      
decision :    p-value<α,Reject null hypothesis               
there is significant difference

.................

i have done all

THANKS

revert back for doubt

please upvote