# 0.2 Practice tests (1-4) and final exams  (Page 16/36)

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83 . $\Sigma X\sim N\left(n{\mu }_{x},\left(\sqrt{n}\right)\left({\sigma }_{x}\right)\right)$ so $\Sigma X\sim N\left(4000,28.3\right)$

84 .The probability is 0.50, because 5,000 is the mean of the sampling distribution of sums of size 40 from this population. Sums of random variables computed from a sample of sufficient size are normally distributed, and in a normal distribution, half the values lie below the mean.

85 . Using the empirical rule, you would expect 95 percent of the values to be within two standard deviations of the mean. Using the formula for the standard deviation is for a sample sum: $\left(\sqrt{n}\right)\left({\sigma }_{x}\right)=\left(\sqrt{40}\right)\left(7\right)=44.3$ so you would expect 95 percent of the values to be between 5,000 + (2)(44.3) and 5,000 – (2)(44.3), or between 4,911.4 and 588.6.

86 . $\mu -\left(\sqrt{n}\right)\left({\sigma }_{x}\right)=5000-\left(\sqrt{40}\right)\left(7\right)=4955.7$

87 . $5000+\left(2.2\right)\left(\sqrt{40}\right)\left(7\right)=5097.4$

## 7.3: using the central limit theorem

88 . The law of large numbers says that as sample size increases, the sample mean tends to get nearer and nearer to the population mean.

89 . You would expect the mean from a sample of size 100 to be nearer to the population mean, because the law of large numbers says that as sample size increases, the sample mean tends to approach the population mea.

90 . X ~ N (0.10, 0.20)

91 . $\overline{X}\sim N\left({\mu }_{x},\frac{{\sigma }_{x}}{\sqrt{n}}\right)$ and the standard deviation of a uniform distribution is $\frac{b-a}{\sqrt{12}}$ . In this example, the standard deviation of the distribution is $\frac{b-a}{\sqrt{12}}=\frac{0.10}{\sqrt{12}}=0.03$
so $\overline{X}\sim N\left(0.15,0.003\right)$

92 .

## 8.1: confidence interval, single population mean, population standard deviation known, normal

Use the following information to answer the next seven exercises. You draw a sample of size 30 from a normally distributed population with a standard deviation of four.

1 . What is the standard error of the sample mean in this scenario, rounded to two decimal places?

2 . What is the distribution of the sample mean?

3 . If you want to construct a two-sided 95% confidence interval, how much probability will be in each tail of the distribution?

4 . What is the appropriate z -score and error bound or margin of error ( EBM ) for a 95% confidence interval for this data?

5 . Rounding to two decimal places, what is the 95% confidence interval if the sample mean is 41?

6 . What is the 90% confidence interval if the sample mean is 41? Round to two decimal places

7 . Suppose the sample size in this study had been 50, rather than 30. What would the 95% confidence interval be if the sample mean is 41? Round your answer to two decimal places.

8 . For any given data set and sampling situation, which would you expect to be wider: a 95% confidence interval or a 99% confidence interval?

## 8.2: confidence interval, single population mean, standard deviation unknown, student’s t

9 . Comparing graphs of the standard normal distribution ( z -distribution) and a t -distribution with 15 degrees of freedom ( df ), how do they differ?

10 . Comparing graphs of the standard normal distribution ( z -distribution) and a t -distribution with 15 degrees of freedom ( df ), how are they similar?

Use the following information to answer the next five exercises. Body temperature is known to be distributed normally among healthy adults. Because you do not know the population standard deviation, you use the t-distribution to study body temperature. You collect data from a random sample of 20 healthy adults and find that your sample temperatures have a mean of 98.4 and a sample standard deviation of 0.3 (both in degrees Fahrenheit).

Uttam
How can I calculate the Class Mark, Relative frequency and the cumulative frequency on a frequency table?
what is the important in business planning and economics
explain the limitation and scope of statistics
mahelt
statistics is limited to use where data can be measured quantitatively. statistics scope is wider such as in economic planning, medical science etc.
Gurpreet
can you send me mcq type questions
Yas
Umar
which books are best to learn applied statistics for data science/ML
Gurpreet
A population consists of five numbers 2,3,6,8,11.consists all possible samples of size two which can be drawn with replacement from this population. calculate the S.E of sample means
A particular train reaches the destination in time in 75 per cent of the times.A person travels 5 times in that train.Find probability that he will reach the destination in time, for all the 5 times.
0.237
Amresh
umesh
p(x=5)= 5C0 p^5 q^0 solve this
Amresh
umesh
ok
umesh
5C0=1 p^5= (3/4)^5 q^0=(1/4)^0
Amresh
Hint(0.75 in time and 0.25 not in time)
kamugi
what is standard deviation?
It is the measure of the variation of certain values from the Mean (Center) of a frequency distribution of sample values for a particular Variable.
Dominic
what is the number of x
10
Elicia
Javed Arif
Jawed
how will you know if a group of data set is a sample or population
population is the whole set and the sample is the subset of population.
umair
if the data set is drawn out of a larger set it is a sample and if it is itself the whole complete set it can be treated as population.
Bhavika
hello everyone if I have the data set which contains measurements of each part during 10 years, may I say that it's the population or it's still a sample because it doesn't contain my measurements in the future? thanks
Alexander
Pls I hv a problem on t test is there anyone who can help?
Peggy
Dominic
Bhavika is right
Dominic
what is the problem peggy?
Bhavika
hi
Sandeep
Hello
hi
Bhavika
hii Bhavika
Dar
Hi eny population has a special definition. if that data set had all of characteristics of definition, that is population. otherwise that is a sample
Hoshyar
three coins are tossed. find the probability of no head
three coins are tossed consecutively or what ?
umair
umair
or .125 is the probability of getting no head when 3 coins are tossed
umair
🤣🤣🤣
Simone
what is two tailed test
if the diameter will be greater than 3 cm then the bullet will not fit in the barrel of the gun so you are bothered for both the sides.
umair
in this test you are worried on both the ends
umair
lets say you are designing a bullet for thw gun od diameter equals 3cm.if the diameter of the bullet is less than 3 cm then you wont be able to shoot it
umair
In order to apply weddles rule for numerical integration what is minimum number of ordinates
excuse me?
Gabriel
why?
didn't understand the question though.
Gabriel
which question? ?
We have rules of numerical integration like Trapezoidal rule, Simpson's 1/3 and 3/8 rules, Boole's rule and Weddle rule for n =1,2,3,4 and 6 but for n=5?
John
Someone should help me please, how can I calculate the Class Mark, Relative frequency and the cumulative frequency on a frequency table?
IJOGI
geometric mean of two numbers 4 and 16 is:
10
umair
really
iphone
quartile deviation of 8 8 8 is:
iphone
sorry 8 is the geometric mean of 4,16
umair
quartile deviation of 8 8 8 is
iphone
can you please expalin the whole question ?
umair
mcq
iphone
h
iphone
can you please post the picture of that ?
umair
how
iphone
hello
John
10 now
John
how to find out the value
can you be more specific ?
umair
yes
KrishnaReddy
what is the difference between inferential and descriptive statistics
descriptive statistics gives you the result on the the data like you can calculate various things like variance,mean,median etc. however, inferential stats is involved in prediction of future trends using the previous stored data.
umair
if you need more help i am up for the help.
umair
Thanks a lot
Anjali
Inferential Statistics involves drawing conclusions on a population based on analysis of a sample. Descriptive statistics summarises or describes your current data as numerical calculations or graphs.
fred
my pleasure😊. Helping others offers me satisfaction 😊
umair
inferential statistics the results of the statistical analysis of the sample data of the population are used for generalization or decision making about the population why descriptive statistics, the analyzed data are presented without generalization or decision making about the population.
IJOGI