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33 . The screening test has a 20 percent probability of a Type II error, meaning that 20 percent of the time, it will fail to detect TB when it is in fact present.

34 . Eighty percent of the time, the screening test will detect TB when it is actually present.

9.3: distribution needed for hypothesis testing

35 . The Student’s t -test.

36 . The normal distribution or z -test.

37 . The normal distribution with μ = p and σ = p q n

38 . t 24 . You use the t -distribution because you don’t know the population standard deviation, and the degrees of freedom are 24 because df = n – 1.

39 . X ¯ ~ N ( 0.95 , 0.051 100 )
Because you know the population standard deviation, and have a large sample, you can use the normal distribution.

9.4: rare events, the sample, decision, and conclusion

40 . Fail to reject the null hypothesis, because α p

41 . Reject the null hypothesis, because α p .

42 . H 0 : μ ≥ 29.0”
H a : μ <29.0”

43 . t 19 . Because you do not know the population standard deviation, use the t -distribution. The degrees of freedom are 19, because df = n – 1.

44 . The test statistic is –4.4721 and the p -value is 0.00013 using the calculator function TTEST.

45 . With α = 0.05, reject the null hypothesis.

46 . With α = 0.05, the p -value is almost zero using the calculator function TTEST so reject the null hypothesis.

9.5: additional information and full hypothesis test examples

47 . The level of significance is five percent.

48 . two-tailed

49 . one-tailed

50 . H 0 : p = 0.8
H a : p ≠ 0.8

51 . You will use the normal test for a single population proportion because np and nq are both greater than five.

10.1: comparing two independent population means with unknown population standard deviations

52 . They are matched (paired), because you interviewed married couples.

53 . They are independent, because participants were assigned at random to the groups.

54 . They are matched (paired), because you collected data twice from each individual.

55 . d = x ¯ 1 x ¯ 2 s p o o l e d = 4.8 4.2 1.6 = 0.375
This is a small effect size, because 0.375 falls between Cohen’s small (0.2) and medium (0.5) effect sizes.

56 . d = x ¯ 1 x ¯ 2 s p o o l e d = 5.2 4.2 1.6 = 0.625
The effect size is 0.625. By Cohen’s standard, this is a medium effect size, because it falls between the medium (0.5) and large (0.8) effect sizes.

57 . p -value<0.01.

58 . You will only reject the null hypothesis if you get a value significantly below the hypothesized mean of 110.

10.2: comparing two independent population means with known population standard deviations

59 . X ¯ 1 X ¯ 2 , i.e., the mean difference in amount spent on textbooks for the two groups.

60 . H 0 : X ¯ 1 X ¯ 2 ≤ 0
H a : X ¯ 1 X ¯ 2 >0
This could also be written as:
H 0 : X ¯ 1 X ¯ 2
H a : X ¯ 1 > X ¯ 2

61 . Using the calculator function 2-SampTtest, reject the null hypothesis. At the 5% significance level, there is sufficient evidence to conclude that the science students spend more on textbooks than the humanities students.

62 . Using the calculator function 2-SampTtest, reject the null hypothesis. At the 1% significance level, there is sufficient evidence to conclude that the science students spend more on textbooks than the humanities students.

10.3: comparing two independent population proportions

63 . H 0 : p A = p B
H a : p A p B

Questions & Answers

what is standard deviation?
Jawed Reply
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
Yeah....the simplest one
IRFAN
what is the number of x
Godgift Reply
10
Elicia
Javed Arif
Jawed
how will you know if a group of data set is a sample or population
Kingsley Reply
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
What's your problem Peggy Abang
Dominic
Bhavika is right
Dominic
what is the problem peggy?
Bhavika
hi
Sandeep
Hello
adeagbo
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
Kanwal Reply
three coins are tossed consecutively or what ?
umair
p(getting no head)=1/8
umair
or .125 is the probability of getting no head when 3 coins are tossed
umair
🤣🤣🤣
Simone
what is two tailed test
Umar Reply
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
Anjali Reply
excuse me?
Gabriel
why?
Tade
didn't understand the question though.
Gabriel
which question? ?
Tade
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
geometric mean of two numbers 4 and 16 is:
iphone Reply
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
srijth Reply
can you be more specific ?
umair
yes
KrishnaReddy
what is the difference between inferential and descriptive statistics
Eze Reply
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
for poisson distribution mean............variance.
mehul Reply
both are equal to mu
Faizan
mean=variance
Faizan
what is a variable
Bonolo Reply
something that changes
Festus
why we only calculate 4 moment of mean? asked in papers.
Faizan Reply
why we only 4 moment of mean ? asked in BA exam
Faizan
Good evening, can you please help me by sharing regression and correlation analysis notes....thank you in advance
Refiloe Reply
Hello, can you please share the possible questions that are likely to be examined under the topic: regression and correlation analysis.
Refiloe
for normal distribution mean is 2 & variance is 4 find mu 4?
Faizan Reply
repeat quastion again
Yusuf
find mu 4. it can be wrong but want to prove how.
Faizan
for a normal distribution if mu 4 is 12 then find mu 3?
Faizan Reply
Question hi wrong ha
Tahir
ye BA mcqs me aya he teen he. 2dafa aya he
Faizan
if X is normally distributed. (n,b). then its mean deviation is?
Faizan
The answer is zero, because all odd ordered central moments of a normal distribution are Zero.
nikita
which question is zero
Faizan
sorry it is (5,16) in place of (n,b)
Faizan
I got. thanks. it is zero.
Faizan
a random variable having binomial distribution is?
Bokaho

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Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
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