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8 . The 99% confidence interval, because it includes all but one percent of the distribution. The 95% confidence interval will be narrower, because it excludes five percent of the distribution.

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

9 . The t -distribution will have more probability in its tails (“thicker tails”) and less probability near the mean of the distribution (“shorter in the center”).

10 . Both distributions are symmetrical and centered at zero.

11 . df = n – 1 = 20 – 1 = 19

12 . You can get the t -value from a probability table or a calculator. In this case, for a t -distribution with 19 degrees of freedom, and a 95% two-sided confidence interval, the value is 2.093, i.e.,
t α 2   = 2.093 . The calculator function is invT(0.975, 19).

13 . E B M =   t α 2 ( s n ) = ( 2.093 ) ( 0.3 20 ) =   0.140
98.4 ± 0.14 = (98.26, 98.54).
The calculator function Tinterval answer is (98.26, 98.54).

14 . t α 2 = 2.861. The calculator function is invT(0.995, 19).
E B M = t α 2 ( s n ) = ( 2.861 ) ( 0.3 20 ) = 0.192
98.4 ± 0.19 = (98.21, 98.59). The calculator function Tinterval answer is (98.21, 98.59).

15 . df = n – 1 = 30 – 1 = 29. t α 2   = 2.045
E B M =   z t ( s n ) = ( 2.045 ) ( 0.3 30 ) =   0.112
98.4 ± 0.11 = (98.29, 98.51). The calculator function Tinterval answer is (98.29, 98.51).

8.3: confidence interval for a population proportion

16 . p = 280 500 = 0.56
q = 1 p = 1 0.56 = 0.44
s = p q n = 0.56 ( 0.44 ) 500 = 0.0222

17 . Because you are using the normal approximation to the binomial, z α 2 = 1.96 .
Calculate the error bound for the population ( EBP ):
E B P =   z a 2 p q n = 1.96 ( 0.222 ) = 0.0435
Calculate the 95% confidence interval:
0.56 ± 0.0435 = (0.5165, 0.6035).
The calculator function 1-PropZint answer is (0.5165, 0.6035).

18 . z α 2 = 1.64
E B P =   z a 2 p q n = 1.64 ( 0.0222 ) = 0.0364
0.56 ± 0.03 = (0.5236, 0.5964). The calculator function 1-PropZint answer is (0.5235, 0.5965)

19 . z α 2 = 2.58
E B P =   z a 2 p q n = 2.58 ( 0.0222 ) =   0.0573
0.56 ± 0.05 = (0.5127, 0.6173).
The calculator function 1-PropZint answer is (0.5028, 0.6172).

20 . EBP = 0.04 (because 4% = 0.04)
z α 2 = 1.96 for a 95% confidence interval
n =   z 2 p q E B P 2 =   1.96 2 ( 0.5 ) ( 0.5 ) 0.04 2 =   0.9604 0.0016 = 600.25
You need 601 subjects (rounding upward from 600.25).

21 . n =   n 2 p q E B P 2 =   1.96 2 ( 0.6 ) ( 0.4 ) 0.04 2 =   0.9220 0.0016 = 576.24
You need 577 subjects (rounding upward from 576.24).

22 . n =   n 2 p q E B P 2 =   1.96 2 ( 0.5 ) ( 0.5 ) 0.03 2 =   0.9604 0.0009 = 1067.11
You need 1,068 subjects (rounding upward from 1,067.11).

9.1: null and alternate hypotheses

23 . H 0 : p = 0.58
H a : p ≠ 0.58

24 . H 0 : p ≥ 0.58
H a : p <0.58

25 . H 0 : μ ≥ $268,000
H a : μ <$268,000

26 . H a : μ ≠ 107

27 . H a : p ≥ 0.25

9.2: outcomes and the type i and type ii errors

28 . a Type I error

29 . a Type II error

30 . Power = 1 – β = 1 – P (Type II error).

31 . The null hypothesis is that the patient does not have cancer. A Type I error would be detecting cancer when it is not present. A Type II error would be not detecting cancer when it is present. A Type II error is more serious, because failure to detect cancer could keep a patient from receiving appropriate treatment.

32 . The screening test has a ten percent probability of a Type I error, meaning that ten percent of the time, it will detect TB when it is not present.

Questions & Answers

Frequency find questions
Rimsha Reply
What is nominal variable
olusola Reply
Write short notes on, nominal variable, ordinal variable, internal variable, ratio variable.
olusola
P( /x-50/ less than or equal to 5 ) where mean =52 and Variance =25
Jay Reply
how I get the mcq
Mukesh Reply
please what is data mining
Josephine Reply
the exploration and analysis of large data to discover meaningful patterns and rules
Hussein
how do we calculate the median
All Reply
f(x)=cx(1-x)^4 as x range 4rm 0<=x<=1. Can someone pls help me find d constant C. By integration only..
Akeem Reply
uses of statistics in Local Government
Saleema Reply
Hi
Tamuno
hello
Saleema
state road transport corporation
Atul
District statistical officer
Atul
statistical services
Atul
Please is this part of the IMT program
Tamuno
testing of drugs
Shambhavi
hii 2
Qamar-ul-
How about population census
Tamuno
Hello every one
Okoi
sample survey is done by local government in each and every field.
syeda
statistics is used in almost every government organisations such as health department, economic department, census, weather forecasting fields
raghavendra
that's true
syeda
statistics is one of the tool that represents the falling and rising of any cases in one sheet either that is in population census whether forecast as well as economic growth
Aadil
statistic is a technique, and statistics is a subject
syeda
what is business statistics
PM Reply
Probability tells you the likelihood of an event happening. ... The higher the probability, the more likely it is to happen. Probability is a number or fraction between 0 and 1. A probability of 1 means something will always happen, and a probability of 0 means something will never happen...
La Reply
Saying it's a number between zero and one means it is a fraction so you could remove "or fraction" from you definition.
Carlos
wouldn't be correct to remove fractions, saying a number is justified as probabilities can also be decimals between 0 and 1.
Denzel
Saying "a number" will include it being a decimal which are themselves fractions in another form.
Carlos
I will simply say a probability is a number in the range zero to one, inclusive.
Carlos
f#$
Carlos
How to delete an entry? This last one was a pocket print.
Carlos
what is probability
sky-D Reply
chance of occurrence
Sikander
what is data
Muhd Reply
raw facts and figures
Sikander
information of any kind
Tahir
What is Statistic
ibrahim Reply
what statistical analysis can i run on growth and yield of spinach.
guillio
format of the frequency distribution table
henry
what is pearson correlation coefficient indicates?
Eticha
Statistic is the mean of the sample.
Raman
can anyone determine the value of c and the covariance and correlation for the joint probability density function Fxy(x,y)=c over the range 0<x<5,0<y,and x-1<y<x-1.
Nuhu
what actually is the definition of range
Chinedu Reply
I need social statistics materials
Chinedu
the range of a set of data is the difference between the largest and smallest values
La
I need more explanation about cluster sampling
Hafsat
write the set of old number that are greater than or equal to minutes 7 butl less than 5 in both of the set notation
Jerry Reply

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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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