<< Chapter < Page
  Introductory statistics     Page 22 / 36
Chapter >> Page >

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

how is useful
how is stem and leaf plot or display differ from double stem and leaf plot or display
Sebili Reply
What is the variances of 568
Helen Reply
what u asking...
friend
what variance would have a single value..?
friend
variance happened only in a group of values..
friend
if we have a group of values...1st we find its average..ie..'mean'..then we calculate each value's difeerence from the mean..then we will square each 'difference value'.then we devide total of sqared value by n or n-1..that is what variance...
friend
compare the relative adrantages and disadvantages of mean mediam and made
News
What is the variances of 258
Helen Reply
66,564
Mampy
what is the sample size if the degree of freedom is 25?
Arthur Reply
26..
friend
25
Tariku
27
Tariku
degrees of freedom may differ with respect to distribution...so tell which distribution you have selected...?
friend
my distribution is 27
Tariku
what is degree of freedom?
Rohit
how to understand statistics
Edwin Reply
you are working for a bank.The bank manager wants to know the mean waiting time for all customers who visit this bank. she has asked you to estimate this mean by taking a sample . Briefly explain how you will conduct this study. assume the data set on waiting times for 10 customers who visit a bank. Then estimate the population mean. choose your own confidence level.
Halpha Reply
what marriage for 10 years
Ambaye Reply
fit a least square model of y on x ? what is the regression coefficient ? x : 2 3 6 8 9 10 y : 5 6 7 10 8 11
Nayab Reply
how can we find the expectation of any function of X?
Jennifer
I've been using this app for some time now. I'm taking a stats class in college in spring and I still have no idea what's going on. I'm also 55 yrs old. Is there another app for people like me?
Tamala
Serious
Hamza
yes I am. it's been decades since I've been in school.
Tamala
who are u
zaheer
is there a private chat we can do
Tamala
hello how can I get PDF of solutions introduction mathematical statistics ( fourth education) who can help me
ahssal
can anyone help me
Halim
what is probability
zaheer Reply
simply probability means possibility.. definition:Probability is a measure of the likelihood of an event to occur.
laraib
fit a least square model of y on x ? what is the regression coefficient ? x : 2 3 6 8 9 10 y : 5 6 7 10 8 11
Nayab
classification of data by attributes is called
Yamin Reply
qualitative classification
talal
tell me details about measure of Dispersion
Halim
Following data provided Class Frequency less than 10 10-20 5 15 10-30 25 12 40 and above Which measure of central tendency would you compute and why?
Nija Reply
a box contains a few red and a few blue balls.one ball is drawn randomly find the probability of getting a red ball if we know that there are 30 red and 40 blue balls in the box
harish Reply
3/7
RICH
Total=30+40=70 P(red balls) =30/70 Therefore the answer is 3/7
Anuforo
define transport statistical unit
Dennis Reply
describe each transport statistical unit
Dennis
explain uses of each transport statistical unit
Dennis
identify various transport statistical units with their example
Dennis
I didn't understand about Chi- square.
Esayas Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play




Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Introductory statistics' conversation and receive update notifications?

Ask