b) The following data shows the number of hours slept by a patient in 1 weeks 12 18 09 16 11 10 08 i. Calculate the unbiased estimate for the population mean ii. Calculate the unbiased estimate for the population standard deviation iii. Calculate a 95% confidence interval for the mean number of hours

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Kindly assist with the below. I also attached a formula sheet to assist. 

 

b) The following data shows the number of hours slept by a patient in 1 weeks
12
18
09
16
11
10
08
i. Calculate the unbiased estimate for the population mean
ii. Calculate the unbiased estimate for the population standard deviation
iii.
Calculate a 95% confidence interval for the mean number of hours
Transcribed Image Text:b) The following data shows the number of hours slept by a patient in 1 weeks 12 18 09 16 11 10 08 i. Calculate the unbiased estimate for the population mean ii. Calculate the unbiased estimate for the population standard deviation iii. Calculate a 95% confidence interval for the mean number of hours
Probability
Confidence Interval
P(A or B) = P(A) + P(B) - P(A and B)
1. z-confidence
interval:
P(A and B) = P(A) x P(B) for independent events
2. t-confidence
interval:
Ittai2a (df =n -1)
P(A and B) = P(A) x P(B|A) for dependent events
3. Confidence interval
for proportion:
P(B|A) =
P(A and B)
p(l- p)
P(A)
Normal Distribution
X- NH, ơ)
Test Statistics
X -4
1. Standard nomal: Z =
1.
z-test for u: 2=
Sampling Distribution
1. H=
X-H
(d.f. = n-1)
2.
tetest for 4:t =
s/Vn
2.
3.
z-test for p: =
np 25 and
P(1- P)
ng 25 (where q = 1-p)
3. Z=
4. Chisquare test starisic = 0-E)
E
Discrete Probability Distribution
1. E(X) = 4, =Ex, P,
2 Var(X) = o =E(x, - H.° P.
Binomial Distribution
X - B(n, p)
P(X = k) =
P (1-
n!
p (1-
%3D
k!(n-k)!
Poisson distribution
x - Po (2)
P(X = x) =
Transcribed Image Text:Probability Confidence Interval P(A or B) = P(A) + P(B) - P(A and B) 1. z-confidence interval: P(A and B) = P(A) x P(B) for independent events 2. t-confidence interval: Ittai2a (df =n -1) P(A and B) = P(A) x P(B|A) for dependent events 3. Confidence interval for proportion: P(B|A) = P(A and B) p(l- p) P(A) Normal Distribution X- NH, ơ) Test Statistics X -4 1. Standard nomal: Z = 1. z-test for u: 2= Sampling Distribution 1. H= X-H (d.f. = n-1) 2. tetest for 4:t = s/Vn 2. 3. z-test for p: = np 25 and P(1- P) ng 25 (where q = 1-p) 3. Z= 4. Chisquare test starisic = 0-E) E Discrete Probability Distribution 1. E(X) = 4, =Ex, P, 2 Var(X) = o =E(x, - H.° P. Binomial Distribution X - B(n, p) P(X = k) = P (1- n! p (1- %3D k!(n-k)! Poisson distribution x - Po (2) P(X = x) =
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