1. Pertemuan 13 Pendugaan Parameter Nilai Tengah
Matakuliah : I Statistika
Tahun : 2005
Versi : Revisi
Pertemuan 13 Pendugaan Parameter Nilai Tengah

2. Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswa
akan mampu :
Mahasiswa akan dapat menghitung pendugaan parameter nilai tengah satu atau dua populasi.

3. Penduigaan nilai tengah satu populasi
Outline Materi
Penduigaan nilai tengah satu populasi
Pendugaan beda dua nilai tengah sampel besar
Pendugaan beda nilai tengah sampel kecil
Pendugaan beda nilai tengah populasi tidak bebas

4. Interval Estimation of a Population Mean: Large-Sample Case
Small-Sample Case
Determining the Sample Size
Interval Estimation of a Population Proportion 
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5. Interval Estimate of a Population Mean: Large-Sample Case (n > 30)
With  Known
where: is the sample mean
1 - is the confidence coefficient
z/2 is the z value providing an area of
/2 in the upper tail of the standard
normal probability distribution
s is the population standard deviation
n is the sample size

6. Interval Estimate of a Population Mean: Large-Sample Case (n > 30)
With  Unknown
In most applications the value of the population standard deviation is unknown. We simply use the value of the sample standard deviation, s, as the point estimate of the population standard deviation.

7. Interval Estimation of a Population Mean: Small-Sample Case (n < 30)
Population is Not Normally Distributed
The only option is to increase the sample size to
n > 30 and use the large-sample interval-estimation
procedures.
Population is Normally Distributed and  is Known
The large-sample interval-estimation procedure can
be used.
Population is Normally Distributed and  is Unknown
The appropriate interval estimate is based on a
probability distribution known as the t distribution.

8. where 1 - = the confidence coefficient
Interval Estimation of a Population Mean: Small-Sample Case (n < 30) with  Unknown
Interval Estimate
where 1 - = the confidence coefficient
t/2 = the t value providing an area of / in the upper tail of a t distribution
with n - 1 degrees of freedom
s = the sample standard deviation

9. Interval Estimate of 1 - 2: Large-Sample Case (n1 > 30 and n2 > 30)
Interval Estimate with 1 and 2 Known
where:
1 -  is the confidence coefficient
Interval Estimate with 1 and 2 Unknown

10. Point Estimator of the Difference Between the Means of Two Populations
Par, Inc. Golf Balls
m1 = mean driving
distance of Par
golf balls
Population 2
Rap, Ltd. Golf Balls
m2 = mean driving
distance of Rap
golf balls
m1 – m2 = difference between
the mean distances
Simple random sample
of n1 Par golf balls
x1 = sample mean distance
for sample of Par golf ball
Simple random sample
of n2 Rap golf balls
x2 = sample mean distance
for sample of Rap golf ball
x1 - x2 = Point Estimate of m1 – m2

11. Interval Estimate with  2 Known
Interval Estimate of 1 - 2: Small-Sample Case (n1 < 30 and/or n2 < 30)
Interval Estimate with  2 Known
where:

12. Interval Estimate with  2 Unknown
Interval Estimate of 1 - 2: Small-Sample Case (n1 < 30 and/or n2 < 30)
Interval Estimate with  2 Unknown
where:

13. Contoh Soal: Specific Motors
Point Estimate of the Difference Between Two Population Means
1 = mean miles-per-gallon for the population
of M cars
2 = mean miles-per-gallon for the population
of J cars
Point estimate of 1 - 2 = = = 2.5 mpg.

14. Contoh Soal: Specific Motors
95% Confidence Interval Estimate of the Difference Between Two Population Means: Small-Sample Case
= or .3 to 4.7 miles per gallon.
We are 95% confident that the difference between the
mean mpg ratings of the two car types is from .3 to 4.7 mpg (with the M car having the higher mpg).

15. Inference About the Difference Between the Means of Two Populations: Matched Samples
With a matched-sample design each sampled item provides a pair of data values.
The matched-sample design can be referred to as blocking.
This design often leads to a smaller sampling error than the independent-sample design because variation between sampled items is eliminated as a source of sampling error.

16. Contoh Soal: Express Deliveries
Delivery Time (Hours)
District Office UPX INTEX Difference
Seattle
Los Angeles
Boston
Cleveland
New York
Houston
Atlanta
St. Louis
Milwaukee
Denver

17. Contoh Soal: Express Deliveries
Inference About the Difference Between the Means of Two Populations: Matched Samples
Let d = the mean of the difference values for the two delivery services for the population of district offices
Hypotheses H0: d = 0, Ha: d 
Rejection Rule
Assuming the population of difference values is approximately normally distributed, the t distribution with n - 1 degrees of freedom applies. With  = .05, t.025 = (9 degrees of freedom).
Reject H0 if t < or if t > 2.262

18. Contoh Soal: Express Deliveries
Inference About the Difference Between the Means of Two Populations: Matched Samples
Conclusion Reject H0.
There is a significant difference between the mean delivery times for the two services.

19. Selamat Belajar Semoga Sukses.