INTRODUCTION TO STATISTICAL INFERENCE Flashcards
Inference vs Observation:
Conclusion reached based on evidence and reasoning
Inference
Inference vs Observation:
Act of paying attention to something in order to gain information; Can be based on second-hand experience
Observation
Inference vs Observation:
Mental process; Logical interpretation and explanation of observations
Inference
Inference vs Observation:
Uses the five senses; First-hand experience
Observation
Descriptive vs Inferential:
Computation of measures of central tendency and variability
Descriptive
Descriptive vs Inferential:
Summarizing and presenting data; Tabular and graphical presentation
Descriptive
Descriptive vs Inferential:
Facilitates understanding, analysis, and interpretation of data
Descriptive
Descriptive vs Inferential:
Estimation of Parameters and Hypotheses Testing
Inferential
Descriptive vs Inferential:
Methods of arriving at conclusions and generalization about a target population based on the information from a sample
Inferential
process of generalizing conclusions based on the obtained results from a sample
Statistical Inference
Uses simple statistics to determine unknown parameters of the population
Summary Measures:
Measures computed using data from the entire population
Parameters
Population; constant regardless of sample
Select an individual observations and test sample, results will be used to make an inference about the population
Usually the unknown in a problem
Summary Measures:
Measures computed using data from the sample
Sample; random variable, it varies, may vary from sample to sample
Statistics
Can be computed from the sample depending on w/c ones were randomly included on the sample
Repeating the sampling may result to a different statistic, because it varies
Available from the sample data
Parameter vs Statistics: ๐ป ๐2 ๐ P
Parameter ๐ป- population mean ๐2-population variance ๐- population SD P- proportion (population)
Parameter vs Statistics: ๐ฅฬ s2 s p
Statistics ๐ฅฬ - sample mean s2- sample variance s- sample SD p- proportion (sample)
2 Main Types of Statistical Inference:
Process by which the statistic computed from a random sample is used to approximate the corresponding parameter in the population.
Estimation
Giving an approximate
2 Main Types of Statistical Inference:
Process of deciding whether or not a hypothesis about the target population is true based on the sample data.
Hypothesis Testing
Hypothesis: statement about the population, usually something about the value of the parameters
Making conclusions or generalizations on the population
To determine the mean exam score of all BIOE211 students for AY 2021-2022:
Target population:
Variable:
Parameter:
Statistics:
all BIOE211 students for AY: 21-22
exam scores
mean exam scores
no statistical inference is needed, because population is already a complete data: Descriptive
Frequency distribution of the statistic computed from each of all the possible samples of the population
Sampling Distribution of a Statistic
mean and proportion
A if only the 1st statement is correct.
B if only the 2nd statement is correct.
C if both statements are correct.
D if neither statement is correct.
Knowing the properties of the sampling distribution will help in:
- Estimating population parameters
- Test hypotheses about population parameters
C
A if only the 1st statement is correct.
B if only the 2nd statement is correct.
C if both statements are correct.
D if neither statement is correct.
- Population parameter is always known
- Sampling distribution can be constructed in reality
D
reflects the frequency distribution of sample means of all possible samples of size n
Sampling Distribution of the Mean
statistical, ๐ฅฬ
TRUE or FALSE: (Properties of the Sampling Distribution of ๐ฅฬ )
The mean of the sampling distribution of ๐ฅฬ (๐๐ฅฬ ) is equal to the population mean ๐.
TRUE
but not always
TRUE or FALSE: (Properties of the Sampling Distribution of ๐ฅฬ )
The standard deviation of the sampling distribution of ๐ฅฬ (๐๐ฅฬ ) = to the population SD (๐) divided by the square root of n
TRUE
TRUE or FALSE: (Properties of the Sampling Distribution of ๐ฅฬ )
Sampling distribution of ๐ฅฬ is approximately normally distributed.
TRUE
If not, sampling distribution of ๐ฅฬ will approximate normality if sample size is large enough (Central limit theorem)
only applicable if sample is random
includes point estimate and interval estimate
Estimation of the Population Mean
Estimation of the Population Mean:
Single number of estimate of parameter
Subjected to sampling errors, because of sampling variations
Point estimate
(Sample mean will not always be exactly equal to population mean)
The best estimate of the population ๐ is the mean of the sample ๐ฅฬ
The study objective is to estimate the mean weight of all school-aged children. Randomly, 30 were sampled and recorded their individual weight in pounds.
Identify:
Variable-
Population-
Sample-
Variable- weight (in pounds) of all school-aged children
Population- all school-aged children
Sample- 30 randomly selected school-aged children
The study objective is to estimate the mean weight of all school-aged children. Randomly, 30 were sampled and recorded their individual weight in pounds. Compute for the point estimate:
50, 60, 65, 72, 54, 64, 75, 70, 70, 59,
79, 79, 74, 75, 64, 74, 71, 62, 63, 63,
56, 62, 60, 65, 73, 67, 63, 72, 57, 76
66.47
Point estimate of the mean weight of all school-aged children is 66.47 lbs
estimate of parameter w/in a range of values
Requires knowledge of ๐ (population SD): from literature and from previous studies, there is reference
Interval Estimate
๐ฅฬ
is an estimate of ๐, but they may not be exactly equal
We can add and subtract a certain amount from ๐ฅฬ
to create an interval that we believe contains ๐, results will be used as the interval estimate
Confidence level : Level of Significance: z-value
90% : ____ : 1.64
___ : 5% : ____
99% : ____ : ____
90% : 10% : 1.64
95% : 5% : 1.96
99% : 1% : 2.58
The study objective is to estimate the mean weight of all school-aged children. Randomly, 30 children were sampled and recorded their individual weight in pounds. The mean was found to be in 66.47 lbs. Based on literature, the standard deviation of weight is 7.59 lbs.
Compute for the 95% confidence interval estimate
LL= 63.75 lbs (manual) UL= 69.19 lbs (manual)
We are 95% confident that the mean weight of all school-aged children is between 63.75 lbs to 69.19 lbs.
A municipal health officer was interested in identifying factors affecting utilization of health services in his area. Among the factors that he considered was accessibility of the RHU. He interviewed a random sample of 25 patients and asked about the distance travelled in going from their homes to the clinic. His findings showed a mean distance travelled of 7 km. with a standard deviation of 3.2 km.
Identify the ff and construct a 95% interval estimate for the population mean: (manual)
๐ฅฬ = s = n = df = ๐ถ = t=
๐ฅฬ = 7 km s = 3.2 km n = 25 df = 24 ๐ถ = 5% or 0.05 t= 2.064
LL= 5.68 km UL= 8.32 km
We are 95% confident that the mean distance travelled to the clinic by all patients is between 6.58 km to 8.32 km.
Mutually exclusive and Exhaustive
number w/ characteristic of interest รท total number of persons examined
Also has Point and Interval Estimate
Population proportion
reflects the frequency distribution of sample proportions of all possible samples of size n.
Sampling Distribution of Population Proportions
Proportion of sample with the characteristic of interest
A random variable
Dependent on the sample randomly selected
Sampling Proportions (p)
A if only the 1st statement is correct.
B if only the 2nd statement is correct.
C if both statements are correct.
D if neither statement is correct.
Properties of the Sampling Distribution of p
- The mean of the sampling distribution of (๐p) is equal to the population proportion P.
- The distribution is normally distributed.
C
A survey was conducted to study the dental health practices of adults in a certain urban population. Of 300 randomly selected and interviewed, 123 indicated that they had regular dental check-ups twice a year.
Identify:
p=
q=
n=
p= 0.41 q= 0.59 n= 300
