INTRODUCTION TO STATISTICAL INFERENCE Flashcards by Ady Cabalquinto

Inference vs Observation:

Conclusion reached based on evidence and reasoning

Inference

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Inference vs Observation:

Act of paying attention to something in order to gain information; Can be based on second-hand experience

Observation

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Inference vs Observation:

Mental process; Logical interpretation and explanation of observations

Inference

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Inference vs Observation:

Uses the five senses; First-hand experience

Observation

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Descriptive vs Inferential:

Computation of measures of central tendency and variability

Descriptive

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Descriptive vs Inferential:

Summarizing and presenting data; Tabular and graphical presentation

Descriptive

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Descriptive vs Inferential:

Facilitates understanding, analysis, and interpretation of data

Descriptive

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Descriptive vs Inferential:

Estimation of Parameters and Hypotheses Testing

Inferential

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Descriptive vs Inferential:

Methods of arriving at conclusions and generalization about a target population based on the information from a sample

Inferential

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process of generalizing conclusions based on the obtained results from a sample

Statistical Inference

Uses simple statistics to determine unknown parameters of the population

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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

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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

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Parameter vs Statistics:
𝝻
𝜎2
𝜎
P

Parameter
𝝻- population mean
𝜎2-population variance
𝜎- population SD
P- proportion (population)

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Parameter vs Statistics:
𝑥̅
s2
s
p

Statistics
𝑥̅- sample mean
s2- sample variance
s- sample SD
p- proportion (sample)

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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

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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

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

reflects the frequency distribution of sample means of all possible samples of size n

Sampling Distribution of the Mean

statistical, 𝑥̅

TRUE or FALSE: (Properties of the Sampling Distribution of 𝑥̅)

The mean of the sampling distribution of 𝑥̅ (𝜇𝑥̅) is equal to the population mean 𝜇.

TRUE

but not always

TRUE or FALSE: (Properties of the Sampling Distribution of 𝑥̅)

The standard deviation of the sampling distribution of 𝑥̅ (𝜎𝑥̅ ) = to the population SD (𝜎) divided by the square root of n

TRUE

TRUE or FALSE: (Properties of the Sampling Distribution of 𝑥̅)

Sampling distribution of 𝑥̅ is approximately normally distributed.

TRUE

If not, sampling distribution of 𝑥̅ 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 𝜇 is the mean of the sample 𝑥̅

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 𝝈 (population SD): from literature and from previous studies, there is reference

Interval Estimate 𝑥̅ is an estimate of 𝜇, but they may not be exactly equal We can add and subtract a certain amount from 𝑥̅ to create an interval that we believe contains 𝜇, 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) ``` 𝑥̅ = s = n = df = 𝜶 = t= ```

``` 𝑥̅ = 7 km s = 3.2 km n = 25 df = 24 𝜶 = 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 ÷ 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 1. The mean of the sampling distribution of (𝜇p) is equal to the population proportion P. 2. The distribution is normally distributed.

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 ```