Estimation of Parameters - Confidence Interval

Estimation of Parameters

(Confidence Interval)

By Melvin Mallare

Multiple Choice

What do you call the process of approximating the value of the population parameter using a number/range of numbers calculated from a sample data?

• Estimation of Parameters

• Estimate

• Point Estimate

• Interval Estimate

Multiple Choice

What is the most commonly used interval estimate with an associated degree of confidence?

• Confidence Interval

• Credible Interval

• Likelihood Interval

• Fiducial Interval

Multiple Choice

The given table shows the result of the latest Pulse Asia survey on the first choice preference of 2400 respondents. What is the parameter being estimated in the result?

• Population Mean

• Population Proportion

• Population Standard Deviation

• Population Variance

Multiple Choice

If the confidence interval has 1.71% margin of error at 95% confidence level, what is the confidence interval for the population proportionof Filipino registered voters who prefer VP Leni Robredo?

• 18.87% < p < 29.13%

• 20.58% < p < 27.42%

• 22.29% < p < 25.71%

• p = 24%

Confidence Interval for Population Proportion

Confidence Interval for Population Mean

Confidence Interval for Population Mean

Multiple Choice

What is the appropriate form of the confidence interval?

z or t-interval

Multiple Choice

What is the critical t-value ( $$t_{\frac{\alpha}{2}}$$ )?

• 2.539

• 2.576

• 2.861

• 2.845

Critical t-value

​Given:

n = 20

CL = 99%​

​

d.f. = n - 1

= 20 - 1​

d.f. = 19​

Multiple Choice

What is the margin of error for 99% confidence interval for $$\mu$$ ?

• 0.2227 kg

• 0.2239 kg

• 0.2284 kg

• 0.2297 kg

Margin of Error

​Given:

s = 0.35

n = 20​

​

Multiple Choice

What is the 99% confidence interval for $$\mu$$ ?

• 49.48 kg < $$\mu$$   < 49.92 kg

• 49.78 kg < $$\mu$$   < 50.22 kg

• 49.48 % < $$\mu$$   < 49.92 %

• 49.78 % < $$\mu$$   < 50.22 %

Margin of Error

Multiple Choice

Based on the constructed 99% confidence interval, is there sufficient evidence of short weighting?

49.48 kg < $$\mu$$   < 49.92 kg

• No, there is no sufficient evidence because the average weight (49.7 kg) of 20 random sacks of rice is within the confidence interval.

• No, there is no sufficient evidence because the confidence interval is just slightly lower than the labeled weight (50 kg).

• Yes, there is sufficient evidence because the labeled weight of the sacks of rice is not within the constructed confidence interval.

• Yes, there is sufficient evidence because the average weight (49.7 kg) of 20 random sacks of rice is obviously lower than their labeled weight (50 kg).

" Most of the time, the population parameter cannot be directly known but it can be estimated.

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BIG IDEA:

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