Podcast
Questions and Answers
What is the sample standard deviation of the customer expenditure?
What is the sample standard deviation of the customer expenditure?
- R0.75 (correct)
- R0.50
- R1.00
- R1.25
The null hypothesis states that there is a significant difference between the parameter values.
The null hypothesis states that there is a significant difference between the parameter values.
False (B)
At a 99% confidence level, what is the Z-score used in hypothesis testing?
At a 99% confidence level, what is the Z-score used in hypothesis testing?
2.58
The _____ hypothesis is not true if there is sufficient evidence against it.
The _____ hypothesis is not true if there is sufficient evidence against it.
Match the following components with their definitions:
Match the following components with their definitions:
What would be the conclusion if the test statistic is Z = -2.5 at 1% level of significance?
What would be the conclusion if the test statistic is Z = -2.5 at 1% level of significance?
A two-tailed test checks for differences in both directions (greater and lesser).
A two-tailed test checks for differences in both directions (greater and lesser).
What is the null hypothesis in the case of Mr.Cake's average daily bread sales?
What is the null hypothesis in the case of Mr.Cake's average daily bread sales?
In a one-tailed hypothesis test with a significance level of 0.05, what is the critical Z value for rejection in the left tail?
In a one-tailed hypothesis test with a significance level of 0.05, what is the critical Z value for rejection in the left tail?
The null hypothesis is rejected if the test statistic is greater than the critical value in a one-tailed test.
The null hypothesis is rejected if the test statistic is greater than the critical value in a one-tailed test.
What is the significance level used in the hypothesis testing example given above?
What is the significance level used in the hypothesis testing example given above?
If a textile company's claim is that the average strength of their fabric is at least 22.7 kg, then the null hypothesis is Ho: μ __________ 22.7 kg.
If a textile company's claim is that the average strength of their fabric is at least 22.7 kg, then the null hypothesis is Ho: μ __________ 22.7 kg.
Match the following values with their corresponding confidence levels:
Match the following values with their corresponding confidence levels:
What conclusion is made if the test statistic calculated is -2.48 when testing the fabric strength claim?
What conclusion is made if the test statistic calculated is -2.48 when testing the fabric strength claim?
In hypothesis testing, the alternative hypothesis is denoted as Ha: μ ≤ 22.7 kg when testing against the company's claim.
In hypothesis testing, the alternative hypothesis is denoted as Ha: μ ≤ 22.7 kg when testing against the company's claim.
What is the test statistic for the example provided in the content?
What is the test statistic for the example provided in the content?
What Z-value corresponds to a 95% confidence level?
What Z-value corresponds to a 95% confidence level?
The Z-table provides probabilities for Z-values greater than or equal to zero only.
The Z-table provides probabilities for Z-values greater than or equal to zero only.
What is the Z-value for a 99% confidence level?
What is the Z-value for a 99% confidence level?
For estimating a finite population when σ is known, we use the ______ method.
For estimating a finite population when σ is known, we use the ______ method.
Match the following confidence levels with their corresponding Z-values:
Match the following confidence levels with their corresponding Z-values:
If the population standard deviation (σ) is unknown and the sample size is greater than 30, which method is used for estimation?
If the population standard deviation (σ) is unknown and the sample size is greater than 30, which method is used for estimation?
In an infinite population, if σ is known, we still estimate using the T-distribution.
In an infinite population, if σ is known, we still estimate using the T-distribution.
Which Z-value indicates an area to the left of 0.5 in the standard normal distribution?
Which Z-value indicates an area to the left of 0.5 in the standard normal distribution?
The smart packaging company is trying to estimate the average ______ per customer.
The smart packaging company is trying to estimate the average ______ per customer.
What value from the Z-table corresponds to a Z-score of 1.0?
What value from the Z-table corresponds to a Z-score of 1.0?
Flashcards
One-tailed test
One-tailed test
A hypothesis test where the region of rejection is on only one side of the sampling distribution.
Standard Normal Table
Standard Normal Table
A table that shows the probabilities associated with different values of a standard normal variable.
90% confidence level
90% confidence level
A level of confidence where there is a 90% probability that the true population parameter lies within the calculated confidence interval.
Left-tailed test
Left-tailed test
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Right-tailed test
Right-tailed test
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95% confidence level
95% confidence level
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Null Hypothesis (Ho)
Null Hypothesis (Ho)
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99% confidence level
99% confidence level
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Alternative Hypothesis (Ha)
Alternative Hypothesis (Ha)
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Estimating when σ is known
Estimating when σ is known
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Estimating when σ is unknown (n > 30)
Estimating when σ is unknown (n > 30)
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Significance Level (α)
Significance Level (α)
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Critical Value (Z critical)
Critical Value (Z critical)
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Population Standard Deviation (σ)
Population Standard Deviation (σ)
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Confidence Interval
Confidence Interval
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Test Statistic
Test Statistic
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Confidence Level
Confidence Level
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Standard Error
Standard Error
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Confidence Interval
Confidence Interval
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Sample Standard Deviation (s)
Sample Standard Deviation (s)
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Hypothesis Testing
Hypothesis Testing
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Null Hypothesis (H0)
Null Hypothesis (H0)
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Alternative Hypothesis (H1)
Alternative Hypothesis (H1)
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Two-Tailed Test
Two-Tailed Test
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Level of Significance (α)
Level of Significance (α)
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Rejection Region
Rejection Region
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Sample Size (n)
Sample Size (n)
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Z-score
Z-score
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Finite Population
Finite Population
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Finite Population Correction Factor
Finite Population Correction Factor
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Study Notes
One-Tailed Hypothesis Tests
- A one-tailed test focuses on one direction of the alternative hypothesis.
- The critical region is located in one tail of the distribution.
- Significance level (α) is the probability of rejecting the null hypothesis when it is true. In one-tailed tests, the significance level is applied entirely to one tail of the distribution.
- The decision rule depends on whether the test is left-tailed or right-tailed.
Two-Tailed Hypothesis Tests
- A two-tailed test considers deviations from the null hypothesis in both directions.
- The critical region is split between the two tails of the distribution.
- Significance level (α) is divided between the two tails.
- The decision rule involves comparing the test statistic to both upper and lower critical values.
Hypothesis Testing
- A procedure for evaluating a claim about a population parameter.
- Hypotheses are statements about the population parameter.
- The objective is to decide if the evidence supports the claim.
- Null hypothesis (H₀) is the statement of no effect or no difference.
- Alternative hypothesis (Hₐ) is the claim being tested.
Confidence Intervals
- An interval estimate of a population parameter calculated from a sample statistic.
- Confidence level represents the probability that the interval contains the true population parameter.
- Confidence level is expressed as a percentage, e.g., 90%, 95%, 99%.
- Common confidence levels have corresponding critical values. These critical values define the range within which the population parameter value is likely to fall. The critical values depend on the confidence level to be achieved.
Sample Size Determination
- Determining the appropriate sample size needed for a given level of accuracy.
- Factors such as confidence level, desired margin of error, and population standard deviation or sample standard deviation play a critical role in this process. The sample size required is influenced by both the desired precision of the calculation and the confidence level.
Standard Error
- Standard deviation of a sampling distribution of a sample statistic
- A function of the standard deviation of the population and the sample size; smaller sample sizes tend to give greater variability, leading to a higher standard error
Examples of Hypothesis Testing
- Testing average fabric strength
- Average spending per customer
- Average number of breads sold daily
- Number of daily newspaper readers.
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Description
This quiz covers the fundamentals of hypothesis testing, including one-tailed and two-tailed tests. Learn how significance levels and decision rules are applied in different testing scenarios. Test your understanding of key concepts related to evaluating claims about population parameters.
