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Questions and Answers
A hypothesis is a statement that speculates something is false.
A hypothesis is a statement that speculates something is false.
False (B)
The null hypothesis asserts there is a remarkable difference between two variables.
The null hypothesis asserts there is a remarkable difference between two variables.
False (B)
The alternative hypothesis is essentially the inverse of the null hypothesis.
The alternative hypothesis is essentially the inverse of the null hypothesis.
True (A)
When formulating hypotheses, '=' is typically used to express the alternative hypothesis.
When formulating hypotheses, '=' is typically used to express the alternative hypothesis.
If the population standard deviation is known and the sample size is 25, a Z-test is appropriate.
If the population standard deviation is known and the sample size is 25, a Z-test is appropriate.
A T-test should be conducted if the population standard deviation is unknown and the sample size exceeds 30.
A T-test should be conducted if the population standard deviation is unknown and the sample size exceeds 30.
In hypothesis testing, if the computed p-value is lower than the significance level (alpha), we fail to reject the null hypothesis.
In hypothesis testing, if the computed p-value is lower than the significance level (alpha), we fail to reject the null hypothesis.
Setting the significance level (alpha) at 0.01 makes it easier to reject the null hypothesis compared to setting it at 0.05.
Setting the significance level (alpha) at 0.01 makes it easier to reject the null hypothesis compared to setting it at 0.05.
A Type I error occurs when we incorrectly fail to reject a false null hypothesis.
A Type I error occurs when we incorrectly fail to reject a false null hypothesis.
A one-tailed test is used when we are only interested in whether the sample mean is greater than the population mean.
A one-tailed test is used when we are only interested in whether the sample mean is greater than the population mean.
If a 95% confidence interval for a population mean includes a specific value, then a hypothesis test at a 5% significance level would reject the null hypothesis that the population mean equals that value.
If a 95% confidence interval for a population mean includes a specific value, then a hypothesis test at a 5% significance level would reject the null hypothesis that the population mean equals that value.
In the coffee consumption example, if after surveying 18 students, the test statistic falls within the critical region, the null hypothesis should be accepted.
In the coffee consumption example, if after surveying 18 students, the test statistic falls within the critical region, the null hypothesis should be accepted.
When testing if Filipinos spent an average of P150,000 on housing, using a sample mean of P155,500, a higher standard deviation would produce a smaller test statistic.
When testing if Filipinos spent an average of P150,000 on housing, using a sample mean of P155,500, a higher standard deviation would produce a smaller test statistic.
When testing the claim about the average salary of private school teachers, using a larger sample of teachers would generally increase the power of the test.
When testing the claim about the average salary of private school teachers, using a larger sample of teachers would generally increase the power of the test.
If we perform a hypothesis test and the result is statistically significant, it definitively proves the alternative hypothesis is true.
If we perform a hypothesis test and the result is statistically significant, it definitively proves the alternative hypothesis is true.
In hypothesis testing, increasing the sample size always reduces the chance of making a Type I error.
In hypothesis testing, increasing the sample size always reduces the chance of making a Type I error.
If the Z-test value for a hypothesis test is 1.90 and the critical value for a two-tailed test at α = 0.05 is 1.96, the null hypothesis should be rejected.
If the Z-test value for a hypothesis test is 1.90 and the critical value for a two-tailed test at α = 0.05 is 1.96, the null hypothesis should be rejected.
Using a t-distribution table, for a one-tailed test with α = 0.05 and 20 degrees of freedom, the critical t-value is approximately 1.725.
Using a t-distribution table, for a one-tailed test with α = 0.05 and 20 degrees of freedom, the critical t-value is approximately 1.725.
The formula for the t-test statistic involves the population standard deviation.
The formula for the t-test statistic involves the population standard deviation.
When performing a hypothesis test about a single mean, the shape of the population distribution is not important if the sample size is reasonably large due to the central limit theorem.
When performing a hypothesis test about a single mean, the shape of the population distribution is not important if the sample size is reasonably large due to the central limit theorem.
Flashcards
Hypothesis
Hypothesis
A statement claiming that something is true.
Null Hypothesis (Ho)
Null Hypothesis (Ho)
Claims no significant difference between variables.
Alternative Hypothesis (Ha)
Alternative Hypothesis (Ha)
The inverse of the null hypothesis.
When to use a Z-test
When to use a Z-test
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When to use a T-test
When to use a T-test
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Study Notes
Hypothesis
- A hypothesis is a statement asserting something as true.
Types of Hypotheses
- Null Hypothesis (Ho) claims no significant difference exists between two variables.
- Alternative Hypothesis (Ha) is the contrary/inverse of the null hypothesis.
Determining Null and Alternative Hypotheses
- Equal (=) corresponds to Not Equal (≠)
- Greater than or equal to (≥) corresponds to less than (<)
- Less than or equal to (≤) corresponds to greater than (>)
One-Sample Tests
- Use a Z-test if the population standard deviation is known and n >= 30
- Use a T-test if the population standard deviation is unknown and n < 30
Examples
- Survey in 2011: Filipinos spent an average of P150,000 annually on housing with a standard deviation of P9,000.
- A suburban community claims their residents did not spend P150,000, and used 48 residents, finding they spent P155,500 annually on average.
- Determine if there is sufficient evidence to support this claim at a 0.05 level of significance.
- A researcher claims the average salary of private school teachers is greater than P40,000 with a standard deviation of P7,500.
- A sample of 35 teachers has a mean salary of P42,000.
- At a 0.05 level of significance, test this claim.
- A study indicated that the average daily coffee consumption of 25-35 year olds is 4 cups per day.
- A university claims their students drink less than 4 cups, and selected 18 students, finding a mean of 3.5 cups with a standard deviation of 1.8 cups.
- With a 0.01 level of significance, test the university's claim.
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