Final Examination in Statistics and Probability

Front

The null and alternative hypothesis are statements about the significant difference between

Back

parameter and statistic

Answer explanation

The null and alternative hypothesis compare a population parameter (like a mean) to a sample statistic (like a sample mean) to determine if there is a significant difference. Thus, the correct choice is parameter and statistic.

Front

Which of the following does not describe an alternative hypothesis?
Options:
It is a hypothesis that has a statement of equality.
It is a hypothesis that has a statement of inequality.
It states a specific difference between a parameter and a statistic.
It states that there is a difference between a parameter and a statistic.

Back

It is a hypothesis that has a statement of inequality.

Answer explanation

The correct choice is 'It is a hypothesis that has a statement of equality.' because the alternative hypothesis typically involves statements of inequality, indicating a difference or effect.

Front

Which of the following does not describe a null hypothesis?
Options:
It is denoted by Ho.
It is the hypothesis to be tested.
It has a statement of equality.
It states a specific difference between a parameter and a statistic.

Back

It states a specific difference between a parameter and a statistic.

Answer explanation

The correct choice is 'It states a specific difference between a parameter and a statistic.' A null hypothesis (Ho) typically asserts no effect or difference, not a specific difference.

Front

What does level of significance mean in a hypothesis testing?

Back

Probability of rejecting the null hypothesis when it is true

Answer explanation

The level of significance, often denoted as alpha (α), represents the probability of rejecting the null hypothesis when it is actually true. This is a critical concept in hypothesis testing, indicating the risk of a Type I error.

Front

If the alternative hypothesis contains the symbol ">", where is the rejection region located?

Back

Right end tail region

Answer explanation

In hypothesis testing, if the alternative hypothesis contains the symbol ">", it indicates that we are looking for values greater than a certain threshold. Therefore, the rejection region is located in the right end tail region.

Front

A teacher claims that the mean math score of all grade 11 students is 90. Where is the rejection region located?

Back

Each end tail regions

Answer explanation

The rejection region for a hypothesis test is typically located in the tails of the distribution. Since the teacher claims a specific mean, we check for extreme values in both directions, making 'each end tail regions' the correct choice.

Front

What is the probability of rejecting the null hypothesis of a left-tailed test given the level of significance alpha=0.01?

Back

0.01

Answer explanation

In a left-tailed test, the probability of rejecting the null hypothesis is equal to the significance level, alpha. Therefore, with alpha set at 0.01, the probability of rejection is 0.01, making it the correct choice.

Front

Mr. Mojica claimed that his operators could finish their work in less than three hours. Which is the correct set of hypotheses to test his belief?

Back

Ho: u > or = 3; Ha: u < 3

Answer explanation

The correct hypotheses are Ho: u >= 3 (null hypothesis) and Ha: u < 3 (alternative hypothesis). This tests Mr. Mojica's claim that the work can be completed in less than three hours.

Front

A group of researchers wants to test the truth in the company's claim that the travel time from Magallanes to Manila takes an average of two hours. What are the possible Type I and Type II errors?

Back

Type I error will occur if the actual average travel time is two hours by Ho is rejected. Type II error will occur if the actual average travel time is not two hours but Ho is not rejected.

Answer explanation

Type I error occurs when we reject the null hypothesis (Ho) when it is true, meaning the average travel time is indeed two hours. Type II error occurs when we fail to reject Ho when it is false, meaning the average is not two hours.

Front

What corresponding value will be calculated when the t-test statistic is computed? Options: Hypothesized population mean, Hypothesized sample mean, Standardized t-value, Standardized z-value

Back

Standardized t-value

Answer explanation

The t-test statistic calculates a standardized t-value, which measures how far the sample mean is from the hypothesized population mean in terms of standard error. This is essential for hypothesis testing.