Statistics & Probability Quiz

Which of following is true about the mean of the sample means?

• The mean of the sample mean is equal to the population mean.

• The mean of the sample mean is equal to the population mean divided by the population variance.

• The mean of the sample mean is equal to the square of population mean.

• The mean of the sample mean is equal to the square root of population mean.

What is true about the standard error of the mean?

• Decreases as the sample size increases.

• It is less than the standard deviation of the population.

• It measures the variability of the mean from sample to sample.

• All of the above

What distribution is used to estimate population parameters when the population variance is unknown, and the sample size is less than 30?

• Chi-square Distribution

• t-Distribution

• Pearson Correlation Coefficient

• z-Distribution

Given µ =10, σ = 3 and n = 40. Which of the following distribution of the sample mean for a normal population when the population variance is known?

• Chi-square Distribution

• t-Distribution

• Pearson Correlation Coefficient

• z-Distribution

A History teacher claims that the average height of Filipino males is 163 centimeters. A student taking up Statistics randomly select 10 Filipino males and measure their heights. Their heights in centimeter are 163,167,159,165,162,164,163,160,169 and 174. To test the claim, which test is appropriate?

• chi-square test

• f-test

• t-test

• z-test

Which of the following states that the sampling distribution of the sample means approaches a normal distribution as the sample size gets larger?

• Central Limit Theorem

• Limit Theorem

• Law of Large Numbers

• Bayes Theorem

What happen to the histogram of the sample means of the random samples in Central Limit Theorem, as n→∞?

• It changes nothing from the original population.

• It shows the variance of the distribution.

• It shows the standard deviation of the distribution.

• It approaches the normalcy of the distribution.

Who developed the t-distribution in 1908?

• William S. Gosset

• Ronald A. Fisher

• Wilhem G. Student

• a student from Gosset Academy

It is a value in the t-distribution that is less than the probability of the given percentage.

• degrees of freedom

• percentile

• t-value

• right-tailed value

In Student's t-distribution, if the sample size is 25, what is the degree of freedom?

• 5

• 24

• 25

• 26