Answer the following
1. In the absence of the population variance and/or if the sample size is small, t of paper. which sampling distribution is being used? A. chi distribution B. z-distribution C. t-distribution D. p distribution 2. Who developed the t-distribution in 1908? A. William S. Gosset B. Wilhem G. Student C. Ronald A. Fisher D. a student from Gosset Academy 3. When do we say that the sample size is sufficiently large? A. When it is greater than or equal to 10. B: When it is greater than or equal to 20. C. When it is greater than or equal to 30. D. When it is greater than or equal to 40. 4. In Student's t-distribution, if the sample size is 25, what is the degree of freedom? A. 5 B. 24 C. 25 D. 26 5. How does t distribution differ from a normal distribution? A. The t-distribution has a thicker tail. B. The t-distribution has a higher peak. C. The t-distribution is centered at 0. D. The t-distribution is symmetric in the middle. 2686. When do you use t-distribution instead of normal distribution? A. When the sample size is less than 30. B. If the sample standard deviation is unknown C. If the population standard deviation is known D. When the sample size is greater than or equal to 30 7. In the estimation of a parameter using the t statistic s, ", why did we replace the population standard deviation, o by the sample standard deviation, s? A. because the given sample size is small B. because o and s differ by a very small amount C. because o is unknown and s is a good estimator of o D. because o is equal to s when we are estimating parameters 8. The t-distribution curve has thicker tails than the normal curve. What does it imply? A. The normal distribution has a greater mean than the t-distribution. B. The t-distribution has lesser variability than the normal distribution. C. The t-distribution has a greater chance for extreme values than the normal distribution. D. Estimation of the parameter using the z-distribution is more accurate than using the t-distribution. For numbers 9 to 11, The CEO of Flying Fire Corporation claims that an average flying fire light bulb lasts 300 days. A researcher randomly selects 15 bulbs for testing. The sampled bulbs last an average of 290 days, with a standard deviation of 50 days. 9. Identify the population mean. A. 300 days B. 290 days C. 50 days D. 15 bulbs 10. What is the number of degrees of freedom? A. 299 B. 289 C. 49 D. 14 11. Compute for the variance of the t distribution using the formula, ,, where v is the number of degrees of freedom. A. 1.17 B. 1.10 C. 1.04 D. 1.01 12. Which property of t-distribution is also a property of normal distribution? A. In t-distribution, the variance is always greater than 1. B. In t-distribution, the standard deviation is always greater than 1. C. The tails of the t-distribution curve are asymptotic to the horizontal axis. D. The shape of the t-distribution curve depends on the degrees of freedom. 13. Which of the following statements is NOT true about the t-distribution? A. The variance of the t-distribution is equal to 1. B. The t-distribution has thicker tails than the normal distribution. distribution. C. As the degrees of freedom increase, the t distribution tends to normal freedom. D. The exact shape of the t-distribution depends on the number of degrees of14. Which of the following probability distribution curves has the lowest peak? A. the standard normal distribution B. a t-distribution with 20 degrees of freedom C. a t-distribution with 15 degrees of freedom D. a t-distribution with 10 degrees of freedom 15. Which of the following probability distribution curves has the thickest tails? A. the standard normal distribution B. a t-distribution with 21 degrees of freedom C. a t-distribution with 19 degrees of freedom D. a t-distribution with 20 degrees of freedomFill in the blank with the correct word or' phrase to complete each sentence. 1. The Student's t-distribution is a probability. distribution that is used to estimate population parameters when the sample size is t and/ 01' when the _ is unknown.\" , i I ' 2. The t-distribution was developed by in. 1908. 3.Like the normal distribution, the, t-distribution is , ___V ' ~shaped, symmetrical about ' ' and has the total area under its curveequalto - ' . - ' . ll, V I 4. The t-distribution has tails that are asymptotic to the ' - ' - ' axis. 5. The mean, median and mode of tdistribution are equal to 6. Theushape of the t-distribution' curve depends on the number of __'_____. 7. The t-distribution has ___'____ peak and ______ tails than the normal curve. ' A , .. . 8. As the degrees of freedom increases, the t-distribution 'tends to the 9. The variance. and the standard deviation of the tdistribution is always than 1. , ' 10. To compute for the variance, use the formula
