Answer with short solution or explanation

Enrichment Activity 1. (5 points) Find the degree of fl'cedom(d1) of the given sample size. 1. n = 23 2. n= 15 3. n= 29 4. n= '3' 5. n = 11 Enrichment Activity 2 (5 points) Find the area under the right tail of the t-distribution of the given degree of freedom (di). (5 points) 1. df= 14, at 0.25 2. df = 25 at 0.10 3. df= 13 at 0.025 4. df = 22 at 0.05 5. df = 28 at 0.025 \"'RI'ITEN TASK N0. 4 Enrichment Activity 1 Directions: Read and analyze each item careilly. Choose the letter of the best answer. Write the chosen letter on a separate sheet of paper. (1 point each) 1. The t-distribution was developed by W.S. min 1908. Why was it called \"Student's t-distribution\"? A. because it was first introduced to senior high school students in 1908 B. because he was still a college student when he rst introduces the t-distribution C. because he used the pen name \"Student\" when he introduces his paper about the t distribution D. because he used the students as samples in his study about the tdistribution 2. When do we consider that the sample size is small? A. when it is less than 30 C. when it is greater than 25 but less than 40 B. when it is between 20 to 40 D. when it is only 1% of the total population 3. In Student's t-distribution, what is the sample size if the degree of freedom is 25? A. 5 B. 24 C. 25 D. 26 4. When do we use t-distribution instead of normal distribution? A. If the sample variance is unknown B. If the population variance is known C. When the sample size is considered small. D. When the sample size is sufciently large. 5. In the estimation of a parameter using the t-distribution, is it possible to replace the population standard deviation, 0' by the sample standard deviation, 5? A. No, because the given sample size is small B. No, because (I and s differ by a signicant amount C. Yes, because 0' is unknown and s is a good estimator of 0'. D. Yes, because a is equal to s when we are estimating parameters 6. What will be the effect on the t distribution curve when we replace 0' by s? A. The t-distribution curve will become bell-shaped. B. The t-distribution curve will be symmetrical to zero. C. The t-distribution curve will be the same as the normal curve. D. The t-distribution curve will have a lower peak and thicker tails. For numbers 7 to 9, refer to the problem below. The principal of Mammlntegrated National High School claimed that the average salary of their teachers is P24, 000 per month. A random sample of 15 teachers in the school has a mean of P23, 220, and a standard deviation of F400. 7. Identify the population mean. A. ?24,000 B. H3220 C. ?400 D. 15 8. Identify the sample mean. A. P24,000 B. H3220 C. ?400 D. 15 9. In testing the principal's claim, can we use the t-distribution? A. Yes, because the population standard deviation is unknown, and the sample size is small. B. Yes, because the sample standard deviation is small, and variance is unknown. C. No, because the population standard deviation is greater than the sample standard deviation. D. No, because the sample size is too small for the given sample standard deviation. 10. Which property of t-distribution is NOT a property of normal distribution? A. The t-distribution curve is bell-shaped. B. The t-distribution curve is symmetrical about zero. C. In t distribution, the variance is always greater than 1. D. The total area under the t distribution curve equal to l. 11. Which of the following probability distribution curves has the lowest peak? A. the standard normal distribution B. a t-distribution with 5 degrees of freedom C. a t-distribution with 7 degrees of freedom D. a t-distribution with 9 degrees of freedom 12. Which of the following probability distribution curves has the thickest tails? A. a t-distribution with 25 degrees of freedom B. a t-distribution with 23 degrees of freedom C. a t-distribution with 21 degrees of freedom D. a t-distribution with 19 degrees of freedom 13. It is a value in the t-distribution that is less than the probability of the given percentage. A. degrees of freedom C. t-value B. percentile D. right-tailed value 14. If the area of the unshaded part of the t-distribution is 0.85, what is the area of the shaded region? A. 0.15 B. 0.75 C. 0.85 D. 85% 15. If the given t-value is 2.056 and the shaded region is on the right of the t distribution with 26 degrees of freedom, what is the area of the unshaded region? A. 0.025 B. 0.15 C. 0.95 D. 0.975 16. What is the area on the left tail of the t-distribution with 14 degrees of freedom corresponding to t-value of 3.787? A. 0.001 B. 0.01 C. 0.975 D. 0.999 17. Which t distribution has an area of 0.10 to the right of 1.333? A. A t-distribution with 5 degrees of freedom B. A t-distribution with 11 degrees of freedom C. A t-distribution with 17 degrees of freedom D. A t-distribution with 23 degrees of freedom 18. The shaded region is on the right tail of the t-distribution. If the degree of freedom is 22 and the area of the shaded region is 0.005, what is the value of t? A. -2.819 B. -2.831 C. 2.819 D. 2.831 19. The shaded region is on the left tail of the t-distribution. If the degree of freedom is 16 and the area of the shaded region is 0.01, what is the value of t? A. 2.583 B. 2.120 C.-2. 120 D. -2. 583 20. Which of the following values is the 90th percentile of the t-distribution with 15 degrees of freedom? A. 1.341 B. 1.345 C. 1.753 D. 1.837 21. What is the 95th percentile of the t-distribution when the sample size is 23? A. 1.721 B. 1.717 C. 1.714 D. 1.703 22. If the degree of freedom is 29, what is the 95th percentile of the t-distribution? A. 2.048 B. 1.701 C 1.699 D. 1.547 23. If the 99th percentile of the t-distribution is 2.650, what is the degree of freedom? A. 16 B. 15 C. 14 D. 13 24. To what percentile of the t-distribution does 1.397 belong if the sample size is 9? A. 90th B. 95th C. 97 D. 99th 25. Why does the right-tailed t-table display only positive values of t? A. Because the area cannot be negative. B. Because t-values are always positive. C. Because t-values on the left tail are positive D. Because t-values on the right tail are positive