COR 006

40. Which of the following t is the t-value when µ= 127, 𝑥̅= 120, s=14 and n=18? A. -2.120 B. -2.110 C. +2.110 D. +2.120

A. -2.120

What is the variance of the sample means of size 3 if the population variance is 6.9375? A. 1.5 B. 1.6 C. 1.7 D. 1.8

A. 1.5

1. A fair coin is tossed three times and the sequence of heads (H) and tails (T) is observed. What is the probability that no heads will appear? A. 1/8 B. 3/8 C. 5/8 D. 2/3

A. 1/8

What is the variance of the probability distribution? A. 2.18 B. 2.19 C. 2.20 D. 2.21

A. 2.18

The mean gasoline consumption of 15 cars is 38 liters with a standard deviation of 2 liters. Using a 95% confidence level, how long is the interval of the sample mean? A. 2.25 B. 2.30 C. 2.35 D. 2.40

A. 2.25

A randomly selected 400 students out of 9000 students at a university with 15-week semesters was asked whether or not they think the semester should be shortened to 14 weeks (with longer classes). Forty-six percent (46%) of the 400 students surveyed answered "yes." What is the sample? A. 400 students B. 9000 students C. 15-week semesters D. 46% who answered "yes"

A. 400 students

35. Human gestation length is said to be normally distributed with a mean of 266 days and a standard deviation of 16 days. Suppose 64 pregnancies are randomly selected. What is the probability that the average gestation length is between 262 and 270 days A. 95.45% B. 95.50% C. 95.75% D. 95.80%

A. 95.45%

29. Which of the following states that the sampling distribution of the sample means approaches a normal distribution as the sample size gets larger? A. Central Limit Theorem B. Law of Large Numbers C. Limit Theorem D. Bayes Theorem

A. Central Limit Theorem

40. Given a set of data, which of the following refers to number of independent observations that are free to vary after a sample statistic has been computed? A. Degrees of freedom B. Mean C. Standard error D. Variance

A. Degrees of freedom

Formulate the steps to solve problems involving sampling distribution of the sample mean. I- Write the formula: II- Solve z. III- Look for the P(z) in the Standard Normal Distribution Table IV- Substitute the values of the terms in the formula. A. I-IV-II-III B. IV-III-II-I C. I-II-III-IV D. III-IV-I-II

A. I-IV-II-III

34. Which concept of random sampling distribution of the sample means using Central Limit Theorem? A. If you have a population mean µ and standard deviation and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately distributed normally. B. The probability of the simultaneous occurrence of two events that are independent is given by the product of their individual probabilities. C. If you have a population mean µ and standard deviation and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately distributed same as the original population. D. The larger the sample size n in sampling distribution of sample mean, the lesser the histogram is to show the normalcy of the distribution.

A. If you have a population mean µ and standard deviation and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately distributed normally.

A set of Mathematics exam scores has a mean of 68 and a standard deviation of 8. A set of English exam scores has a mean of 75 and a standard deviation of 10. For which exam would a score of 78 have a higher standing? A. Math B. English C. both Math & English D. cannot be determined

A. Math

What are the possible values of a random variable when a coin is tossed once? A. Tail (T) and Head (H) B. The number of dots 1,2,3,4,5,6 C. Tail and Tail (TT), and Head and Head (HH) D. The pair of even number of dots (2,2),(2,4),(2,6),(4,2),(4,4),(4,6),(6,2),(6,4) and (6,6)

A. Tail (T) and Head (H)

Which of following is true about the mean of the sample means? A. The mean of the sample mean is equal to the population mean. B. The mean of the sample mean is equal to the population mean divided by the population variance. C. The mean of the sample mean is equal to the square of population mean. D. The mean of the sample mean is equal to the square root of population mean. For items 25-26. Below are the scores of 8 Grade 11 students in Statistics quiz. 7, 8, 12, 15, 10, 11, 9, 14

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

1. Which of the following is a discrete random variable? A. the number of patients in a hospital B. the average weight of female athletes C. the average amount of electricity consumed D. the amount of paint used in repainting a building

A. the number of patients in a hospital

Which probability value would satisfy the given probability distribution? A. 0.16 B. 0.17 C. 0.18 D. 0.19

B. 0.17

44. Which of the following is the length of the interval between 45.5 and 60? A. 10.5 B. 14.5 C. 45.5 D. 60

B. 14.5

44. What percentile of the t distribution does 2.500 belong if the sample size is 24? A. 80th B. 90th C. 95th D. 99th

B. 90th

The area under the part of normal curve in the standard normal distribution that lies within 2 standard deviations of the mean is A. 68% B. 95% C. 99.7% D. 100%

B. 95%

What is the first step in finding the variance of a discrete probability distribution? A. Calculate the standard deviation B. Find the mean of the probability distribution C. Subtract the mean from each value of the random variable X D. Multiply the square of the difference of X and the mean by each value of the random variable.

B. Find the mean of the probability distribution

How do you compare the formula from ? A. Former is used when solving z from original population while the latter is used in random sample. B. Former is used when solving z from random sample while the latter is used in original population. C. Former is used in random sample and original population but the latter can only be used for random sample.

B. Former is used when solving z from random sample while the latter is used in original population.

21. A randomly selected sample of 400 students at a university with 15-week semesters was asked whether or not they think the semester should be shortened to 14 weeks (with longer classes). Forty-six percent (46%) of the 400 students surveyed answered "yes." Which one of the following statements about the number 46% is correct? A. It is a sample statistic B. It is a random variable C. It is a population parameter D. It is a quantitative discrete variable

B. It is a random variable

What happen to the histogram of the sample means of the random samples in Central Limit Theorem, as n→∞? A. It changes nothing from the original population. B. It shows the variance of the distribution. C. It shows the standard deviation of the distribution. D. It approaches the normalcy of the distribution.

B. It shows the variance of the distribution.

1. Which statement is NOT true about the variance of a discrete random variable? A. Variance is always nonnegative. B. It tells the average of the items in a discrete probability distribution C. It measures how far apart the elements of the set are spread out D. High variance indicates that the data points are very spread out around the mean.

B. It tells the average of the items in a discrete probability distribution

The expected value of a random variable is the A. largest value that will ever occur. B. mean value over an infinite number of observations of the variable. C. most common value over an infinite number of observations of the variable. D. value that has the highest probability of occurring. For items 7-10. Cardo sells a maximum of 3 tickets per customer. Let T be the number of tickets sold to a random customer. Below is the probability distribution of T.

B. mean value over an infinite number of observations of the variable.

What is the mean and variance of the probability distribution? A. 1.64 B. 1.65 C. 1.66 D. 1.67

C. 1.66

44. In a t-distribution, if the sample size is 15, what is the degree of freedom? A. 12 B. 13 C. 14 D. 15

C. 14

The midterm examination scores in Statistics and Probability follows a normal distribution with mean of 38 and a standard deviation of 2. If Felix is included in the top 5%, what minimum score should Felix have? A. 40 B. 41 C. 42 D. 43

C. 42

Evaluate the score of the student in a biology test where the equivalent z-score is 0.98. The mean of the test was 88 with a standard deviation of 9.5. A. 95 B. 96 C. 97 D. 98

C. 97

47. A researcher found that the mean score of Grade 9 students in the Math exam is normally distributed with a mean of 82 and a standard deviation of 2.5. The margin of error was known to be 0.65 at a 99% confidence level. How large a sample must be? A. 90 B. 92 C. 99 D. 10

C. 99

A randomly selected sample of 400 students at a university with 15-week semesters was asked whether or not they think the semester should be shortened to 14 weeks (with longer classes). Forty-six percent (46%) of the 400 students surveyed answered "yes." Which one of the following statements about the number 46% is correct? A. It is a sample statistic B. It is a random variable C. It is a population parameter D. It is a quantitative discrete variable

C. It is a population parameter

Which of the following is NOT a property of a normal curve? A. The total area under it is 1. B. The curve is symmetric about the center. C. It is divided into positive 2 and negative 2 standard deviations. D. The mean, median, and mode have the same value and are located at the same point.

C. It is divided into positive 2 and negative 2 standard deviations.

What do you call a portion or representative of population? A. Parameter B. Population C. Sample D. Statistic

C. Sample

35. Which is NOT a correct statement? A. The total probability distribution of the sample mean is always equal to 1. B. There are 10 possible samples of size 3 drawn in the population N = 5. C. There are 31 possible samples of size 3 drawn in the population N = 7. D. There are 20 possible samples of size 3 drawn in the population N = 6.

C. There are 31 possible samples of size 3 drawn in the population N = 7.

A local club plans to invest P10,000 to host a basketball game. They expect to sell tickets worth P15,000. But if it rains on the day of the game, they won't sell any tickets, and the club will lose all the money invested. If the weather forecast for the day of the game is 20% possibility of rain, is this a good investment? A. No because the expected value is positive P2,000 B. No because the expected value is negative P2,000 C. Yes because the expected value is positive P2,000 D. Yes because the expected value is negative P2,000

C. Yes because the expected value is positive P2,000

1. It is a variable being measured to produce numerical observations associated with the random outcomes of a chance experiment. A. fixed variable B. dependent variable C. independent variable D. random variable

C. independent variable

22. What distribution is used to estimate population parameters when the population variance is unknown, and the sample size is less than 30? A. Chi-square Distribution B. Pearson Correlation Coefficient C. t-Distribution D. z-Distribution

C. t-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? A. chi-square test B. f-test C. t-test D. z-test

C. t-test

What is the mean of the sample means of size 3? A. 9.50 B. 9.75 C. 10.50 D. 10.75

D. 10.75

The record of weights of the male population follows the normal distribution. Its mean and standard deviation are 70 kg and 15 kg respectively. If a researcher considers the records of 50 males, what would be its standard deviation? A. 2.11 B. 2.12 C. 2.13 D. 2.14

D. 2.14

47. What is the needed sample size if the margin of error is 0.8 and the standard deviation is 8 with a 95% confidence level? A. 325 B. 335 C. 345 D. 385

D. 385

What is true about the standard error of the mean? A. Decreases as the sample size increases. B. It is less than the standard deviation of the population. C. It measures the variability of the mean from sample to sample. D. All of the above

D. All of the above

The following are characteristics of t-distribution except A. It is symmetric about the mean 0. B. It is bell-shaped but has a heavier tail. C. It depends on the degrees of freedom. D. As the degrees of freedom decreases, it approaches to standard normal distribution.

D. As the degrees of freedom decreases, it approaches to standard normal distribution.

What is the estimate, if sample size of random sampling using Central Limit Theorem is almost normal in accordance to Statisticians? A. If n= 2 B. If n= 3 C. If n= 10 D. If n= 30

D. If n= 30

What would be the best interpretation you can create given the mean of the probability distribution? A. Most customers will purchase 3 tickets. B. Cardo can expect to have more tickets sold. C. A group of 10 customers will purchase exactly 29 tickets. D. If we look at a large number of customers, then each customer, on the average, will have purchased about 1.66 tickets.

D. If we look at a large number of customers, then each customer, on the average, will have purchased about 1.66 tickets.

Predict the length of the confidence interval and the sample size as the confidence level increases. A. The length of the confidence interval decreases and the sample size increases. B. The length of the confidence interval increases and the sample size decreases. C. The length of the confidence interval decreases and the sample size decreases. D. The length of the confidence interval increases and the sample size increases.

D. The length of the confidence interval increases and the sample size increases.

40. The following are common properties of z-distribution and t-distribution, except: A. The mean, median, and mode are zero. B. The total area under the curve is 100%. C. The curve is asymptotic to the x-axis. D. The variance is always greater than 1.

D. The variance is always greater than 1.

29. 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? A. Chi-square Distribution B. Pearson Correlation Coefficient C. t-Distribution D. z-Distribution

D. z-Distribution