FOURTH QUARTER EXAMINATION

STATISTICS AND PROBABILITY

SENIOR HIGH SCHOOL

Name: ___________________________________ LRN: _________________Score: __________________

Grade/Section: ____________________________ Teacher: ______________________________________

Direction: Choose the letter of the best/correct answer. Encircle the letter of best/correct answer.

1. What term is being used to describe a proposed explanation, assertion, or assumption about a
population parameter or about the distribution of a random variable?
a. statistic c. hypothesis
b. decision d. probability

2. In a one-tailed test, in which critical values below will the computed z of 2.312 falls in the non-
rejection region?
a. 1.383 c. 2.228
b. 1.533 d. 2.354

3. When is a Type I error committed?

a. We reject a null hypothesis that is true.
b. We reject a null hypothesis that is false.
c. We fail to reject a null hypothesis that is true.
d. We fail to reject a null hypothesis that is false

4. Mother V wants to estimate the average shower time of teenagers. From the sample of 50
teenagers, she found out that it takes 5 minutes for teenagers to shower. What is the parameter?
a. sample of 50 teenagers
b. 50 teenagers in 5 minutes
c. average shower time of teenagers
d. took 5 minutes for teenagers to shower

5. Which of the following denotes the true value that would be obtained if a census rather than a
sample was undertaken?
a. sample c. parameter
b. statistic d. population

6. A researcher thinks that if expectant mothers use vitamins, the birth weight of the babies will
increase. The average birth weight of the population is 3.9 kgs. What is the alternative hypothesis?
a. 𝐻𝑎: 𝜇 > 3.9 c. 𝐻𝑎: 𝜇 = 3.9
b. 𝐻𝑎: 𝜇 < 3.9 d. 𝐻𝑎: 𝜇 ≠ 3.9

7. According to the report, the average weight of a Filipino newborn baby is 2.8 kgs. Aneeza wants to
perform a significance test to see if this holds true in her nation. She takes a random sample of
babies and observes that the average weight of newborns is 3kgs. What is the null hypothesis?
a. 𝐻o: 𝜇 > 2.8 c. 𝐻o: 𝜇 = 2.8
b. 𝐻o: 𝜇 < 2.8 d. 𝐻o: 𝜇 ≠ 2.8

8. Based on the Central Limit Theorem, when the sample (n) is extremely large and the variance is
unknown, what is the statistical test to be used?
a. t-test c. two-tailed test
b. z-test d. one- tailed test
 9. What appropriate tool is applicable if the population is normal, sample standard deviation is
known, and sample is less than 30?
a. t-test c. normal test
b. z-test d. Central Limit Theorem

10. The supervisor of a certain company claimed that the mean workday of his workers is 8.3 hours per
day. A sample of 20 workers was taken and it was found out that the mean workday is 8 hours with
standard deviation of 1 hour. At 0.01 level of significance, is the mean workday less than 8.3 hours?
What test statistic is to be used in the given problem?
a. z-test c. right-tailed test
b. t-test d. left-tailed test

11. Based on the graph, which of the following is TRUE?

a. This is a two-tailed test.
b. This is a right-tailed test.
c. Level of significance is 0.025.
d. The rejection region is 𝑡 ≤ -1.725

12. Which of the following defines the area encompassed by the values not included in the non-
rejection region or also the area of the tails of the distribution?
a. critical value c. level of significance
b. rejection region d. population variance

13. For a two-tailed test with variance unknown, n= 16, and 𝛼 = 0.05, what is the critical value?
a. ±2.092 c. ±2.145
b. ±2.134 d. ±2.145

14. For a one-tailed test with a sample of 15, the null hypothesis will not be rejected at 5% level of
significance if the test statistics is:
a. 𝑡 ≤ −1.761 c. 𝑡 ≤ −1.703
b. 𝑡 ≤ −1.753 d. 𝑡 ≤ −1.697

15. Given the graph of the normal curve at the right, what are the directional test of hypothesis and
critical z value if 𝛼 = 0.01?
a. two-tailed test, ±2.33
b. two-tailed test, ± 2.575
c. left-tailed test, −1.645
d. right-tailed test, 1.645

For numbers 16-17, refer to the problem below:

Milky Milk is sold in packets with an advertised mean weight of 0.5kgs. The standard deviation is
known to be 0.11 kilograms. A consumer group wishes to check the accuracy of the advertised mean and
takes a sample of 36 packets finding an average weight of 0.47kgs.

16. What test statistic should be used?

a. t-test c. population mean
b. z-test d. standard deviation
17. What is the computed value?
 a. – 1. 636 c. 0. 833
b. -1.488 d. 5. 551

For # 18, refer to the problem below:

Given: 𝐻𝑜: μ = 7.25 𝐻𝑎: μ < 7.25

The study has a sample mean of 8.1 and a standard deviation of 1.18 conducted among 15
respondents. Use 𝛼 = 0.01.
18. What is the computed value?
a. - 2.790 c. 2.368
b. b. -2.368 d. 2.790
19. The z-computed value is 2.113 and the critical value is 1.645. What conclusion can be drawn?
a. Reject the null hypothesis.
b. Fail to reject the null hypothesis.
c. Reject both the null and alternative hypotheses.
d. Support both the null and alternative hypotheses.

20. A drink vending machine is adjusted so that, on average, it dispenses 200ml of fruit juice with a
standard deviation of 13ml into a plastic cup. However, the machine tends to go out of adjustment
and periodic checks are made to determine the average amount of fruit juice being dispensed. The
operator thinks that the amount dispensed is less than 200 ml. So to verify, a sample of 25 drinks is
taken to test the adjustment of the machine and a mean of 195 is obtained. For α = 5%, an
appropriate decision rule would be _________________________________.
a. retain the null hypothesis c. support the null hypothesis
b. reject the null hypothesis d. fail to reject the null hypothesis
21. Perform a hypothesis test on the null hypothesis where μ = 6.9. A random sample of 25 items is
selected. The sample mean is 7.1 and the sample standard deviation is 2.4. It can be assumed that
the population is normally distributed at α = .01.
a. There is enough evidence to reject the claim.
b. There is enough evidence to support the claim.
c. There is no enough evidence to reject the claim.
d. There is no enough evidence to support the claim.
22. If the computed t-value is 2.130 while the critical value is 2.086, what conclusion can be drawn?
a. Reject both the null and alternative hypotheses.
b. Fail to reject the null and alternative hypotheses.
c. Reject the null hypothesis in favor of the alternative hypothesis.
d. Fail to reject the null and the alternative hypothesis is not supported.
23. Before the opening of classes, parents were asked to answer a survey. Those in favor of alternative
learning mode were 1,900 out of 5,000 randomly selected parents. Using α = 0.10 level, is there
enough evidence to conclude that the percentage of parents who are in favor of alternative
learning mode is less than 38%? What is the appropriate alternative hypothesis?
a. Ha : p > .38 c. Ha : p < .38
b. Ha :p = .38 d. Ha : p ≠ .3
24. In problem # 23, formulate the correct null hypothesis.
a. The proportion of parents who are in favor of alternative learning mode is 38%.
b. The proportion of parents who are in favor of alternative learning mode is not equal to 38%.
c. The proportion of parents who are in favor of alternative learning mode has increased by
38%.
d. The proportion of parents who are in favor of alternative learning mode is more than 38%.
25. In a learning study, 1,200 respondents were asked if they can assimilate concepts while watching
television wherein 586 said YES. What is the proportion of those who said yes?
a. a.0.40 b. 0.49 c. 0.51 d. 0.58\
For numbers 26- 27, refer to the situation below.

A researcher claims that 75% of college students would rather spend their extra money for internet
access loads than food. Another researcher would like to verify this claim. She randomly selected 400
students. Among them, 296 said that they would rather use their extra money for internet access loads
than food. Answer the following questions to determine if there is enough evidence to conclude that the
percentage of students who would want to spend their extra money in internet access loads than food is
different from 75% at 0.05 level of significance.

26. Which of the following represents the alternative hypothesis?

a. Ha : p > 0.75 c. Ha : p ≠ 0.75
b. Ha : p < 0.75 d. Ha : p = 0.75
27. Which of the following is the critical value?
a. ± 2.325 b. ± 1.960 c. ± 1.645 d. ± 1.245

For numbers 28-29, refer to the problem below.

A research conducted on a certain company last year revealed that 25% of the employees prefer
drinking milk tea than coffee during break time. The company has decided to give free milk tea during
break time. In a recent study, out of 100 randomly sampled employees, 28% said that they would rather
drink milk tea than coffee.

28. What is the value of the hypothesized population proportion?

a. 0.25 b. 0.28 c. 0.75 d. 100
29. What is the z-value?
a. 0.5682 b. 0.6065 c. 0.6928 d. 0.7713
30. Which is the correct decision for the given values/results below?
Ho : p = 0.13 Ha : p < 0.13
α= 0.05 Zcom = -2.688 p-value = 0.003
a. There is no possible decision.
b. Reject the null hypothesis.
c. Fail to reject the null hypothesis.
d. Change the alternative hypothesis.

31. A hypothesis test is done in which the alternative hypothesis is that more than 10% of the
population is left-handed. The calculated p-value for the test is 0.25. Which statement is correct?
a. We can conclude that exactly 25% of the population is left-handed.
b. We can conclude that more than 10% of the population is left-handed.
c. We can conclude that more than 25% of the population is left-handed.
d. We cannot conclude that more than 10% of the population is left- handed.
32. “A student asked his 30 classmates their Body Mass Index (BMI) and the number of glasses of water
they drink daily. He found out that those students who consume 8-12 glasses of water daily have
normal BMI.” What type of data is presented on the situation above?
a. bivariate c. trivariate
b. multivariate d. univariate
c.
33. It is a graphical representation that shows the correlation of two variables using points or dots.
a. bar graph c. pictograph
b. line graph d. scatter plot
 34. Which of the following tables corresponds to the scatter plot below?

a.

b.

c.

d.

35. Robert noticed that the points on a scatter plot follow a trend of rising from left to right. He also
noticed that the points are moderately scattered from the trend line. What is the correlation of the
variables involved?
a. strong negative correlation c. weak negative correlation
b. strong positive correlation d. weak positive correlation
36. Which of the following values CANNOT represent a correlation coefficient r ?
a. -1 b. 0 c. 0.25 d. 1.001
37. Using the following summation values below, what is the value of Pearson r ?
n = 6, ∑ x =21, ∑ y=105 ∑ xy =465 , ∑ x 2=91 , ∑ y2 =2,425
a. 0.962 c. – 0.962
b. 0.542 d. – 0.542

38. In item #38, what will be the strength of association between the bivariate data?
a. strong negative correlation c. Weak negative correlation
b. strong positive correlation d. No correlation

For numbers 39 - 40, refer to the following situation:

The law of demand is an economic principle that explains the correlation between the price of a
good and its demand. The table below shows the price of a good and its quantity of demand.

39. What is the computed Pearson’s sample correlation coefficient?

a. 0.94 b. 0.04 c. -0.84 d. -0.94
40. Based on the findings, which of the following best describes the result?
 a. As the price of goods increases, the quantity of demand increases.
b. As the price of goods decreases, the quantity of demand decreases.
c. As the price of goods increases, the quantity of demand decreases.
d. As the price of goods increases, the quantity of demand remains the same.

41. As a person’s exposure to sunlight increases, his or her chance of developing cancer increases. In
the given findings, which are the variables?
a. Person
b. Increases
c. exposure to sunlight
d. exposure to sunlight and chance of developing cancer.

42. What is the slope in the regression equation: ŷ = −2𝑥 + 7?

a. 7 b. 2 c. -2 d. -7
43. What is the y-intercept in the regression equation: ŷ = −4𝑥 − 5?
a. 5 b. 4 c. -4 d. -5

44. What is the relationship between independent variable x and the dependent variable y when the
regression equation has a positive slope?
a. There is no relationship.
b. There is a positive relationship.
c. There is a negative relationship.
d. Relationship cannot be determined.

45. What is the relationship between independent variable x and the dependent variable y when the
regression equation has a negative y-intercept?
a. There is no relationship.
b. There is a positive relationship.
c. There is a negative relationship.
d. Relationship cannot be determined.

For numbers 46 to 47, refer to the situation below:

Students in a group of chess teams submitted data about hours of weekly team practice and the
number of matches the team won. The data gathered are represented by this linear regression equation: 𝑦̂
= 3.52 + 3.14x.

46. What does the slope of the linear regression equation represent?
a. hours of weekly practice
b. number of team members
c. number of matches the team won
d. increase in the team’s number of wins per hour of practice

47. If the team practices 4.5 hours per week next year, which is the best prediction of the number of
chess matches the team could expect to win?
a. about 8 c. about 18
b. about 12 d. about 24

For numbers 48 to 50, refer to the situation described below.

 A pastillas manufacturer is interested in estimating how sales are influenced by the price of their
pastillas. They randomly chose 6 cities with similar characteristics and offered pastillas jars at different
prices, then collected the following data:

48. What is the estimated slope of the regression equation?

a. 213.2 b. – 213.2 c. 1.56 d. – 1.56
49. What is the y-intercept of the regression equation?
a. 213.2 b. – 213.2 c. 1.56 d. – 1.56
50. What is the average number of jars sold if the price of a pastillas jar is ₱95?
a. 76 b. 78 c. 80 d. 82