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FREE DOWNLOAD SECOND QUARTER EXAM in Statistics and Probability School Year
2022-2023
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SECOND QUARTER EXAM in Statistics and Probability

School Year 2022-2023

Name: _______________________________________ Date:____________________

Grade &Section:_______________________________ Score:___________________

General Directions: Read the following questions thoroughly and choose the correct answer from the given choices. Write the LETTER of your correct answer legibly on the blank before each number.

_____1. It is a proposed explanation, assertion, or assumption about a population parameter or about the distribution of a random variable.

A. Decision C. Probability

B. Statistics D. Hypothesis

_____2. What is the statistical method used in making decisions using experimental data?

A. Simple analysis C. Hypothesis testing

B. Analytical testing D. Experimental testing

_____3. It is also the probability of committing an incorrect decision about the null hypothesis.

A. Level of error C. Level of acceptance

B. Level of hypothesis D. Level of significance

_____4. Which of the following describes an alternative hypothesis using a two-tailed test?

A. Ha = 100 C. Ha > 100

B. Ha ≠ 100 D. Ha < 100

_____5. In a one-tailed test, in which critical value listed below will the computed z of 2.313 fall in the acceptance region?

A. 1.383 C. 2.228

B. 1.533 D. 2.365

_____6. Which of the following would be an appropriate null hypothesis?

A. The mean of a sample is equal to 75.

B. The mean of the population is equal to 75.

C. The mean of a sample is not equal to 75.

D. The mean of a population is greater than 75

_____7. When is a Type I error committed?

A. We reject a null hypothesis that is false.

B. We reject a null hypothesis that is true.

C. We fail to reject a null hypothesis that is true.

D. We fail to reject a null hypothesis that is false.

_____8. When is a Type II 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.

_____9. Which of the following is a Type I error?

A. 𝐻0 is true; reject H0.

B. 𝐻0 is false; reject H0.

C. 𝐻0 is true; fail to reject H0.

D. D. 𝐻0 is false; fail to reject H0.

_____10. Which of the following describes an alternative hypothesis in a left-tailed test?

A. Ha > 100 C. Ha = 100

B. Ha < 100 D. Ha ≠ 100

_____11. Which of the following population parameters is used as symbol for the mean or average population?

A. 𝜎 B. 𝜇 C. 𝜌 D. 𝑥

_____12. Which of the following statements best describes a parameter?

A. It describes the sample. C. It describes the hypothesis.

B. It describes the researcher. D. It describes the population.

_____13. A researcher estimates that the average height of buildings in a large city is at least 700 feet. Based on the given data, which is the parameter?

A. the researcher C. buildings in the large city

B. at least 700 feet D. the average height of the building

_____14. The average height of a 1-year-old child is 29 inches. What is the parameter?

A. a one-year-old child

B. the mean height of 33 inches

C. the average height of 29 inches

D. a random sample of 30 children who are 1-year old

_____15. Which is the parameter in the given situation below? “The average age of 10 college students is 24 years.”

A. 24 years C. age of the college students

B. 10 college students D. the average age of 24 years

_____16. A parameter is...

A. a numerical value summarizing the sample data

B. a planned activity with results yielding a set of data

C. a numerical value that summarizes all the data of an entire population

D. the set of values collected from the variable from each of the elements that belongs to

the sample

_____17. Which of the following is a parameter?

A. 𝑆𝑥 B. 𝑥̅ C. 𝑝̂ D. µ

_____18. Which of the following symbols represents population standard deviation?

A. 𝑝 B. 𝜎 C. 𝑝̂ D. µ

_____19. SWS survey was trying to see if people in the Philippines thought the pollution was too high. Which choice best represents a parameter?

A. all people in the Philippines

B. 500 randomly selected residents of the Philippines

C. 71% of the residents surveyed who thought the pollution was too high

D. percentage of all people in the Philippines who thought the pollution was too high

_____20. Research conducted on a certain company last year showed that 25% of the employees would rather drink coffee than soft drinks during break time. Which choice best represents a parameter?

A. 25 employees C. the percentage of employees

B. all employees D. coffee rather than soft drinks

Consider the given situation.

The father of a senior high school student is listing down the expenses he will

incur when he sends his daughter to the university. At the university where he wants

his daughter to study, he hears that the average tuition fee is at least Php20,000 per

semester. He wants to do a test of the hypothesis. Suppose from a simple random sample

of 16 students, a sample mean of Php19,750 was obtained. Further, the variable of

interest, which is the tuition fee in the university, is said to be normally distributed with

an assumed population variance equal to Php160,000 and a level of significance

α = 5% 0r 0.05.

_____21. What is the appropriate null hypothesis?

A. The average tuition fee in the targeted university is at most Php20,000.

B. The average tuition fee in the targeted university is at least Php20,000.

C. The average tuition fee in the targeted university is less than Php20,000.

D. The average tuition fee in the targeted university is more than Php20,000.

_____22. What will be the appropriate alternative hypothesis?

A. The average tuition fee in the targeted university is less than Php20,000.

B. The average tuition fee in the targeted university is more than Php20,000.

A. The average tuition fee in the targeted university is at most Php20,000.

B. The average tuition fee in the targeted university is at least Php20,000

_____23. Identify the level of significance.

A. 5% B. 0.5% C. 0.10 D. 0.5

_____24. What kind of test will be used?

A. One-tailed test. C. Three-tailed test

B. Two-tailed test D. No-tailed test

_____25. Based on the decision, what is the appropriate conclusion?

A. Therefore, the father can say that the average tuition fee at the university where he

wants his daughter to study is at least Php20,000.

B. Therefore, the father can say that the average tuition fee at the university where he

wants his daughter to study is less than Php20,000.

C. Therefore, the father can say that the average tuition fee in the university where he

wants his daughter to study is at most Php20,000.

D. Therefore, the father can say that the average tuition fee at the university where he

wants his daughter to study is greater than Php20,000.

_____26. In hypothesis testing, this denotes that there is no difference between two parameters.

A. Alternative hypothesis C. Population mean

B. Population proportion D. Null hypothesis

_____27. The rejection region refers to the region where the value of the test statistic lies for

which we will reject the null hypothesis. This region is also called

A. Hypothesis testing region C. Z – score region

B. Critical region D. Probability region

_____28. This refers to an intelligent guess about a population proportion.

A. Hypothesis C. Decision

B. Test-statistic D. Interpretation

_____29. What mathematical model is appropriate for decision making?

A. Graphical representation C. test-statistic

B. Normal Curve D. None of these

_____30. When the null hypothesis is rejected, which of the following is true?

A. There is sufficient evidence to back up the decision.

B. There is no sufficient evidence to back up the decision.

C. The conclusion is guaranteed.

D. The conclusion is not guaranteed.

_____31. When the alternative hypothesis utilizes the ≠ symbol, the test is said to be

A. Directional C. critical

B. Non-directional D. not equal

_____32. When the alternative hypothesis utilizes the > or the < symbol, the test is said to be

A. Directional C. critical

B. Non-directional D. not equal

_____33. When can we decide to reject a null hypothesis in the left-tail level of significance?

A. If the absolute computed value of the test statistic is greater than the absolute

critical value.

B. If the absolute critical value of the test statistic is greater than the absolute

computed value.

C. If the significance level is equal to the test statistic.

D. If the first four steps are met, then we decide to reject a null hypothesis.

_____34. Every hypothesis testing begins with the _________________________.

A. Statement of hypothesis C. Conclusion

B. Decision D. Significance Level

_____35. The level of significance is the maximum probability of committing a type I Error.

This probability is symbolized by the Greek letter _______.

A. ρ (which means Rho) C. α (means alpha)

B. σ (means sigma) δ D. (means delta)

_____36. After a significance level is chosen, a ______ is selected from a table for the

appropriate test.

A. Computed value C. Absolute value

B. A range of values D. Critical value

_____37. The rejection region can be located on the following except.

A. On top of the normal curve

B. On both sides with the nonrejection region in the middle

C. On the left side of the nonrejection region

D. On the right side of the nonrejection region

_____38. It refers to a value calculated from sample data that is needed in deciding whether the null hypothesis is rejected or not.

A. test statistics C. null hypothesis

B. critical region D. alternative hypothesis

_____39. What test statistic will be used if the sample size is above 30?

A. t-test C. population mean

B. z-test D. standard deviation

_____40. What test statistic can be used when the population standard deviation is known?

A. t-test C. population mean

B. z-test D. standard deviation

_____41. What test statistic can be used when the population standard deviation is unknown?

A. t – test C. population mean

B. z – test D. standard deviation

For nos. 10 – 12, refer to the given problem below:

The Choco Toppings, Inc. is one of the manufacturers of chocolate toppings that uses a machine to dispense liquid ingredients into bottles that move along a filling line. The owner claims that the machine can dispense at an average of 50 grams with a standard deviation of 0.7 grams. A sample of 35 bottles was selected and it was found out that the average amount dispensed in the sample is 49.3 grams. Test the claims of the owner of the company at 5% level of significance.

_____42 Which of the following information is correct?

A. 𝛼 = 0.5 C. 𝑥̅= 35

B. 𝜎 = 0.7 D. 𝜇 = 49.3

_____43. What test statistic will be used?

A. t-test C. population mean

B. z-test D. standard deviation

_____44. Find the computed value.

A.-5.916 C. 4.950

B. -4.950 D. 5.916

_____45. Which test statistic will be used if the sample size is 15?

A. t-test C. can be determined

B. z-test D. neither t-test nor z-test

_____46. Which statistical method can you use when you have a normal distribution of data?

A.t–test only C. either t–test or z–test

B.z–test only D. neither t–test nor z–test

_____47. A tire manufacturer claims that its tires have a mean life of 40,000 km. A random sample of 46 of these tires is tested and the sample mean is 38,000 km. Assume that the population’s standard deviation is 2,000 km and the lives of the tires are approximately normally distributed. Determine the computed value at a 5% level of significance.

A.-6.782 C. 3.033

B. -3.033 D. 6.782

_____48. What is the critical value in a one-tailed test with 5% level of significance and a degree of freedom of 18?

A.1.734 C. 2.567

B. 2.101 D. 2.898

_____49. If the absolute value of the computed test statistic is greater than the critical value, then we ________

A. retain the null hypothesis C. reject the alternative hypothesis

B. reject the null hypothesis D. do not reject the null hypothesis

_____50. When we failed to reject the null hypothesis, which of the following statements is true?

A. The conclusion is guaranteed.

B. The conclusion is not guaranteed.

C. There is enough evidence to back up the claim.

D. There is no enough evidence to reject the claim.

_____51. If the t-computed value is 1.093 and the critical value is 1.699, what will be the decision?

A. Reject both hypotheses.

B. Reject the null hypothesis.

C. Do not reject the null hypothesis.

D. Support the alternative hypothesis.

_____52. On the given figure below, the t-computed value is 2.130. What conclusion can be drawn?

A. Reject the null hypothesis.

B. Fail to reject the null hypothesis.

C. Reject only the alternative hypothesis.

D. Reject both the null and alternative hypotheses.

_____53. What does it mean when the null hypothesis is rejected?

A. The null hypothesis is incorrect.

B. The alternative hypothesis is correct.

C. There is sufficient evidence to support the null hypothesis.

D. There is sufficient evidence to disprove the null hypothesis.

_____54. If the z-computed value is 2.505 and the critical value is 2.011, what will be the decision?

A. Reject both hypotheses. C. Support the null hypothesis.

B. Reject the null hypothesis. D. Do not reject the null hypothesis.

_____55. From the given figure below, the z-computed value is 1.375. What conclusion can be drawn?

A. Reject the null hypothesis.

B. Failed to reject the null hypothesis.

C. Reject only the alternative hypothesis.

D. Reject both the null and alternative hypotheses.

_____56. In a right-tailed test, if the critical value is greater than the computed value, then we ________.

A. reject both the null and alternative hypotheses

B.do not reject both the null and alternative hypotheses

C. reject the null hypothesis and support the alternative hypothesis

D. fail to reject the null hypothesis and the alternative hypothesis is not supported

_____57. 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 200ml. 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. rejecting the null hypothesis

B. not rejecting the null hypothesis

C. rejecting both the null and alternative hypotheses

D. supporting both the null and alternative hypotheses

_____58. Which of the following is the correct symbol for hypothesized proportion?

A. po B. p C. Hp D. Ho

_____59. What is the correct alternative hypothesis in sentence form of the statement: Ha: p ≠ 0.21?

A. The proportion of male in a certain barangay is 21%.

B. The proportion of male in a certain barangay is fewer by 21%.

C. The proportion of male in a certain barangay is different from 21%.

D. The proportion of male in a certain barangay has increased by 21%.

_____60. Which of the following words is used in a null hypothesis written in sentence form?

A. equal B. fewer C. higher D. lower

_____61. A researcher will use a one-tailed test on his research study concerning population proportions. A one-tailed test is also called ________.

A. one-sided C. directional

B. one-region D. non-directional

_____62. Which of the following statements is true about the alternative hypothesis on a population proportion?

A. It is represented by Ha.

B. It is used as a basis to determine the location of the extreme values.

C. It is the competing claim that the parameter is equal to a specific value.

D. It is a claim that the proportion is equal to the hypothesized proportion.

_____63. Before the opening of classes, parents were asked to answer a survey. Those in favor of the 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 ≠ .38

_____64. In problem no. 6, formulate the correct null hypothesis.

A. The proportion of parents who are in favor of alternative learning modes is 38%.

B. The proportion of parents who are in favor of alternative learning modes is not equal

to 38%.

C. The proportion of parents who are in favor of alternative learning modes has increased

by 38%.

D. The proportion of parents who are in favor of alternative learning modes is more than 38

%.

_____65. A survey conducted last year by certain barangay officials showed that 40% of the residents owned a private car. This year a new survey is conducted on 375 residents selected randomly from the same barangay. It was found out that 190 of them own a car. Test if the claim is fewer at α = 0.01 level. Formulate the appropriate null hypothesis.

A. Ho : p = .40 C. Ho : p < .40

B. Ha : p = .40 D. Ha : p < .40

_____66. In problem #8, what is the correct alternative hypothesis in sentence form?

A. The proportion of residents who owned a private car is 40%.

B. The proportion of residents who owned a private car is higher than 40%.

C. The proportion of residents who owned a private car has changed to 40%.

D. The proportion of residents who owned a private car is fewer than 40%.

_____67. In a certain senior high school, a study found that 972 out that 1,100 Grade 12 students use smartphones. Using α = 0.10 level, is there enough evidence to conclude that the percentage of students who are using smartphones is different from 25%? What is the appropriate alternative hypothesis?

A. Ha: p > .25 C. Ha: p = .25

B. Ha: p < .25 D. Ha: p ≠ .25

_____68. Which of the following alternative hypotheses in sentence form is NOT a one-tailed test (directional)?

A. The proportion of female students who enrolled is greater than 10%.

B. The proportion of male teachers who has a master’s degree is lower than 5%.

C. The proportion of the number of tourists who visited the park is not equal to 50%.

D. The proportion of athlete students who joined the competition has increased by 25%.

_____69. The proportion of patients with heart disease is higher among smokers than non-smokers. Which is true about this statement?

A. It is a null hypothesis that is directional.

B. It is a null hypothesis that is non-directional.

C. It is an alternative hypothesis that is directional.

D. It is an alternative hypothesis that is non-directional.

_____70. Which of the following words suggests a right-tailed test?

A. smaller C. increased

B. different D. unequal

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